Handbook For Sound Engineers - PDFCOFFEE.COM (2024)

Handbook for Sound Engineers Fourth Edition

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Handbook for Sound Engineers Fourth Edition

Glen M. Ballou Editor

Focal Press is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright © 2008, Elsevier Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333,E-mail: [emailprotected]. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Support & Contact” then “Copyright and Permission” and then “Obtaining Permissions.” Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN: 978-0-240-80969-4 For information on all Focal Press publications visit our website at www.elsevierdirect.com 08 09 10 11 5 4 3 2 1 Printed in the United States of America

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi Trademark Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Part 1—Acoustics Chapter 1 Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Don and Carolyn Davis

Chapter 2 Fundamentals of Audio and Acoustics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Pat Brown

Chapter 3 Psychoacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Peter Xinya Zhang

Chapter 4 Acoustical Noise Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Doug Jones

Chapter 5 Acoustical Treatment for Indoor Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Jeff Szymanski

Chapter 6 Small Room Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Doug Jones

Chapter 7 Acoustics for Auditoriums and Concert Halls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Dr. Wolfgang Ahnert and Hans-Peter Tennhardt

Chapter 8 Stadiums and Outdoor Venues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Eugene T. Patronis, Jr.

Chapter 9 Acoustical Modeling and Auralization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Dominique J. Chéenne

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Part 2—Electronic Components Chapter 10 Resistors, Capacitors, and Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Glen Ballou

Chapter 11 Audio Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Bill Whitlock

Chapter 12 Tubes, Discrete Solid State Devices, and Integrated Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Glen Ballou, Les Tyler and Wayne Kirkwood

Chapter 13 Heatsinks and Relays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Glen Ballou and Henry Villaume

Chapter 14 Transmission Techniques: Wire and Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Steve Lampen and Glen Ballou

Chapter 15 Transmission Techniques: Fiber Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 Ron Ajemian

Part 3—Electroacoustic Devices Chapter 16 Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Glen Ballou, Joe Ciaudelli and Volker Schmitt

Chapter 17 Loudspeakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Jay Mitchell

Chapter 18 Loudspeaker Cluster Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Ralph Heinz

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Part 4—Electronic Audio Circuits and Equipment Chapter 19 Power Supplies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667 Glen Ballou

Chapter 20 Amplifier Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 Eugene T. Patronis, Jr.

Chapter 21 Preamplifiers and Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733 Bill Whitlock, Michael Pettersen and Glen Ballou

Chapter 22 Attenuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Glen Ballou

Chapter 23 Filters and Equalizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783 Steven McManus

Chapter 24 Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805 Steven McManus

Chapter 25 Consoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817 Steve Dove

Chapter 26 VI Meters and Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 Glen Ballou

Part 5—Recording and Playback Chapter 27 Analog Disc Playback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013 George Alexandrovich and Glen Ballou

Chapter 28 Magnetic Recording and Playback. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039 Dale Manquen and Doug Jones

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Contents Chapter 29

MIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099 David Mules Huber

Chapter 30 Optical Disc Formats for Audio Reproduction and Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131 Ken Pohlmann

Part 6—Design Applications Chapter 31 DSP Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159 Dr. Craig Richardson

Chapter 32 Grounding and Interfacing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179 Bill Whitlock

Chapter 33 System Gain Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1221 Pat Brown

Chapter 34 Sound System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233 Chris Foreman

Chapter 35 Computer Aided Sound System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337 Dr. Wolfgang Ahnert and Stefan Feistel

Chapter 36 Designing for Speech Intelligibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385 Peter Mapp

Chapter 37 Personal Monitor Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1413 Gino Sigismondi

Chapter 38 Virtual Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437 Ray Rayburn

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Chapter 39 Digital Audio Interfacing and Networking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457 Ray Rayburn

Chapter 40 Message Repeaters and Evacuation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1513 Glen Ballou and Vic Cappetta

Chapter 41 Interpretation and Tour Group Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1529 Glen Ballou

Chapter 42 Assistive Listening Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1543 Glen Ballou

Chapter 43 Intercoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1559 Glen Ballou

Chapter 44 The Fundamentals of Display Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1577 Alan C. Brawn

Chapter 45 Surround Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1591 Joe Hull

Part 7—Measurements Chapter 46 Test and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1605 Pat Brown

Chapter 47 What’s the Ear For? How to Protect It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1631 Les Blomberg and Noland Lewis

Chapter 48 Fundamental and Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645 Glen Ballou Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1689

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Preface When the first edition of the Handbook for Sound Engineers came out in 1987, it was subtitled the new Audio Cyclopedia so that people who were familiar with Howard Tremain’s Audio Cyclopedia would understand that this is an updated version of it. Today, the book stands on its own. We have seen a tremendous change in the field of sound and acoustics since the first edition of the Handbook for Sound Engineers came out. Digital is certainly finding its place in all forms of audio, however, does this mean analog circuitry will soon be a thing of the past? Analog systems will still be around for a long time. After all, sound is analog and the transfer of a sound wave to a microphone signal is analog and from the electronic signal to the sound wave produced by the loudspeaker is analog. What is changing is our methods of producing, reproducing, and measuring it. New digital circuitry and test equipment has revolutionized the way we produce, reproduce and measure sound. The Handbook for Sound Engineers discusses sound through seven sections, Acoustics, Electronic Components, Electro-Acoustic Devices, Audio Electronic Circuits and Equipment, Recording and Playback, Design Application, and Measurements. When we listen to sound in different size rooms with different absorptions, reflections, and shape, we hear and feel the sound differently. The Handbook for Sound Engineers explains why this occurs and how to control it. Rooms for speech are designed for intelligibility by controlling shape, reflections and absorption while rooms for music require very different characteristics as blend and reverberation time are more important than speech intelligibility. Multipurpose rooms must be designed to satisfy both speech and music, often by changing the RT60 time acoustically by use of reflecting/absorbing panels or by designing for speech and creating the impression of increased RT60 through ambisonics. Open plan rooms require absorbent ceilings and barriers and often noise masking. Studios and control rooms have a different set of requirements than any of the above. There are many types of microphones. Each installation requires a knowledge of the type and placement of microphones for sound reinforcement and recording. It is important to know microphone basics, how they work, the various pickup patterns, sensitivity and frequency response for proper installation. To build, install, and test loudspeakers, we need to know the basics of loudspeaker design and the standard methods of making measurements. Complete systems can be purchased, however, it is imperative the designer understand each individual component and the interrelation between them to design and install custom systems. With the advent of digital circuitry, sound system electronics is changing. Where once each analog stage decreased the SNR of the system and increased distortion, digital circuitry does not reduce the SNR or increase distortion in the normal way. Digital circuitry is not without its problems however. Sound is analog and to transfer it to a digital signal and change it back to an analog signal does cause distortions. To understand this the Handbook for Sound Engineers delves into DSP technology, virtual systems, and digital interfacing and networking. Analog disk and magnetic recording and playback have changed considerably in the past few years and are still used around the world. The CD has been in the United States since 1984. It is replacing records for music libraries because of its ability to almost instantly locate a spot in a 70+ minute disc. Because a disc can be recorded and rerecorded from almost any personal computer, disc jockeys and home audiophiles are producing their own CDs. Midi is an important part of the recording industry as a standardized digital communications language that allows multiple related devices to communicate with each other whether they be electronic instruments, controllers or computers. The design of sound systems requires the knowledge of room acoustics, electroacoustic devices and electronic devices. Systems can be single source, multiple source, distributed, signal delayed, installed in good rooms, in bad rooms, in large rooms, or small rooms, all with their own particular design problems. Designing a system which should operate to our specs, but where we did not take into consideration the proper installation techniques such as grounding and common mode signal, can make a good installation poor and far from noise and trouble free. The Handbook for Sound Engineers covers these situations, proper installation techniques, and how to design for best speech intelligibility or music reproduction through standard methods and with computer programs. The new integrated circuits, digital circuitry and computers have given us new sophisticated test gear unthought of a few years ago, allowing us to measure in real time, in a noisy environment, and measure to accuracies never before realized. It is important to know, not only what to measure, but how to measure it and then how to interpret the results.

Fiber optic signal transmission is solidly in the telephone industry and it is becoming more popular in the audio field as a method of transmitting signals with minimum noise, interference and increased security. This does not mean that hard-wired transmission will not be around for a long time. It is important to understand the characteristics of fiber optics, wire and cable and their affects on noise, frequency response and signal loss. The book also covers message repeaters, interpretation systems, assistive listening systems, intercoms, modeling and auralization, surround sound, and personal monitoring. The sound level through mega-loudspeakers at rock concerts, through personal iPods, and random noise from machinery, etc. is constantly increasing and damaging our hearing. The Handbook for Sound Engineers addresses this problem and shows one method of monitoring noisy environments. Many of us know little about our audio heritage, therefore a chapter is dedicated to sharing the history of these men who, through their genius, have given us the tools to improve the sound around us. No one person can be knowledgeable in all the fields of sound and acoustics. This book has been written by those people who are considered, by many, as the most knowledgeable in their field. Glen Ballou

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Trademark Acknowledgments All terms mentioned in this book that are known to be trademarks or service marks are listed below. In addition, terms suspected of being trademarks or service marks have been appropriately capitalized. Focal Press cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. Abffusor is a trademark of RPG Diffuser Systems, Inc. Audio Spotlight is a registered trademark of Holosonic Research Labs, Inc. AutoCAD is a trademark of Autodesk, Inc. Beldfoil is a registered trademark of Belden Electronics Division. Bidiffusor is a trademark of RPG Diffuser Systems, Inc. Biffusor is a trademark of RPG Diffuser Systems, Inc. Boogie is a registered trademark of Mesa Engineering. C-Quam is a registered trademark of Motorola, Inc. Co-Netic® is a registered trademark of Magnetic Shield Corp. CobraCAD is a registered trademark of Peak Audio. CobraNet is a registered trademark of Peak Audio. dbx is a trademark of DBX Professional Products, AKG, Inc. Diffractal is a trademark of RPG Diffuser Systems, Inc. Diffusor is a trademark of RPG Diffuser Systems, Inc. Dolby is a trademark of Dolby Laboratories Licensing Corporation. Dolby SR is a trademark of Dolby Laboratories Licensing Corporation. Electro-Voice, a product brand of Telex Communications, Inc. Enkasonic is a registered trademark Colbond. Fiberglas is a registered trademark of Owens Corning. Flutterfree is a trademark of RPG Diffuser Systems, Inc. FMX is a registered trademark of Broadcast Technology Partners. Freon-11 is a trademark of E.I. Dupont de Nemours & Co., Inc. Holophone® is a registered trademark of Rising Sun ProductionsLimited. Hot Spot is a trademark of Galaxy Audio. HyMu® is a registered trademark of Carpenter Technology Corp. InGenius® is a registered trademark of THAT Corporation. ISO-MAX® is a registered trademark of Jensen Transformers, Inc. Isoloop is a registered trademark of 3M Company. ITE is a trademark of Synergetic Audio Concepts. Jensen Twin-Servo is a registered trademark of Jensen Transformers, Inc. Jensen-Hardy Twin-Servo® is a registered trademark of Jensen Transformers, Inc. Korner-Killer is a trademark of RPG Diffuser Systems, Inc. LEDE is a trademark of Synergetic Audio Concepts. Magneplanar is a registered trademark of Magnepan, Inc. Mumetal® is a registered trademark of Telcon Metals, Ltd. Mylar is a trademark of E.I. Dupont de Nemours & Co., Inc. Omniffusor is a trademark of RPG Diffuser Systems, Inc. OpticalCon® is a registered trademark ofNeutrik AG. OptiFiber® is a registered trademark of Fluke Networks. PAR is a trademark of Synergetic Audio Concepts. PCC is a registered trademark of Crown International, Inc. Performer is a trademark of Mark of the Unicorn, Inc. Permalloy® is a registered trademark of B & D Industrial & Mining Services, Inc. PZM is a registered trademark of Crown International, Inc. QRD is a trademark of RPG Diffuser Systems, Inc.

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QRDX is a trademark of RPG Diffuser Systems, Inc. Romex® is a registered trademark of General Cable Industries, Inc. RPG is a trademark of RPG Diffuser Systems, Inc. SASS is a trademark of Crown International, Inc. Scotchguard is a trademark of 3M Co. Series Manifold Technology is a trademark of Electro-Voice, Inc. Source Independent Measurements is a trademark of Meyer Sound Laboratories, Inc. Stereo Ambient Sampling System is a trademark of Crown International, Inc. TEF is a trademark of Gold Line. Teflon is a trademark of E.I. Dupont de Nemours & Co., Inc. Tektronix is a registered trademark of Tektronix. Time Align is a trademark of Ed Long Associates. Triffusor is a trademark of RPG Diffuser Systems, Inc. UniCam® is a registered trademark of Corning, Inc. Variac is a registered trademark of Gen Rad. Voice Development System is a trademark of Musicode.

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Contributors Professor Dr. Ing. Habil. Wolfgang Ahnert Dr. Wolfgang Ahnert graduated in Dresden in 1975 and from 1975 to 1990 he worked in an engineering office in Berlin and in 1990 founded ADA Acoustic Design Ahnert. In 2000 he founded SDA Software Design Ahnert GmbH to increase the output in writing source codes for acoustic and electronic applications. In 2002 the ADA foundation was established to support universities and colleges with acoustic software including EASE and the measurement tools EASERA and EASERA SysTune. The Ahnert Feistel Media Group was established in 2006 to coordinate all the above activities. In 1993 he became an honorary professor at the Hochschule fuer Film und Fernsehen Potsdam, and in 2001 he became an honorary professor at Lomonossov University in Moscow. Since 2005 he has been a visiting professor at the Rensselaer Institute for Architecture in Troy, New York. Dr. Ahnert has been a member of the AES since 1988 and was made a fellow of the Audio Engineering Society in 1995. He has been a fellow of the Acoustical Society of America since 2005. He is a member of the German DEGA and the British Institute of Acoustics. More than sixty five scientific lectures by Dr. Ahnert have been published. Dr. Ahnert is one of the authors of the book Fundamentals of Sound Reinforcement (1981, and 1984 in Russian) and the book Sound Reinforcement—Basics and Practice (1993, and fully updated in English in 2000, in Chinese in 2002, and in Russian in 2003). He wrote with coauthors chapters in the 3rd edition of Handbook for Sound Engineer, [Handbuch der Audiotechnik] (2008 Springer) and Akustische Messtechnik (2008 Springer), both in German.

Ronald G. Ajemian Ronald G. Ajemian is an instructor at the Institute of Audio Research, New York, NY, where he has been teaching audio technology for over 25 years. Ron was employed with the Switched Services Department of Verizon for 32 years in New York City and recently took an early retirement. Mr. Ajemian is a graduate of RCA Institute and the school of electrical engineering at Pratt Institute of Brooklyn, NY. He has contributed many articles in the field of audio electronics, telephony, and fiber optics. Mr. Ajemian is a member of many professional organizations, including the Audio Engineering Society (AES), the Telephone Pioneers of America, Communication Workers of America (CWA), and the Optical Society of America to name a few. He is sometimes referred to as Dr. FO (fiber optics), for his expertise in the field of fiber optics. Mr. Ajemian is also a guest lecturer at NYU and for the Audio Engineering Society. Mr. Ajemian held the position of the Chair of the AES New York Section in 2000–2001 and is currently the Chair of the AES Standards Task Group SC-05-02-F on Fiber Optic Connections. Mr. Ajemian is owner and consultant of Owl Fiber Optics in New York, specializing in fiber optic technology and education for proaudio/video and broadcast.

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Contributors George Alexandrovich

George Alexandrovich, born in Yugoslavia, attended schools in Yugoslavia, Hungary, and Germany. After coming to the United States, he studied at the RCA Institute and at Brooklyn Polytech, earning a B.S.E.E. At Telectro Industries Corp., he was involved in the design and development of the first tape recorders and specialized military electronic test and communications equipment. After service in the Korean war, he ran Sherman Fairchild’s private research lab. While with Fairchild Recording Equipment Corp., he designed and manufactured turntables, tonearms, pickups, mixing consoles and amplifiers, equalizers, reverberation chambers, the first light-activated compander, Autoten, Lumiten compressors, limiters, and a line of remote-controlled audio components. He also designed the first professional multichannel portable console, a disk-cutting lathe, and stereo cutters. As vice president and general manager his responsibilities included designing and manufacturing the Voice of America recording facilities, NBC-TV studio consoles for Johnny Carson, Huntley-Brinkley Newsroom, KNX, KCBS, and other radio stations. When Fairchild Recording Equipment Corp. merged with Robins Corp., George also became involved in manufacturing magnetic tape along with a full line of consumer accessories in the hi-fi market. At Stanton Magnetics, Inc., as vice president of field engineering and the professional products manager for phonograph cartridge research, he traveled extensively, holding seminars, giving lectures, and conducting conferences. George was the author of the monthly column “Audio Engineer’s Handbook” for dB Magazine and of over eighty articles and papers in American and foreign trade journals. He has also presented a number of technical papers at the Audio Engineering Society (AES) conventions and is a fellow and a past governor of the AES. He holds eighteen patents in the audio field and is past chairman of the Electronics Industry Association (EIA) P8.2 Standards Committee. At the present time George is retired after spending 11 years as principal engineer at ESD/Parker Hannifin Corp. where he conducted R&D in the field of avionics transducers. He is now president and owner of Island Audio Engineering, manufacturing and consulting firm.

Glen Ballou Glen Ballou graduated from General Motors Institute in 1958 with a bachelor’s degree in Industrial Engineering and joined the Plant Engineering Department of the Pratt & Whitney Aircraft Division of United Technologies Corporation. There he designed special circuits for the newly developed tape control machine tools and was responsible for the design, installation, and operation of the 5,000,000 ft2 plant public address and two-way communication system. In 1970, Glen transferred to the Technical Presentations and Orientation section of United Technologies’ corporate office, where he was responsible for the design and installation of electronics, audio-visual, sound, and acoustics for corporate and division conference rooms and auditoriums. He was also responsible for audio-visual and special effects required for the corporation’s exhibit program. Glen transferred to the Sikorsky Aircraft division of United Technologies as manager of Marketing Communications in 1980, where his responsibilities included the Sikorsky exhibit and special events program, plus operation and design of all conference rooms. After his retirement from Sikorsky, Glen and his wife, Debra, opened Innovative Communications, a company specializing in sound system design and installation, and technical writing. Glen is the editor/author of the 1st, 2nd, 3rd, and 4th editions of the Handbook for Sound Engineers. He also was a contributing author for The Electrical Engineering Handbook (CRC Press). Glen has written many article for Sound and Video Contractor and Church Production magazines.

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He has been active in the Audio Engineering Society (AES) as Governor, three times Papers Chairman and four times Facilities Chairman, and Vice Chairman and Chairman of the 1989 AES Convention, for which he received the Governor’s award. He was also a member of SMPTE and the IEA.

Les Blomberg Les Blomberg is a hearing conservation and noise policy expert. He is the inventor of a hearing test to detect temporary changes in hearing ability and is the author of numerous articles and papers on hearing conservation and noise. He is the founding Executive Director of the Noise Pollution Clearinghouse.

Alan C. Brawn CTS, ISF, ISF-C. Alan Brawn is a principal of Brawn Consulting LLC, an audio-visual consulting, educational development, and market intelligence firm with national exposure to major manufacturers, distributors, and integrators in the industry. He was formerly President of Telanetix and previously National Business Development and Product Marketing Manager, Pro AV Group, Samsung Electronics. Alan is an AV industry veteran with experience spanning over two decades including years managing a commercial AV systems integration company after which he became one of the founding members of Hughes-JVC. He is a recognized author for leading AV industry magazines and newsletters such as Systems Contractor News, Digital Signage Magazine, Rental & Staging, Display Daily, and Electrograph’s Emerge. Brawn is an Imaging Science Foundation Fellow and the Managing Director of ISF Commercial. Alan is CTS certified and an adjunct faculty member of Infocomm sitting on their PETC council. He is an NSCA instructor and Learning Unit Provider. He was the recipient of the Pro AV Hall of Fame recognition from rAVe in 2004. Alan can be reached at [emailprotected].

Pat Brown Pat Brown is president of Synergetic Audio Concepts, Inc. Syn-Aud-Con conducts educational seminars in audio and acoustics worldwide, as well as private seminars for audio manufacturers and corporations. He has owned and operated several businesses, including design build, retail, and consulting audio firms. He received an A.A.S. from the University of Louisville in Electrical Engineering Technology. His current duties include teaching, consulting, and authoring technical articles for industry magazines and the Syn-Aud-Con Newsletter, which he and his wife, Brenda, publish from their headquarters in Greenville, Indiana.

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Contributors Dominique J. Chéenne, Ph.D.

Dominique J. Chéenne holds a Brevet de Technicien Supérieur from the University of Caen, France. He received a Master’s degree and a Ph.D., both in Electrical Engineering, from the University of Nebraska, Lincoln. His doctoral dissertation dealt with the modeling of sound propagation over seating surfaces. In 1979 he founded C & C Consultants, a consulting practice specializing in architectural acoustics and environmental noise control. Since its inception C & C Consultants has provided design services on hundreds of projects nationwide including individual residences, performing arts spaces, schools, offices, factories, churches, as well as local, state, and federal government facilities. In 1995, Dr. Chéenne accepted an offer to join the faculty of Columbia College. He is currently serving as a tenured member of the faculty in the Audio Arts and Sciences Department where he directs the acoustics program. His main research interests are in the application of computer models to architectural and environmental acoustics issues. Dr. Chéenne is a member of the Audio Engineering Society and of the Acoustical Society of America.

Don and Carolyn Davis Don and Carolyn Davis form a unique husband and wife team working in audio, starting in 1951 with The Golden Ear in Lafayette, IN, selling eclectic high-fidelity equipment. Don was Paul Klipsch’s President in charge of Vice in the late 50s, and worked for Altec Lansing from 1959 until 1972 where he was co-inventor of 1/3octave equalization. The Davises founded Synergetic Audio Concepts in 1973 in response to the growing need in the audio industry for training in the fundamentals of sound reinforcement. Their work in equalization, speech intelligibility, and recording technologies provided the backbone for developing training seminars and workshops. When they turned Syn-Aud-Con over to Pat and Brenda Brown in 1995, Don and Carolyn had been responsible for the education of more than 10,000 sound contractors, designers, and consultants. Don has authored three books, Acoustical Tests and Measurements in 1965; How to Build Speaker Enclosures in 1968, co-authored with Alex Badmaieff, which has sold over 200,000 copies, and Sound System Engineering, co-authored with his wife, Carolyn, in 1975. They recently completed the 3rd edition with co-author, Dr. Eugene Patronis. In the process of communicating with the grads of their seminars on audio and acoustics, a quarterly newsletter was established. Most of the newsletter was technical in nature, but it also contained the evolving mindset that bonded teachers and grads into something not originally expected—a fraternity of people dedicated to changing an industry. After enduring poor sound quality at a meeting of a professional audio society, Don uttered in frustration, If Bad Sound Were Fatal, Audio Would Be the Leading Cause of Death, hence the title of Don and Carolyn’s book, by that name. They used nontechnical excerpts from the Syn-Aud-Con newsletters, annotated by them in 2003, that go back to the beginning of these changes in the industry up to the Davises’ retirement in 1995. The book provides a remarkable insight into entrepreneur teachers’ communication with entrepreneur students. The typical attendees at their seminars were already successful in their chosen industry, but knew in their hearts that there was a higher standard and they actively sought it. They have spent their professional careers writing and lecturing on sound system engineering. The audio industry has generously recognized their efforts as instrumental in the better sound quality we enjoy today. Don and Carolyn are both Fellows of the Audio Engineering Society and have received many awards in the audio industry, including the Distinguished Award in Sound Design and Technology from USITT. Don and Carolyn reside in Arizona in the winter and on their farm in southern Indiana in the summer.

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Steve Dove Steve Dove is a native to Oxfordshire, England, and is now a resident of Pennsylvania. He has designed mixing consoles in every genre from valves to DSP. On the basis of an early foray with ICs, he became initially a wireman for—until fired for his atrocious soldering—a designer for, and later a director of Alice, a major manufacturer of broadcast, film, and recording consoles. Concurrently, he provided engineering and acoustics expertise to major rock bands, theatres, and studios worldwide. As a design consultant his clients included Sony Broadcast, Shure Bros., Solid State Logic, Altec Lansing, Clair Bros., Harman/JBL, Crest, and Peavey. He is now Minister of Algorithms for Wheatstone Corporation. A widely published author with a long list of innovative design techniques and award-winning products to his credit, he is presently realizing an ambition to achieve the class and fluidity of the best of analogue audio in digital signal processing.

Dipl.-Phys. Stefan Feistel Stefan Feistel studied physics at the University of Rostock and at the Humboldt University of Berlin and graduated with a Master’s degree in Theoretical Physics in 2004. His collaboration with Dr. Wolfgang Ahnert, the owner of ADA Acoustic Design Ahnert, started in 1996. The main target was, and still is, the development of the electro- and room-acoustic simulation software EASE. In 2000, Wolfgang Ahnert and Stefan Feistel founded the company SDA Software Design Ahnert GmbH, which is dedicated to the development of acoustic modeling and measuring software. In 2003, the nonprofit organization ADA Foundation was established to support universities and colleges with software products such as the simulation software EASE and the measurement tool EASERA. To coordinate all these activities, the Ahnert Feistel Media Group (AFMG) was established in 2006. Stefan Feistel has authored or co-authored more than thirty articles as a result of the continuously progressing work on software projects like EASE, EASE SpeakerLab, EASE Focus, and EASERA and the related mathematical, numerical, and experimental background studies.

Chris Foreman Chris Foreman is Vice President and Chief Operating Officer for Community Professional, a loudspeaker manufacturer in Chester, Pennsylvania. During his pro audio career, Chris has worked in manufacturing, contracting, and tour sound. Chris is widely published, having written numerous magazine articles and technical papers. Chris co-authored the book Audio Engineering for Sound Reinforcement with the late John Eargle and he is author of the sound reinforcement chapter of the 1st, 2nd, and 3rd editions of the Handbook for Sound Engineers edited by Glen Ballou. He can be reached at [emailprotected].

Contributors Ralph Heinz Ralph Heinz joined Renkus-Heinz in 1990 with a background in mechanical engineering. Very quickly he developed a thorough understanding of acoustics and has made many proprietory loudspeaker technologies and patients including ComplexConic Horns, CoEntrant Topology, and True Array Principle.

David Miles Huber David Miles Huber has written such books as the industry standard text Modern Recording Techniques (www.modrec.com), The MIDI Manual, and Professional Microphone Techniques. He’s also a producer and musician in the dance, chill and downtempo genres, whose CDs, have sold over the million mark. His latest music and collaborations with artists in the United States, United Kingdom, and Europe can be heard at www.51bpm.com and www.MySpace/51bpm.

Joe Hull Joe Hull started his career in audio in the early 1960s working as a retail salesman in Cambridge, Massachusetts, at a time when some customers still needed convincing that stereo really was better than mono. In 1970, he joined the legendary Advent Corporation, where he worked for 8 years in a variety of sales and marketing positions, concluding that what he liked best was writing about hightechnology products, such as the first cassette decks with Dolby B, for a lay audience. He’s been doing just that for Dolby Laboratories since 1978, with a few years’ hiatus out on his own as a freelance writer. Joe works and lives in San Francisco.

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Doug Jones Doug Jones has worked in recording and small-room acoustics for more than 20 years and still consults on such projects. He has earned a Master’s degree from Columbia College, Chicago, where he is Professor of Acoustics and the founding chairman of the Sound Department. There, he directs accredited Bachelor’s-degree programs in recording, architectural acoustics, live-sound reinforcement, sound-forpicture, and sound installation. Mr. Jones is a member of the Acoustical Society of America and the Audio Engineering Society, where he is active in committee work. His publications have appeared in IEEE Proceedings and International Computer Music Proceedings, and he is an every-month columnist in Live Sound International magazine. In addition to his teaching duties at the College, he organizes advanced TEF workshops and other in-service technical training for the audio industry.

Steve Lampen Steve Lampen has worked for Belden for 17 years and is currently Multimedia Technology Manager. Prior to Belden, Steve had an extensive career in radio broadcast engineering and installation, film production, and electronic distribution. Steve holds an FCC Lifetime General License (formerly a First Class FCC License) and is an SBE Certified Radio Broadcast Engineer. On the data side he is a BICSI Registered Communication Distribution Designer. His latest book, The Audio-Video Cable Installer’s Pocket Guide is published by McGraw-Hill. His column “Wired for Sound” appears in Radio World Magazine.

Noland Lewis Noland Lewis is a graduate of University of San Francisco and has served as Chief Engineer for HC Electronics/Phonic Ear—a manufacturer of Auditory Trainers and Hearing Aids. Noland has also served on FDA committees relative to hearing aids and has conducted FCC presentations relative to new rule making. He was the Chief Engineer of HC Electronics (Phonic Ear) where he developed a line of FM Auditory Trainers and Wireless Microphones serving the needs of hearing-impaired children and adults worldwide. He has served on FDA committees relative to hearing aid regulations and submitted new laws that became part of the FCC regulations. Noland is founder and president of ACO Pacific, Inc., a company he established in 1978—now celebrating 30 years of serving the worldwide community. Over the past 30 years ACO Pacific, Inc. has become a major international supplier of measurement microphones and systems. Noland created the SLARM™ several years ago to provide a means to assist businesses and communities in the resolution of noise pollution issues. ACO Pacific is a sustaining member of INCE, INCE USA, AES, ASA, and the Canadian Acoustical Society. He has been a member of numerous committees in these organizations.

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Contributors Peter Mapp, BSc, MSc, FIOA, FASA, FAES, CPhys, CEng, MinstP, FinstSCE MIEE.

Peter Mapp is principal of Peter Mapp Associates, an acoustic consultancy, based in Colchester, England, that specializes in the fields of room acoustics, electro-acoustics, and sound system design. He holds an honors degree in applied physics and a master’s degree in acoustics. He is a Fellow of the Institute of Acoustics, the Acoustical Society of America, and the Audio Engineering Society. Peter has a special interest in speech intelligibility prediction and measurement and has authored and presented numerous papers and articles on this subject both in Europe and the United States. He currently serves on both British and International Standards committees concerning the sound system design and speech intelligibility. Peter has been responsible for the design and commissioning of over 500 sound systems, varying from concert halls and theatres, to churches, cathedrals, and other religious buildings, to arenas, stadiums, power stations, and transportation terminals. He is also known for his extensive research work into Distributed Mode Loudspeakers and their application to sound reinforcement. Peter is a regular contributor to the audio technical press, having written over 100 articles and papers. He is also a contributing author to a number of international reference books including the Loudspeaker Handbook. He is currently the chairman of the AES international working group on speech intelligibility and convenor of IEC 6026816, the standard relating to the measurement of STI and Speech Intelligibility.

Steven McManus Steven McManus graduated from the University of Edinburgh in 1990 with a B. E. in Electrical and Electronic Engineering. During this time he also worked on a computer-aided navigation and charting project through the University of Dundee. An early interest in sound recording expanded into a production and installation company that he ran for 8 years. Steve moved to the United States in 1999 after returning to Herriot-Watt University for an update in programming skills. He was with the TEF division of Gold Line for 6 years working on both software and hardware. He is currently working for Teledyne Benthos in Massachusetts with underwater acoustic communication and navigation systems.

James E. Mitchell James (Jay) Mitchell began work in the fields of music and audio in 1972. He was awarded a Bachelor of Science in Physics in 1983 and a Master of Science in Physics in 1985, both from the Georgia Institute of Technology. Since 1985, he has been involved in the design and development of loudspeakers and associated electronics. His design credits include the IMAX Proportional Point Source loudspeaker and the line of loudspeakers currently manufactured by Frazier Loudspeakers. He is currently president of Frazier Loudspeakers, in Dallas, Texas. He is a member of the Audio Engineering Society.

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Eugene T. Patronis, Jr. Eugene T. Patronis, Jr. is Professor Emeritus of Physics at the Georgia Institute of Technology in Atlanta, Georgia, where he has taught for over 50 years. During the majority of that time he has also served as an industrial and governmental consultant in the fields of acoustics and electronics. He is the co-author with Don Davis of the 3 edition of Sound System Engineering.

Michael Pettersen Michael Pettersen is the Director of Applications Engineering for Shure Incorporated. Fascinated by sound and audio since building a crystal radio set as a lad, he earned a B.A. in Music Theory from the University of Illinois in 1974. Employed by Shure since 1976, Michael helped develop and market five different models of automatic microphone mixers. He has presented papers on automatic microphone mixers to the National Association of Broadcasters, the Acoustical Society of America, the National Systems Contractor Association, the European Institute of Acoustics, the Michigan Bar Association, the Voice of America, and others. He is a member of the Acoustical Society of America and directs Shure’s Consultant Liaison Program, a program that informs acoustical consultants worldwide about new product developments from Shure. Michael also plays guitar with jazz big bands in the Chicago area.

Ken C. Pohlmann Ken Pohlmann serves as an engineering consultant in the design of digital audio systems, in the development of mobile audio systems for automobile manufacturers, and as an expert witness in technology patent litigation. Some of his consulting clients include Alpine Electronics, Analog Devices, AOL Time Warner, Apple, Bertlesmann, Blockbuster, Cirrus Logic, DaimlerChrysler, Ford, Fujitsu Ten, Harman International, Hughes, Hyundai, IBM, Kia, Lexus, Matsushita, Microsoft, Motorola, Nippon Columbia, Onkyo, Philips, Real Networks, Recording Industry Association of America, Samsung, Sony, TDK, Toyota, and United Technologies. Mr. Pohlmann is a Professor Emeritus at the University of Miami in Coral Gables, Florida, where he served as a tenured full professor and director of the Music Engineering Technology program in the Frost School of Music. He initiated new undergraduate and graduate courses in acoustics and psychoacoustics, digital audio, advanced digital audio, Internet audio, and studio production and founded the first Master’s degree in Music Engineering in the United States. Mr. Pohlmann holds B.S. and M.S. degrees in electrical engineering from the University of Illinois in Urbana-Champaign. Mr. Pohlmann is the author of Principles of Digital Audio (5th edition, 2005, McGraw-Hill) and The Compact Disc Handbook (2nd edition, 1992, A-R Editions); co-author of The Master Handbook of Acoustics (5th edition, 2009, McGraw-Hill), Writing for New Media (1997, Wiley), and editor and co-author of Advanced Digital Audio

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Contributors

(1991, Sams). He has written over 2,500 articles for audio magazines and is contributing editor, columnist, and blogger for Sound & Vision magazine. Mr. Pohlmann chaired the Audio Engineering Society’s International Conference on Digital Audio in Toronto in 1989 and co-chaired the Society’s International Conference on Internet Audio in Seattle in 1997. He was presented two AES Board of Governor’s Awards (1989 and 1998) and an AES Fellowship Award (1990) by the Audio Engineering Society for his work as an educator and author in the field of audio engineering. In 1991 he was elected to serve on the AES Board of Governors and in 1993 to serve as the AES Vice President of the Eastern U.S. and Canada Region. In 1992 he was awarded the Philip Frost Award for Excellence in Teaching and Scholarship. In 2000 he was elected as a nonboard member of the National Public Radio Distribution/Interconnection Committee. In 2000 he was elected as a member of the Board of Directors of the New World Symphony.

Ray A. Rayburn Ray A. Rayburn has an ASET from New York Institute of Technology and has worked in the fields of audio, electroacoustics and telecommunications for over 38 years. He has taught audio at Eastman School of Music, Institute of Audio Research, and InfoComm. He designed recording facilities for Broadway Video, Eurosound, Photo-Magnetic Sound, db Studios, and Saturday Night Live. His recording credits range from the Philadelphia Orchestra to Frank Zappa. Equipment he has designed includes film dubbers, tape duplicators, specialty telecommunication equipment for the stock brokerage industry, and a polymer analyzer. He has been a consultant on sound systems for the U.S. Senate, U.S. House, Wyoming Senate and House, Georgia Dome, Texas House of Representatives, and University of Hawaii Special Events Arena, among many others. Currently, Ray is a Senior Consultant with K2 Audio of Boulder, Colorado. He is a member of the Audio Engineering Society (AES), the Acoustical Society of America, the National Systems Contractor’s Association, and InfoComm. He is Chairman of the AES Standards Subcommittee on Interconnections and the working group on Audio Connectors. He is a member and former Chairman of the AES Technical Committee on Signal Processing. He was a member of the American National Standards Institute (ANSI) Accredited Standards Committee (ASC) S4 on Audio Engineering. He is a member of the AES Standards working group on Microphone Measurement and Characteristics and of several other Standards working groups. He devotes much of his spare time to educating churches worldwide on how to improve their sound and acoustics through Curt Taipale’s Church Sound Check email discussion group. Ray has a personal web site at www.SoundFirst.com.

Dr. Craig Richardson Dr. Craig Richardson is a vice president and general manager of Polycom’s Installed Voice Business. In this role, Richardson leads the development of installed voice products and recently introduced the Sound Structure audio conferencing products—the first installed conferencing products that provide both mono and stereo echo cancellation capabilities for an immersive conferencing experience. Prior to joining Polycom, Richardson was president and CEO of ASPI Digital and focused the company on creating the EchoFree™ teleconferencing products for the audio/video integrator marketplace. ASPI’s products allowed users to experience full-duplex communication in situations never before thought possible, such as distance learning, telemedicine and courtroom applications. In 2001, ASPI Digital was acquired by Polycom Inc., the leader in unified collaborative communication. Richardson led algorithm development at ASPI Digital as the director of Algorithm Development working on an advanced low-bit-rate video coder, the MELP military standard voice coder, digital filter design products, computer telephony products, multimedia algorithms for speech, audio, and image processing applications for TMS320 family of digital signal processors. He has written

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numerous papers and book chapters, has been granted four patents, and is the co-author (with Thomas P. Barnwell, III, and Kambiz Nayebi) of Speech Coding A Computer Laboratory Textbook, a title in the Georgia Tech Digital Signal Processing Laboratory Series published by John Wiley & Sons. Richardson is a member of Tau Beta Pi, Sigma Xi, and a senior member of the IEEE. He was graduated from Brown University with a bachelor’s degree in electrical engineering and received both his Master’s and doctoral degrees in electrical engineering from the Georgia Institute of Technology.

Gino Sigismondi Gino Sigismondi, a Chicago native and Shure Associate since 1997, has been active in the music and audio industry for nearly 15 years. Currently managing the Technical Training division, Gino brings his years of practical experience in professional audio to the product training seminars he conducts for Shure customers, dealers, distribution centers, and internal staff. Gino spent over 9 years as a member of Applications Engineering, assisting Shure customers with choosing and using the company’s vast array of products, and is the author of the Shure educational publications Selection and Operation of Personal Monitors, Audio Systems Guide for Music Educators, and Selection and Operation of Audio Signal Processors. He was recently awarded status as an Adjunct Instructor by the InfoComm Academy. Gino earned his B.S. degree in Music Business from Elmhurst College, where he was a member of the jazz band as both guitar player and sound technician. After college, he spent several years working as a live sound engineer for Chicago-area sound companies, night clubs, and several local acts. Gino continues to remain active as a musician and sound engineer, consulting musicians on transitioning to in-ear monitors and expanding his horizons beyond live music to include sound design for modern dance and church sound.

Jeff D. Szymanski Jeff D. Szymanski is an Acoustical Engineer with Black & Veatch Corporation, a leading global engineering, consulting, and construction company specializing in infrastructure development in energy, water, information, and government market sectors. Jeff’s experience covers many areas of acoustics, including architectural acoustics design, industrial noise and vibration control, environmental noise control, and A/V systems design. He has over 13 years of experience in the acoustical manufacturing and consulting industries. Prior to joining Black & Veatch, Jeff was the Chief Acoustical Engineer for Auralex Acoustics, Inc., where he was the key designer on several award-winning projects. In 2004–5, he and the Auralex team collaborated with members of the Russ Berger Design Group to develop and launch the award-winning pArtScience brand of acoustic treatment products. Jeff has written and presented extensively on the subjects of acoustics and noise control. He is a full member of the Acoustical Society of America and the Institute of Noise Control Engineering, holds two U.S. patents for acoustic treatment products, is a licensed professional engineer, and he plays guitar pretty well, too.

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Contributors Hans-Peter Tennhardt

Hans-Peter Tennhardt was born in Annaberg/Erzgebirge, Germany in 1942. From 1962–1968, Mr. Tennhardt studied at the Technical University Dresden, Department of Electrotechnics—Low-current Engineering. His field of study was Electroacoustics with Professor Reichardt. Mr. Tennhardt graduated in 1968 as a Diploma’d Engineer for Electrotechnics— Low-current Engineering at the TU Dresden, with an extension of the basic study at the Academy of Music Dresden. His Diploma thesis was on the subject “Model Investigations in Town Planning.” From 1968–1991, Mr. Tennhardt was a Scientific Collaborator in the Department Building and Room Acoustics at the Building Academy in Berlin, with Professor Fasold. He became Deputy Head of the Department Building and Room Acoustics of the Institute for Heating, Ventilation, and Fundamentals of Structural Engineering at the Building Academy in 1991. In 1992 Mr. Tennhardt became Group Leader for room acoustics at the Institute of Building Physics (IBP) of the Frauenhofer Institute Stuttgart, Berlin Branch. Since then he has been Head of the Department Building Physics and of the Special Section Building and Room Acoustics at the Institute for Maintenance and Modernization of Buildings (IEMB) of the Technical University Berlin.

Bill Whitlock Bill Whitlock was born in 1944 and was building vacuum-tube electronics at the age of 8 and running a radio repair business at the age of 10. He grew up in Florida, attended St. Petersburg Junior College, and graduated with honors from Pinellas County Technical Institute in 1965. He held various engineering positions with EMR/Schlumberger Telemetry, General Electric Neutron Devices, and RCA Missile Test Project (on a ship in the Pacific) before moving to California in 1971. His professional audio career began in 1972 when he was interviewed by Deane Jensen and hired as chief engineer by custom console maker Quad-Eight. There he developed Compumix®, a pioneering console automation system, and other innovations. From 1974 to 1981, he designed automated image synthesis and control systems, several theater sound systems, and patented a multichannel PCM audio recording system for producers of the Laserium® laser light show. In 1981, Bill became manager of Electronic Development Engineering for Capitol Records/EMI where he designed high-speed cassette duplicator electronics and other specialized audio equipment. He left Capitol in 1988 to team with colleague Deane Jensen, developing hardware for Spatializer Audio Labs, among others. After Deane’s tragic death in 1989, Bill became President and Chief Engineer of Jensen Transformers. His landmark paper on balanced interfaces was published in the June 1995 AES Journal. He is an active member and former chairman of the AES Standards Committee Working Group that produced AES48-2005. Over the years, Bill has presented many tutorial seminars and master classes for the AES as well as presentations to local AES chapters around the world. He suggested major changes to IEC test procedures for CMRR, which the IEC adopted in 2000. He has written numerous magazine articles and columns for Mix, EDN, S&VC, System Contractor News, Live Sound, Multi-Media Manufacturer, and others. Since 1994, he has taught myth-busting seminars on grounding and interfacing to thousands at industry trades shows, Syn-Aud-Con workshops, private companies, and universities— most recently as an invited lecturer at MIT. Bill is a Fellow of the Audio Engineering Society and a Senior Member of the Institute of Electrical and Electronic Engineers. His patents include a bootstrapped balanced input stage, available as the InGenius® IC from THAT Corporation, and a high-speed, feed-forward AC power regulator, available from ExactPower®. Bill currently designs audio, video, and other signal interfacing devices at Jensen and handles much of their technical support. He also does

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consulting work as time permits. In his leisure time, Bill enjoys travel, hiking, music, and restoring vintage radio and TV sets.

Peter Xinya Zhang Peter Xinya Zhang is a faculty member at Columbia College, Chicago. His field is psychoacoustics, specifically sound localization. He received a B.S. in physics from Peking University, P.R. China, and received his Ph.D. in physics from Michigan State University, Lansing. In his doctoral thesis, he investigated human binaural pitch effects to test various binaural models, and developed a new technique to simulate a 3D sound field for virtual reality with loudspeakers. He has published papers in the Journal of Acoustical Society of America, presented at various conferences, and served as co-chair in the session of psychological and physiological acoustics at the 4th Joint Conference of the Acoustical Society of America and Acoustical Society of Japan. He has lectured on psychoacoustics and sound localization at various institutes including Loyola University in Chicago, Peking University (China), Institute of Acoustics at Chinese Academy of Sciences (China), and Shanghai Conservatory (China). Dr. Zhang is a member of the Acoustical Society of America and of the Audio Engineering Society.

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Part 1

Acoustics

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Chapter

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? by Don and Carolyn Davis Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Genesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1893—The Magic Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Bell Laboratories and Western Electric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Harvey Fletcher (1884–1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Negative Feedback—1927 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Harry Nyquist (1889–1976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The dB, dBm and the VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Bell Labs and Talking Motion Pictures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Motion Pictures—Visual versus Auditory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Transition from Western Electric to Private Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Audio Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The “High” Fidelity Equipment Designers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Sound System Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Professional-Level Audio Equipment Scaled to Home Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Edwin Armstrong (1890–1954) The Invention of Radio and Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Acoustic Measurements—Richard C. Heyser (1931–1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Calculators and Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 The Meaning of Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors?

Introduction This chapter is the DNA of my ancestors, the giants who inspired and influenced my life. If you or a hundred other people wrote this chapter, your ancestors would be different. I hope you find reading the DNA of my ancestors worthwhile and that it will provoke you into learning more about them. Interest in my audio and acoustic ancestors came about by starting the first independent Hi-Fi shop, The Golden Ear, in Lafayette, Indiana in early 1952. The great men of hi-fi came to our shop to meet with the audio enthusiasts from Purdue: Paul Klipsch, Frank McIntosh, Gordon Gow, H.H. Scott, Saul Marantz, Rudy Bozak, Avery Fisher—manufacturers who exhibited in the Hi-Fi shows at the Hollywood Roosevelt and the Hilton in New York City. We sold our shops in Indianapolis and Lafayette in 1955, and took an extended trip to Europe. In 1958 I went to work for Paul Klipsch as his “President in charge of Vice.” Mr. Klipsch introduced me to Lord Kelvin, the Bell Labs West Street personnel, as well as his untrammeled genius. Altec was the next stop, with my immediate manager being “the man who made the motion picture talk.” At Altec I rubbed against and was rubbed against by the greats and those who knew the greats of the inception of the Art. This resulted in our awareness of the rich sense of history we have been a part of and we hope that sharing our remembrance will help you become alert to the richness of your own present era. In 1972 we were privileged to work with the leaders in our industry who came forward to support the first independent attempt at audio education, Synergetic Audio Concepts (Syn-Aud-Con). These manufacturers represented the best of their era and they shared freely with us and our students without ever trying to “put strings on us.”

Genesis The true history of audio consists of ideas, men who envisioned the ideas, and those rare products that represented the highest embodiment of those ideas. The men and women who first articulated new ideas are regarded as discoverers. Buckminster Fuller felt that the terms realization and realizer were more accurate. Isaac Newton is credited with “We stand on the shoulders of giants” regarding the advancement of human thought. The word science was first coined in 1836 by Reverend William Hewell, the Master of Trinity College, Cambridge. He felt the term, natural philosopher, was too broad, and that physical science deserved a

separate term. The interesting meaning of this word along with entrepreneur-tinkerer allows one a meaningful way to divide the pioneers whose work, stone by stone, built the edifice we call audio and acoustics. Mathematics, once understood, is the simplest way to fully explore complex ideas but the tinkerer often was the one who found the “idea” first. In my youth I was aware of events such as Edwin Armstrong’s construction of the entire FM transmitting and reception system on breadboard circuits. A successful demonstration then occurred followed by detailed mathematical analysis by the same men who earlier had used mathematics to prove its impossibility. In fact, one of the mathematician’s papers on the impossibility of FM was directly followed at the same meeting by a working demonstration of an FM broadcast by Armstrong. The other side of the coin is best illustrated by James Clerk Maxwell (1831–1879), working from the non-mathematical seminal work of Michael Faraday. Michael Faraday had a brilliant mind that worked without the encumbrance of a formal education. His experiments were with a n e a r l y Vo l t a c e l l , g i v e n h i m b y Vo l t a whe n he trav el ed t o Italy with Sir Humphry Davy as Davy’s assistant. This led to his experiments with the electric field and compasses. Faraday envisioned fields of force around wires where others saw some kind of electric fluid flowing through wires. Faraday was the first to use the terms electrolyte, anode, cathode, and ion. His examination of inductance led to the electric motor. His observations led his good friend, James Clerk Maxwell, to his remarkable equations that defined electromagnetism for all time. A conversation with William Thomson (later Lord Kelvin) when Thomson was 21 led Faraday to a series of experiments that showed that Thomson’s question as to whether light was affected by passing through an electrolyte—it wasn’t—led to Faraday’s trying to pass polarized light past a powerful magnet to the discover the magneto-optical effect (the Faraday effect). Diamagnetism demonstrated that magnetism was a property of all matter. Faraday was the perfect example of not knowing mathematics freed him from the prejudices of the day.

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James Clerk Maxwell was a youthful friend of Faraday and a mathematical genius on a level with Newton. Maxwell took Fara d a y ’s t h e o r i e s o f electricity and magnetic lines of force into a mathematical formulation. He showed that an oscillating electric c h a rg e p ro d u c e s a n electromagnetic field. The four partial differential equations were first published in 1873 and have since been thought of as the greatest achievement of the 19th century of physics. Maxwell’s equations are the perfect example of mathematics predicting a phenomenon that was unknown at that time. That two such differing mind-sets as Faraday and Maxwell were close friends bespeaks the largeness of both men. These equations brought the realization that, because charges can oscillate with any frequency, visible light itself would form only a small part of the entire spectrum of possible electromagnetic radiation. Maxwell’s equations predicted transmittable radiation which led Hertz to build apparatus to demonstrate electromagnetic transmission. J. Willard Gibbs, America’s greatest contributor to electromagnetic theory, so impressed Maxwell with his papers on thermodynamics that Maxwell constructed a three-dimensional model of Gibbs’s thermodynamic surface and, shortly before his death, sent the model to Gibbs. G.S. Ohm, Alessandro Volta, Michael Faraday, Joseph Henry, Andre Marie Ampere, and G.R. Kirchhoff grace every circuit analysis done today as resistance in ohms, potential difference in volts, current in amperes, inductance in henrys, and capacity in farads and viewed as a Kirchhoff diagram. Their predecessors and contemporaries such as Joule (work, energy, heat), Charles A. Coulomb (electric charge), Isaac Newton (force), Hertz (frequency), Watt (power), Weber (magnetic flux), Tesla (magnetic flux density), and Siemens (conductance) are immortalized as international S.I. derived units. Lord Kelvin alone has his name inscribed as an S.I. base unit. As all of this worked its way into the organized thinking of humankind, the most important innovations

were the technical societies formed around the time of Newton where ideas could be heard by a large receptive audience. Some of the world’s best mathematicians struggled to quantify sound in air, in enclosures, and in all manner of confining pathways. Since the time of Euler (1707–1783), Lagrange (1736–1813), and d’Alembert (1717–1783), mathematical tools existed to analyze wave motion and develop field theory. By the birth of the 20th century, workers in the telephone industry comprised the most talented mathematicians and experimenters. Oliver Heaviside’s operational calculus had been superseded by Laplace transforms at MIT (giving them an enviable technical lead in education).

1893—The Magic Year At the April 18, 1893 meeting of the American Institute of Electrical Engineers in New York City, Arthur Edwin Kennelly (1861–1939) gave a paper entitled “Impedance.” That same year General Electric, at the insistence of Edwin W. Rice , bou ght R u d o l p h E i c k e m e y e r ’s company for his transformer patents. The genius Charles Proteus Steinmetz (1865–1923) worked for Eickemeyer. In the saga of great ideas, I have always been as intrigued by the managers of great men as much as the great men themselves. E.W. Rice of General Electric personified true leadership when he looked past the misshapened dwarf that was St e i n m e t z t o t h e m i n d present in the man. General Electric’s engineering preeminence proceeded d i r e c t l y f r o m R i c e ’s extraordinary hiring of Steinmetz.

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? Dr. Michael I. Pupin of Columbia University was present at the Kennelly paper. Pupin mentioned Oliver Heaviside’s use of the word impedance in 1887. This meeting established the correct definition of the word and established its use within the electric industry. Kennelly’s paper, along with the ground-work laid by Oliver Heaviside in 1887, was instrumental in introducing the terms being established in the minds of Kennelly’s peers. The truly extraordinary Arthur Edwin Kennelly (1861–1939) left school at the age of thirteen and taught himself physics while working as a telegrapher. He is said to “have planned and used his time with great efficiency,” which is evidenced by his becoming a member of the faculty at Harvard in 1902 while also holding a joint appointment at MIT from 1913–1924. He was the author of ten books and the co-author of eighteen more, as well as writing more than 350 technical papers. Edison employed A.E. Kennelly to provide physics and mathematics to Edison’s intuition and cut-and-try experimentation. His classic AIEE paper on impedance in 1893 is without parallel. The reflecting ionosphere theory is jointly credited to Kennelly and Heaviside and known as the Kennelly-Heaviside layer. One of Kennelly’s Ph.D. students was Vannevar Bush, who ran American’s WWII scientific endeavors. In 1893 Kennelly proposed impedance for what had been called apparent resistance, and Steinmetz suggested reactance to replace inductance speed and wattless resistance. In the 1890 paper, Kennelly proposed the name henry for the unit of inductance. A paper in 1892 that provided solutions for RLC circuits brought out the need for agreement on the names of circuit elements. Steinmetz, in a paper on hysteresis, proposed the term reluctance to replace magnetic resistance. Thus, by the turn of the 20th century the elements were in place for scientific circuit analysis and practical realization in communication systems. Arthur E. Kennelly’s writings on impedance were meaningfully embellished by Charles Proteus Steinmetz’s use of complex numbers. Michael Pupin, George

A. Campbell, and their fellow engineers developed filter theory so thoroughly as to be worthwhile reading today. Steinmetz was not at the April 18, 1893 meeting, but sent in a letter of comment which included, It is, however, the first instance here, so far as I know, that the attention is drawn by Mr. Kennelly to the correspondence between the electric term “impedance” and the complex numbers. The importance hereof lies in the following: The analysis of the complex plane is very well worked out, hence by reducing the technical problems to the analysis of complex quantities they are brought within the scope of a known and well understood science. The fallout from this seminal paper, its instantaneous acceptance by the other authorities of the day, its coalescing of the earlier work of others, and its utilization by the communication industry within a decade, makes it easily one of the greatest papers on audio ever published, even though Kennelly’s purpose was to aid the electric power industry in its transmission of energy. The generation, transmission, and distribution of electromagnetic energy today has no meaning in itself, but only gains meaning if information is conveyed, thus the tragedy of the u s e o f m a n k i n d ’s p r e c i o u s resources to convey trash. Nikola Tesla (1856–1943) working with Westinghouse designed the AC generator that was chosen in 1893 to power the Chicago World’s Fair

Bell Laboratories and Western Electric The University of Chicago, at the end of the turn of the 19th century into the 20th century, had Robert Millik a n , A m e rica’s foremost physicist. Frank Jewett, who had a doctorate in physics from MIT, and now worked for Western Electric, was able to recruit Millikan’s top students.

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George A. Campbell (1870–1954) of the Bell Telephone Laboratories, had by 1899 developed successful “loading coils” capable of extending the range and quality of the, at that time, unamplified telephone circuits. Unfortunately, Professor Michael Pupin had also conceived the idea and beat him to the patent office. Bell Telephone paid Pupin $435,000 for the patent and by 1925 the Campbell-designed loading coils had saved Bell Telephone Co. $100,000,000 in the cost of copper wire alone. To sense the ability of loading coils to extend the range of unamplified telephone circuits, Bell had reached New York to Denver by their means alone. Until Thomas B. Doolittle evolved a method in 1877 for the manufacture of hard drawn copper, the metal had been unusable for telephony due to its inability to support its own weight over usable distances. Copper wire went from a tensile strength of 28,000 lbs/in 2 with an elongation of 37% to a tensile strength of 65,000 lbs/in2, an elongation of 1%. Campbell’s paper in 1922, “Physical Theory of the Electric Wave Filter” is still worthw h i l e r e a d i n g t o d a y. I remember asking Dr. Thomas Stockham, “Do digital filters ring under transient conditions?” Dr. Stockham, (his wife, Martha, said that she worshipped the air he walked on), replied “Yes” and pointed out that it’s the math and not the hardware that determines what filters do. Papers like Campbell’s are pertinent to Quantum filters, when they arrive, for the same reasons Dr. Stockham’s answer to my question about digital filters was valid. Bell Telephone Laboratories made an immense step when H.D. Arnold designed the first successful electronic repeater amplifier in 1913. H.D. Arnold at Bell Laboratories had taken DeForest’s vacuum tube, discarded DeForest’s totally false understanding of it, and, by establishing a true vacuum, improved materials and a correct electrical analysis of its properties enabled the electronic amplification of

voice signals. DeForest is credited with putting a “grid” into a Fleming value. Sir Ambrose J. Fleming (1848–1945) is the English engineer who invented the two-electrode rectifier which h e cal led the t hermio nic valve. It later achieved fame as the Fleming valve and was patented in 1904. DeForest used the Fleming valve to place a grid element in between the filament and the plate. DeForest didn’t understand how a triode operated, but fortunately Armstrong, Arnold, and Fleming did. Another Fleming—Sir Arthur (1881–1960)— invented the demountable high power thermionic valves that helped make possible the installation of the first radar stations in Great Britain just before the outbreak of WWII. The facts are that DeForest never understood what he had done, and this remained true till his death. DeForest was never able, in court or out, to correctly describe how a triode operated. He did however; provide a way for large corporations to challenge in court the patents of men who did know. With the advent of copper wire, loading coils, and Harold D. Arnold’s vacuum tube amplifier, transcontinental telephony was established in 1915 using 130,000 telephone poles, 2500 tons of copper wire, and three vacuum tube devices to strengthen the signal. The Panama Pacific Exposition in San Francisco had originally been planned for 1914 to celebrate the completion of the Panama Canal but the canal was not completed until 1915. Bell provided not only the first transcontinental telephony, but also a public address system at those ceremonies. The advances in telephony led into recording technologies and by 1926–1928 talking motion pictures. Almost in parallel was the development of radio. J.P. Maxfield, H.C. Harrrison, A.C. Keller, D.G. Blattner were the Western Electric Electrical recording pioneers. Edward Wente’s 640A condenser microphone made that component as uniform as the amplifiers, thus insuring speech intelligibility and musical integrity.

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? Harvey Fletcher (1884–1981) In 1933, Harvey Fletcher, Steinberg and Snow, Wente and Thuras and a host of other Bell Lab engineers gave birth to “Audio Perspective” demonstrations of three-channel stereophonic sound capable of exceeding the dynamic range of the live orchestra. In the late 60s, William Snow was working with John Hilliard at Ling Research, just down the street from Altec. It was a thrill to talk with him. He told me that hearing the orchestra level raised several dB was more astounding to him than the stereophonic part of the demonstration. Edward C. Wente and Albert L. Thuras were responsible for full range, low distortion, high-powered sound reproduction using condenser microphones, compression drivers, multicelluar expo nential horns, heavy duty loaded low-frequency enclosures, the bass reflex enclosures, and both amplifiers and transmission lines, built to standards still challenging today. The Fletcher loudspeaker was a three-way unit consisting of an 18 inch low-frequency driver, horn loaded woofer, the incomparable W.E. 555 as a midrange, and the W.E. 597A high-frequency unit.

In 1959, I went with Paul W. Klipsch to Bell Labs where we jointly presented our redo of their 1933 Audio Perspective geometry tests. The demo was held in the Arnold Auditorium and afterward we were shown one of the original Fletcher loudspeakers. Western Electric components like the 555 and 597 are to be found today in Japan where originals sell for up to five figures. It is estimated that 99% of the existing units are in Japan. (As a side note, I genuinely earned a “Distinguished Fear of Flying Cross” with Paul Klipsch in his Cessna 180, the results of which entertained many Syn-Aud-Con classes. The We s t e r n Electric 640A was superseded by the 64 0 A A c o nd e n s er microphone in 1942, still used today as a measurement standard by those fortunate enough to own one. The 640A was a key component in the reproduction of the full orchestra in 1933. When redesigned in 1942 as the 640AA, Bell Labs turned over the manufacturing of the capsule to Bruel and Kjaer as the B&K 4160. Rice and Kellogg’s seminal 1925 paper and Edward Wente’s 1925 patent #1,333,744 (done without knowledge of Rice and Kellogg’s work) established the basic principle of the direct-radiator loudspeaker with a small coil-driven mass controlled diaphragm in a baffle possessing a broad mid-frequency range of uniform response. Rice and Kellogg also contributed a more powerful amplifier design and the comment that for reproduced music the level should be that of the original intensity.

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Negative Feedback—1927 In 1927 Harold S. Black, while watching a Hudson River ferry use reverse propellers to dock, conceived negative feedback for power amplifiers. With associates of the caliber of Harry Nyquist and Hendrik Bode, amplifier gain, phase, and stability, became a mathematical theory of immense use in remarkably diverse technical fields. Black’s patent took nine years to issue because the U.S. Navy felt it revealed too much about how they adjusted their big guns and asked that its publication be delayed. The output signal of an amplifier is fed back and compared with the input signal, developing a “difference signal” if the two signals are not alike. This signal, a measure of the error in amplification, is applied as additional input to correct the functioning of the amplifier, so as to reduce the error signal to zero. When the error signal is reduced to zero, the output corresponds to the input and no distortion has been introduced. Nyquist wrote the mathematics for allowable limits of gain and internal phase shift in negative feedback amplifiers, insuring their stability.

Harry Nyquist (1889–1976) Harry Nyquist worked at AT & T ’s D e p a r t m e n t o f Development and Research from 1917 to 1934 and continued when it became Bell Telephone Laboratories in that year, until his retirement in 1954. The word inspired means “to have been touched by the hand of God.” Harry Nyquist’s 37 years and 138 U.S. patents while at Bell Telephone Laboratories personifies “inspired.” In acoustics the Nyquist plot is by far my favorite for first look at an environment driven

by a known source. The men privileged to work with Harry Nyquist in thermal noise, data transmission, and negative feedback all became giants in their own right through that association. Nyquist worked out the mathematics that allowed amplifier stability to be calculated leaving us the Nyquist plot as one of the most useful audio and acoustic analysis tools ever developed. His cohort, Hendrik Bode, gave us the frequency and phase plots as separate measurements. Karl Kupfmuller (1897–1977) was a German engineer who paralleled Nyquist’s work independently, deriving fundamental results in information transmission and closed-loop modeling, including a stability criterion. Kupfmuller as early as 1928 used block diagrams to represent closed-loop linear circuits. He is believed to be the first to do so. As early as 1924 he had published papers on the dynamic response of linear filters. For those wishing to share the depth of understanding these men achieved, Ernst Guillemin’s book, Introductory Circuit Theory, contains clear steps to that goal. Today’s computers as well as digital audio devices were first envisioned in the mid-1800s by Charles Babbage and the mathematics discussed by Lady Lovelace, the only legitimate daughter of Lord Byron. Lady Lovelace even predicted the use of a computer to generate musical tones. Harry Nyquist later defined the necessity for the sampling rate for a digital system to be at least twice that of the highest frequency desired to be reproduced. Nyquist and Shannon went from Nyquist’s paper on the subject to develop “Information Theory.” Today’s audio still uses and requires Nyquist plotting, Nyquist frequency, the Nyquist-Shannon sampling theorem, the Nyquist stability criterion, and attention to the Johnson-Nyquist noise. In acoustics the Nyquist plot is by far my favorite for first look at an environment driven by a known source. The dB, dBm and the VI The development of the dB from the mile of standard cable by Bell Labs, their development and sharing of the decibel, dB, the dBm, and the VU via the design of VI devices changed system design into engineering design. Of note here to this generation, the label VU is just that, VU, and has no other name, just as the instrument is called a volume indicator, or VI. In today’s world, a majority of technicians do not understand the dBm and its remarkable usefulness in system design. An engineer must know this parameter to be taken seriously.

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? Bell Labs and Talking Motion Pictures Bell Telephone Laboratories by the mid to late 1930s had from the inception of talking motion pictures in 1927–1928 brought forth the condenser microphone, exponential high frequency horns, exponential low frequency loudspeakers, compression drivers, the concepts of gain and loss, the dBm, the VU, in cooperation with the broadcasting industry, and installed sound in 80% of the existing theater market. Yes, there were earlier dabblers thinking of such ideas but their ideas remained unfulfilled. What generated the explosive growth of motion picture sound—even through the deepest depression—was that only (1) entertainment, (2) tobacco, and (3) alcohol were affordable to the many and solaced their mental depression. For physicists, motion picture sound was that age’s “space race” and little boys followed the sound engineers down the street saying, “He made the movie talk.” Dr. Eugene Patronis sent me a picture of the W.E. loudspeaker system installed in the late 1930s in which the engineer had actually aligned the H.F. and L.F. drivers. Dr. Patronis had worked in the projector booth as a teenager. He later designed an outstanding loudspeaker system for the AMC theater chain that was aligned and installed above rather than behind the screen, thereby allowing much brighter images. The system maintained complete spatial location screen-center for the audio.

Motion Pictures—Visual versus Auditory The first motion pictures were silent. Fortunes were made by actors who could convey visual emotion. When motion pictures acquired sound in 1928, a large number of these well-known personalities failed to make the transition from silent to sound. The faces and figures failed to match the voices the minds of the silent movie viewers had assigned them. Later, when radio became television, almost all the radio talent was able to make a transition because the familiar voices predominated over any mental visual image the radio listener had assigned to that performer.

Often, at the opera, the great voices will not look the part but, just a few notes nullify any negative visual impression for the true lover of opera, whereas appearance will not compensate for a really bad voice. The Transition from Western Electric to Private Companies A remarkable number of the giants in the explosion in precision audio products after WWII were alumni of Western Electric-Bell Labs, MIT, and General Radio, and in some cases, all three. In 1928, a group of Western Electric engineers became the Electrical Research Products, Inc. (ERPI), to service the theaters. Finally a consent decree came down, as a result of litigation with RCA, for W.E. to divest itself of ERPI. At this point the engineers formed All Technical Services or Altec. That is why it is pronounced all-tech, not al-tech. They lived like kings in a depressed economy. As one of these pioneer engineers told me, “Those days were the equivalent of one ohm across Fort Knox.” They bought the W.E. Theater inventory for pennies on the dollar. The motion picture company MGM had assembled, via Douglas Shearer, head of the sound department, John Hilliard, Dr. John Blackburn, along with Jim Lansing, a machinist, and Robert Stephens, a draftsman. A proprietary theater loudspeaker was named the Shearer horn. Dr. Blackburn and Jim Lansing did the high frequency units with Stephens, adapting the W.E. multicell to their use. It was this system that led to John Hilliard’s correction of the blurred tapping of Eleanor Powell’s very rapid tap dancing by signal aligning the high and low frequency horns. They found that a 3 inch misalignment was small enough to not smear the tapping. (Late in the 1980s, I demonstrated that from 0 to 3 inch misalignment resulted in a shift in the polar response.) Hilliard had previously found that there was on the order of 1500q in phase shift in the early studio amplification systems. He corrected the problem and published his results in the 1930s. After WWII, Hilliard and Blackburn, who both were at MIT doing radar work during the war, went their separate ways, with Hilliard joining Altec Lansing. Hilliard received an honorary Ph.D. with a degree from the Hollywood University run by Howard Termaine, the author

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of the original Audio Encyclopedia, the forerunner to this present volume, The Handbook for Sound Engineers. Robert Lee Stephens left MGM in 1938 to found his own company. In the early 1950s I witnessed demonstrations of the Altec 604, the Stephens TruSonic co-axial and the Jensen Triaxial, side by side in my hi-fi shop, The Golden Ear. The Tru-Sonics was exceptionally clean and efficient. Stephens also made special 15 inch low-frequency drivers for the early Klipschorns. Hilliard, Stephens, Lansing and Shearer defined the theater loudspeaker for their era with much of the design of the Shearer multicells manufactured by Stephens. When James Lansing (aka James Martinella) first came west he adopted the Hollywood technique of a name change. His brother, who worked for Altec through his entire career, shortened his name to Bill Martin, a truly skilled machinist who could tool anything. In 1941, Altec bought Lansing Manufacturing Company and changed the Altec name to Altec Lansing Corp. James Lansing was enjoined by Altec to the use of JBL rather than Lansing for product names. He committed suicide in 1949, and JBL would have vanished except Edmond May, considered the most valuable engineer ever at JBL, stepped into the design breach with a complete series of high quality products. In 1947, Altec purchased Peerless Electrical Products Co. This brought in not only the first designers of 20–20,000 Hz output transformer, Ercel Harrison and his talented right-hand man, Bob Wolpert, but also the ability to manufacture what they designed. Ercel Harrison’s Peerless transformers are still without peer even today. In 1949, Altec acquired the Western Electric Sound Products Division and began producing the W.E. product lines of microphones and loudspeakers. It was said that all the mechanical product tooling, such as turntables and camera items were dumped in the channel between Los Angeles and Catalina. Jim Noble, H.S. Morris, Ercel Harrison, John Hillard, Jim Lansing, Bob Stevens and Alex Badmieff (my co-author for How to Build Speaker Enclosures) were among the giants who populated Altec and provided a glimpse into the late 1920s, the fabulous 1930s, and the final integration of W.E. Broadcasting and Recording technologies into Altec in the 1950s. Paul Klipsch in 1959 introduced me to Art Crawford, the owner of a Hollywood FM station, who devel-

oped the original duplex speaker. The Hollywood scene has always had many clever original designers whose ideas were for “one only” after which their ideas migrated to manufacturers on the West coast. Running parallel through the 20s and 30s with the dramatic developments by Western Electric, Bell Labs, and RCA were the entrepreneurial start-ups by men like Sidney N. Shure of Shure Brothers, Lou Burroughs and Al Kahn of what became Electro-Voice, and E. Norman Rauland who from his early Chicago radio station WENR went on to become an innovator in cathode ray tubes for radar and early television. When I first encountered these in men in the 50s, they sold their products largely through parts pistributors. Starting the 1960s they sold to sound contractors. Stromberg-Carlson, DuKane, RCA, and Altec were all active in the rapidly expanding professional sound contractor market. A nearly totally overlooked engineer in Altec Lansing history is Paul Veneklasen, famous in his own right for the Western Electro Acoustic Laboratory, WEAL. During WWII, Paul Veneklasen researched and designed, through extensive outdoor tests with elaborate towers, what became the Altec Voice of the Theater in postwar America. Veneklasen left Altec when this and other important work (the famed “wand” condenser microphone) were presented as Hilliard’s work in Hilliard’s role as a figurehead. Similar tactics were used at RCA with Harry Olson as the presenter of new technology. Peter Goldmark of the CBS Laboratories was given credit for the 331/3 long playing record. Al Grundy was the engineer in charge of developing it, but was swept aside inasmuch as CBS used Goldmark as an icon for their introductions. Such practices were not uncommon when large companies attempted to put an “aura” around personnel who introduced their new products, to the chagrin and disgust of the actual engineers who had done the work. “This is the west, sir, and when a legend and the facts conflict, go print the legend.” From Who Shot Liberty Valance

Audio Publications Prior to WWII, the IRE, Institute of Radio Engineers, and the AIEE, American Institute of Electrical Engineers, were the premier sources of technology applicable to audio. The Acoustical Society of America filled the role in matters of acoustics. I am one year older than the JASA, which was first published in 1929. In 1963, the IRE and AIEE merged to become the IEEE, the Institute of Electrical and Electronic Engineers.

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? In 1947, C.G. McProud published Audio Engineering that featured construction articles relevant to Audio. Charles Fowler and Milton Sleeper started High Fidelity in 1954. Sleeper later published Hi Fi Music at Home. These magazines were important harbingers of the explosive growth of component sound equipment in the 1950s. The Audio Engineering Society, AES, began publication of their journal in January 1953. The first issue contained an article written by Arthur C. Davis entitled, “Grounding, Shielding and Isolation.” Readers need to make a clear distinction in their minds between magazines designed as advertising media for “fashion design” sound products and magazines that have the necessary market information requiring the least reader screening of foolish claims. The right journals are splendid values and careful perusal of them can bring the disciplined student to the front of the envelope rapidly.

The “High” Fidelity Equipment Designers By the beginning of WWII, Lincoln Walsh had designed what is still today considered the lowest distortion power amplifier using all triode 2A3s. Solid state devices, even today, have yet to match the perfection of amplifiers such as Lincoln Walsh’s Brook with its all triode 2A3s or Marantz’s EL34 all triode amplifier. The Walsh amplifiers, with the linearity and harmonic structure achieved by these seminal tube amplifiers, are still being constructed by devotees of fidelity who also know how to design reasonable efficiency loudspeakers. One engineer that I have a high regard for tells the story, It wasn’t that long ago I was sitting with the editor of a national audio magazine as his $15,000 transistor amplifier expired in a puff of smoke and took his $22,000 speakers along for the ride. I actually saw the tiny flash of light as the woofer voice coil vaporized from 30 A of dc offset—true story folks. In the 1950s, a group of Purdue University engineers and I compared the Brook 10 W amplifier to the then very exciting and unconventional 50 W McIntosh. The majority preferred the 10 W unit. Ralph Townsley, chief engineer at WBAA, loaned us his peak reading meter. This was an electronic marvel that weighed about 30 lbs

but could read the true full peak side-by-side with the VU reading on two beautiful VI instruments. We found that the ticks on a vinyl record caused clipping on both amplifiers but the Brook handled these transients with far more grace than the McIntosh. We later acquired a 200 W tube-type McIntosh and found that it had sufficient headroom to avoid clipping over the Klipschorns, Altec 820s, etc. When Dr. R.A. Greiner of the University of Wisconsin published his measurements of just such effects, our little group were appreciative admirers of his extremely detailed measurements. Dr. Greiner could always be counted on for accurate, timely, and when necessary, myth-busting corrections. He was an impeccable source of truth. The home entertainment section of audio blithely ignored his devastating examination of their magical cables and went on to fortunes made on fables. Music reproduction went through a phase of, to this writer, backward development, with the advent of extremely low efficiency book shelf loudspeaker packages with efficiencies of 20–40 dB below the figures which were common for the horn loudspeakers that dominated the home market after WWII. Interestingly, power amplifiers today are only 10–20 dB more powerful than a typical 1930s triode amplifier. I had the good fortune to join Altec just as the fidelity home market did its best to self-destruct via totally unreliable transistor amplifiers trying to drive “sinkholes” for power loudspeakers in a marketing environment of spiffs, department store products, and the introduction of source material not attractive to trained music listeners. I say “good fortune” as the professional sound was, in the years of the consumer hiatus, to expand and develop in remarkable ways. Here high efficiency was coupled to high power, dynamic growth in directional control of loudspeaker signals, and the growing awareness of the acoustic environment interface.

Sound System Equalization Harry Olson and John Volkmann at RCA made many advances with dynamical analogies, equalized loudspeakers, and an array of microphone designs. Dr. Wayne Rudmose was the earliest researcher to perform meaningful sound system equalization. Dr. Rudmose published a truly remarkable paper

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in Noise Control (a supplementary journal of the Acoustical Society of America) in July 1958. At the AES session in the fall of 1967, I gave the first paper on the 1 » 3 octave contiguous equalizer. Wayne Rudmose was the chairman of the session. In 1969, a thorough discussion of acoustic feedback that possessed absolute relevance to real-life equalization appeared in the Australian Proceedings of the IREE. “A Feedback-Mode Analyzer/Suppressor Unit for Auditorium Sound System Stabilization” by J.E. Benson and D.F. Craig, illustrating the step-function behavior of the onset and decay of regeneration in sound systems. These four sources constitute the genesis of modern system equalization. Fixed equalization was employed by many early experimenters including Kellogg and Rice in the early 1920s, Volkmann of RCA in the 1930s, and Dr. Charles Boner in the 1960s. Dr. Boner is shown here in the midst of installing filters hardwired one at a time “until the customer ran out of money”— was a famous quote. His demonstrations of major improvements in sound systems installed in difficult environments encouraged many to further investigate sound system design and installation practices, followed by custom 1 » 3 octave equalization. His view of himself was “that the sound system was the heart patient and he was the Dr. DeBakey of sound.” The equalization system developed at Altec in 1967 by Art Davis (of Langevin fame), Jim Noble, chief electronics engineer, and myself was named Acousta-Voicing. This program, coupled precision measurement equipment and specially trained sound contractors, resulted in larger more powerful sound systems once acoustic feedback was tamed via band rejection filters spaced at 1 » 3 octave centers.

Equalization dram a t i c a l l y a ff e c t e d quality in recording studios and motion picture studios. I introduced variable system equalization in special sessions at the screening facilities in August 1969 to the sound heads of MGM—Fred Wi l s o n , D i s n e y — Herb Taylor, and Al Green—Warner Bros/7 Arts. Sound system equalization, room treatment such as Manfred Schroeder’s Residue Diffusers designed and manufactured by Peter D’Antonio, and the signal alignment of massive arrays led to previously unheard of live sound levels in large venues.

Acoustics As Kelvin was to electrical theory so was John William Strutt, Third Baron Rayleigh, to acoustics. He was known to later generations as Lord Rayleigh (1842–1919). I was employed by Paul W. Klipsch, a designer and manufacturer of high quality loudspeaker systems in the late 1950s. He told me to obtain and read Lord Rayleigh’s The Theory of Sound. I did so to my immense long term benefit. This remarkable three-volume tome remains the ultimate example of what a gentleman researcher can achieve in a home laboratory. Lord Rayleigh wrote, The knowledge of external things which we derive from the indications of our senses is for the most part the result of inference. The illusionary nature of reproduced sound, the paper cone moving back and forth being inferred to be a musical instrument, a voice, or other auditory stimuli, was vividly reinforced by the famous Chapter 1. In terms of room acoustics, Wallace Clement Sabine was the founder of the science of architectural acoustics. He was the acoustician for Boston Symphony Hall, which is considered to be one of the three finest concert halls in the world. He was the mountain surrounded by men like Hermann, L.F. von Helmholtz, Lord Rayleigh, and

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? others—early insights into how we listen and perceive. As one both researches and recalls from experience the movers and shakers of the audio-acoustic industry, the necessity to publish ideas is paramount. Modern communication theory has revealed to us a little of the complexity of the human listener. The h u ma n b r a in h a s from 10 15 to 10 1 7 bits of storage and we are told an operating rate of 100,000 Teraflops per second. No wonder some “sensitives” found difficulties in early digital recordings and even today attendance at a live unamplified concert quickly dispels the notion that reproduced sound has successfully modeled live sound. We have arrived in the 21st century with not only fraudulent claims for products (an ancient art) but deliberately fraudulent technical society papers hoping to deceive the reader. I once witnessed a faulty technical article in a popular audio magazine that caused Mel Sprinkle (authority on the gain and loss of audio circuits) to write a Letter to the Editor. The Editor wrote saying Mel must be the one in error as a majority of the Letters to the Editor sided with the original author—a case of engineering democracy. We pray that no river bridges will be designed by this democratic method. Frederick Vinton Hunt of Harvard was one of the intellectual offspring of men like Wallace Clement Sabine. As Leo Beranek wrote, At Harvard, Hunt worked amid a spectacular array of physicists and engineers. There was George Washington Pierce, inventor of the crystal oscillator and of magnetostriction transducers for underwater sound; Edwin H. Hall of the Hall effect; Percy Bridgeman, Nobel Lareate, whose wife had been secretary to Wa l l a c e S a b i n e ; A . E . K e n n e l l y o f t h e Kennelly-Heaviside layer; W.F. Osgood, the mathematician; O.D. Kellog of potential theory; and F.A. Saunders, who was the technical heir at Harvard to Sabine. Hunt’s success in 1938 of producing a wide range 5 gram phonograph pickup that replaced the 5 oz units then in use led to Hunt and Beranek building large exponentially folded horns, a very high power amplifier and the introduction of much higher fidelity than had previously been available.

Dr. Hunt attended the technical session at the Los Angeles AES meeting in 1970 when I demonstrated the computation of acoustic gain for the sound system at hand, followed by Acousta-Voicing equalization in real time on the first H.P. Real Time Analyzer, all in 20 minutes. Dr. Hunt’s remark to the audience following the demonstration insured the immediate acceptance of what we had achieved without any questions from the previous doubters. Dr. Hunt took genuine interest in the technology and was generous in his praise of our application of it. He said, “I don’t fully understand how you have done it, but it certainly works.”

Professional-Level Audio Equipment Scaled to Home Use World War II had two major consequences in my life (I just missed it by one year). The first was going to college with the returning G.I.s and discovering the difference in maturity between a gung-ho kid and a real veteran only one or two years older. The chasm was unbridgeable and left a lifelong respect for anyone who has served their country in the armed services. As a young ham operator, I had obtained a very small oscilloscope, McMillan, for use as a modulation monitor. I had seen the General Radio type 525A at Purdue University, without realizing until many years later, the genius it embodied by Professor Bedell of Cornell, inventor of the linear sweep circuit, and H.H. Scott while working on it as a student at MIT with a job at General Radio as well. The second was the pent-up explosion of talent in the audio industry especially that part misnamed hi-fidelity. Precision high quality it was, fidelity we have yet to achieve. Directly after WWII a demand arose for professional level sound equipment scaled to “in the home use.” Innovators such as Paul Klipsch, Lincoln Walsh, Frank McIntosh, Herman Hosmer Scott, Rudy Bozak, Avery Fisher, Saul Marantz, Alex Badmieff, Bob Stevens, and James B. Lansing met the needs of those desiring quality sound capable of reproducing the FM broadcasts and the fuller range that the advent of 331 /3 vinyl records brought about. During the early 50s, Lafayette and West Lafayette were two small towns across from each other on the banks of the Wabash River. Our clientele, Indiana’s first hi-fi shop, the Golden Ear, was drawn from Purdue University and men like those named above could draw audiences equipped to appreciate their uniqueness. At that period Purdue had one of the finest minds in audio in charge of its broadcast station WBAA, Indiana’s first

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broadcasting station and consequently a “clear channel” that Ralph Townsley utilized to modulate 20–20,000 Hz low distortion AM signals. Those of us who had Sargent Rayment TRF tuners had AM signals undistinguishable from FM, except during electrical storms. Any graduating Electrical engineer who could pass Townsley’s basic audio networks test, for a job at WBAA, was indeed an engineer who could think for himself or herself about audio signals. Great audio over AM radio in the late 1920s and early 1930s ran from the really well-engineered Atwater Kent tuned radio frequency receiver (still the best way to receive AM signals via such classics as the Sargent Rayment TRF tuner) to the absolutely remarkable, for its time, E.H. Scott’s Quaranta (not to be confused with the equally famous H.H. Scott of postwar years). This was a 48 tube superheterodyne receiver built on six chrome chassis weighing 620 lbs with five loudspeakers (two woofers, midrange, and high frequency units) biamped with 50 W for the low frequencies and 40 W for the high frequencies. My first view of one of these in the late 1930s revealed that wealth could provide a cultural life.

regenerative circuit work. The regenerative circuit allowed great amplification of the received signal and also was an oscillator, if desired, making continuous wave transmission possible. This single circuit became not only the first radio amplifier, but also the first continuous wave transmitter that is still the heart of all radio operations. In 1912–1913 Armstrong received his engineering degree from Columbia University, filed for a patent, and then returned to the university as assi stant to professor and inventor Michael Pupin. Dr. Pupin was a mentor to Armstrong and a great teacher to generations at Columbia University. World War I intervened and Armstrong was commissioned as an officer in the U.S. Army Signal Corps and sent to Paris. While there and in the pursuit of weak enemy wireless signals, he designed a complex eight tube receiver called the superheterodyne circuit, the circuit still used in 98% of all radio and television receivers. In 1933 Armstrong invented and demonstrated wide-band frequency modulation that in field tests gave clear reception through the most violent storms and the greatest fidelity yet witnessed. The carrier was constant power while the frequency was modulated over the bandpass chosen.

Edwin Armstrong (1890–1954) The Invention of Radio and Fidelity The technical history of radio is best realized by the inventor/engineer Edwin Howard Armstrong. Other prominent figures were political and other engineers were dwarfed by comparison to Armstrong. In the summer of 1912, Armstrong, using the new triode vacuum tube, devised a new regenerative circuit in which part of the signal at the plate was fed back to the grid to strengthen incoming signals. In spite of his youth, Armstrong had his own pass to the famous West Street Bell Labs because of his

He had built the entire FM transmitter and receiver on breadboard circuits of Columbia University. After the fact of physical construction, he did the mathematics. Armstrong, in developing FM, got beyond the equations of the period which in turn laid the foundations for information theory, which quantifies how bandwidth can be exchanged for noise immunity. In 1922, John R. Carson of AT&T had written an IRE paper that discussed modulation mathematically. He showed that FM could not reduce the station band-

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? width to less than twice the frequency range of the audio signal, “Since FM could not be used to narrow the transmitted band, it was not useful.” Edwin Armstrong ignored narrowband FM and moved his experiments to 41 MHz and used a 200 kHz channel for wideband, noiseless reproduction. FM broadcasting allowed the transmitter to operate at full power all the time and used a limiter to strip off all amplitude noise in the receiver. A detector was designed to convert frequency variations into amplitude variations. Paul Klipsch was a personal friend of Edwin Armstrong: Mr. Klipsch had supplied Klipschorns for the early FM demonstration just after WWII. This was when Armstrong, through Sarnoff’s political manipulation, had been forced to move FM from 44–50 MHz to 88–108 MHz, requiring a complete redesign of all equipment. It was a stark lesson on how the courts, the media, and really big money can destroy genuine genius. Armstrong had literally created radio: the transmitters, the receivers for AM-FM-microwave in their most efficient forms. David Sarnoff made billions out of Armstrong’s inventions, as well as an economic-political empire via the AM radio networks. No court or any politician should ever be allowed to make a technical judgment. Those judgments should be left to the technical societies as the “least worst” choice. The history of audio is not the forum for discussing the violent political consequences—Sarnoff of RCA totally controlled the powerful AM networks of the time. In 1954 attorneys for RCA and AT&T led to Armstrong’s death by suicide. The current AM programming quality put on FM leaves quality FM radio a rare luxury in some limited areas. The few, myself included, who heard the live broadcasts of the Boston Symphony Orchestra over the FM transmitter given them by Armstrong and received on the unparalleled, even today, precedent FM receivers know what remarkable transparency can be achieved between art and technology.

Acoustic Measurements—Richard C. Heyser (1931–1987) Plato said, “God ever geometrizes.” Richard Heyser, the geometer, should feel at ease with G o d . To t h o s e whose minds respond to the visual, Heyser’s measurements shed a bright light on difficult mathematical concepts. The Heyser Spiral displays the concepts of the complex plane in a single visual flash. Heyser was a scientist in the purest sense of the word, employed by NASA, and audio was his hobby. I am quite sure that the great scientists of the past were waiting at the door for him when he past through. His transform has yet to be fully understood. As with Maxwell, we may have to wait a hundred years. When I first met Richard C. Heyser in the mid-1960s, Richard worked for Jet Propulsion Labs as a senior scientist. He invited me to go to his basement at his home to see his personal laboratory. The first thing he showed me on his Time Delay Spectrometry equipment was the Nyquist plot of a crossover network he was examining. I gave the display a quick look and said, “That looks like a Nyquist plot!” He replied, “It is.” “But,” I said, “No one makes a Nyquist analyzer.” “That’s right,” he replied. At this point I entered the modern age of audio analysis. Watching Dick tune in the signal delay between his microphone and the loudspeaker he was testing until the correct bandpass filter Nyquist display appeared on the screen was a revelation. Seeing the epicycles caused by resonances in the loudspeaker and the passage of non-minimum phase responses back through all quadrants opened a million questions. Dick then showed me the Bode plots of both frequency and phase for the same loudspeaker but I was to remain a fan of seeing everything at once via the Nyquist plot.

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To put all this in perspective (I worked at Altec at the time) I knew of no manufacturer in audio capable of making any of these measurements. We all had Bruel and Kjaer or General Radio frequency analyzers and good Tektronics oscilloscopes, but zero true acoustic phase measurement capabilities. I do not mean to imply that the technology didn’t exist because Wente calculated the phase response of 555A in the 1920s, but rather that commercial instruments available in audio did not exist until Richard Heyser demonstrated the usefulness of the measurements and Gerald Stanley of Crown International actually built a commercially available device. Heyser’s remarkable work became the Time, Envelope, Frequency (TEF) system, first in the hands of Crown International, and later as a Gold Line instrument. The early giants of audio computed theoretical phase responses for minimum phase devices. A few pure scientists actually measured phase—Weiner, Ewask, Marivardi and Stroh, but their results had failed to go beyond their laboratories. From 1966 until today, 42 years later, such analysis can now be embodied in software in fast, large memory computers. Dennis Gabor’s (1900– 1979) analytic signal theory appeared in Heyser’s work as amplitude response, phase response, and Envelope Time Curves (ETC). One glance at the Heyser Spiral for impedance reveals Gabor’s analytic signal and the complex numbers as real, imaginary, and Nyquist plot. The correlation of what seems first to be separate components into one component is a revelation to the first time viewer of this display. The unwinding of the Nyquist plot along the frequency axis provides a defining perspective. Heyser’s work led to loudspeakers with vastly improved spatial response, something totally unrecognized in the amplitude-only days. Arrays became predictable and coherent. Signal alignment entered the thought of designers. The ETC technology resulted in the chance to meaningfully study loudspeaker–room interactions. Because the most widely taught mathematical tools proceed from impulse responses, Heyser’s transform is perceived “through a glass darkly.” It is left in the hands of practitioners to further the research into the transient behavior of loudspeakers. The decades-long lag of academia will eventually apply the lessons of the Heyser

transform to transducer signal delay and signal delay interaction. I have always held Harry Olson of RCA in high regard because, as editor of the Audio Engineering Society Journal in 1969, he found Richard C. Heyser’s original paper in the waste basket—it had been rejected by means of the idiot system of non-peer review used by the AES Journal.

Calculators and Computers In the late 1960s, I was invited to Hewlett Packard to view a new calculator they were planning to market. I was working at this time with Arthur C. Davis (not a relative) at Altec, and Art was a friend of William Hewlett. Art had purchased one of the very first RC oscillators made in the fabled HP garage. He had used them for the audio gear that he had designed for the movie—Fantasia. The 9100 calculator– computer was the first brainchild that Tom Osborne took t o H P, a f t e r having been turned down by SCM, IBM, Friden and Monroe. (I purchased one; it cost me $5100. I used it to program the first acoustic design programs.) In 1966, a friend introduced Osborne to Barney Oliver at HP. After reviewing the design he asked Osborne to come back the next day to meet Dave and Bill, to which Osborne said, “Who?” After one meeting with “Dave & Bill,” Osborne knew he had found a home for his 9100. Soon Bill Hewlett turned to Tom Osborne, Dave Cochran, and Tom Whitney, who worked under the direction of Barney Oliver, and said, “I want one in a tenth the volume (the 9100 was IBM typewriter size), ten times as fast, and at a tenth of the price.” Later he added that he “wanted it to be a shirt pocket machine.” The first HP 35 cost $395, was 3.2 × 5.8 × 1.3 inches and weighed 9 oz with batteries. It also fit into Bill Hewlett’s shirt pocket. (Bill Hewlett named the calculator the HP 35 because it had 35 keys.) Art Davis took me to lunch one day with Mr. Hewlett. Because I had been an ardent user of the HP 9100 units, I was selected to preview the HP 35 during its initial tests in Palo Alto.

Audio and Acoustic DNA—Do You Know Your Audio and Acoustic Ancestors? In my mind, these calculators revolutionized audio education, especially for those without advanced university educations. The ability to quickly and accurately work with logarithm, trigonometric functions, complex numbers, etc., freed us from the tyranny of books of tables, slide rules, and carefully hoarded volumes such as Massa’s acoustic design charts and Vegas’s ten place log tables. For the multitude of us who had experienced difficulty in engineering courses with misplaced decimal points and slide rule manipulation and extrapolation, the HP 35 released inherent talents we didn’t realize we possessed. The x^y key allowed instant K numbers. The ten-place log tables became historical artifacts. When I suggested to the then president of Altec that we should negotiate being the one to sell the HP 35s to the electronics industry (Altec then owned Allied Radio,) his reply stunned me, “We are not in the calculator business.” I thought as he said it, “Neither is Hewlett Packard.” His decision made it easy for me to consider leaving Altec. I soon left Altec and started Synergetic Audio Concepts, teaching seminars in audio education. I gave each person attending a seminar an HP 35 to use during the 3-day seminar. I know that many of those attending immediately purchased an HP calculator, which changed their whole approach to audio system design. As Tom Osborne wrote, “The HP 35 and HP 65 changed the world we live in.” Since the political demise of the Soviet Union, “Mozarts-without-a-piano” have been freed to express their brilliance. Dr. Wolfgang Ahnert, from former East Germany, was enabled to use his mathematical skills with matching computer tools to dominate the audio-acoustic design market place.

The Meaning of Communication The future of audio and acoustics stands on the shoulders of the giants we have discussed, and numerous ones that we have inadvertently overlooked. The discoverers of new and better ways to generate, distribute, and control sound will be measured consciously or unconsciously by their predecessor’s standards. Fad and fundamentals will be judged eventually. Age councils that “the ancients are stealing our inventions.” The uncovering of an idea new to you is as thrilling as it was to the first person to do so.

The history of audio and acoustics is the saga of the mathematical understanding of fundamental physical laws. Hearing and seeing are illusionary, restricted by the inadequacy of our physical senses. The science and art of audio and acoustics are essential to our understanding of history inasmuch as art is metaphysical (above the physical). Also art precedes science. That the human brain processes music and art in a different hemisphere from speech and mathematics suggests the difference between information, that can be mathematically defined and communication that cannot. A message is the flawless transmission of a text. Drama, music, and great oratory cannot be flawlessly transmitted by known physical systems. For example, the spatial integrity of a great orchestra in a remarkable acoustic space is today even with our astounding technological strides only realizable by attending the live performance. The complexity of the auditory senses defies efforts to record or transmit it faithfully. The perception of good audio will often flow from the listener’s past experience, i.e., wow and flutter really annoys musicians whereas harmonic distortion, clipping, etc., grate on an engineer’s ear–mind system. I have not written about today’s highly hyped products as their history belongs to the survivors of the early 21st century. It can be hoped that someday physicists and top engineers will for some magic reason return to the development of holographic audio systems that approach fidelity. Telecommunication technology, fiber optics, lasers, satellites, etc. have obtained worldwide audiences for both trash and treasure. The devilish power that telecommunications has provided demagogues is frightening, but shared communication has revealed to a much larger audience the prosperity of certain ideas over others, and one can hope that the metaphysics behind progress will penetrate a majority of the minds out there. That the audio industry’s history has barely begun is evidenced every time one attends a live performance. We will, one day, look back on the neglect of the metaphysical element, perhaps after we have uncovered the parameters at present easily heard but unmeasurable by our present sciences. History awaits the ability to generate the sound field rather than a sound field. When a computer is finally offered to us that is capable of such generation, the question it must answer is,

“How does it feel?”

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Bibliography Lynn Olson, The Soul of Sound, revised and updated in 2005—a superb, accurate, and insightful picture of the greats and ingrates of consumer audio. American Institute of Electrical Engineers, April 18, 1893. Ms. Mary Ann Hoffman of the IEEE History Center at Rutgers University is in the process of rescuing these seminar papers and getting them to restorers. She graciously provided me with a copy of the original. Eugene Patronis, pictures of 1930s Western Electric theater loudspeaker. William T. McQuaide, Audio Engineering Society, picture of Lincoln Walsh. 36 years of Syn-Aud-Con Newsletters for pictures, dates, and equipment. Michael P. Frank, Physical Limits of Computing, University of Florida. The ownership of some 750 audio and acoustic technical volumes now owned and preserved by Mary Gruska, who sensed their metaphysical value and purchased “the infinite with the finite.” Lawrence Lessing, Man of High Fidelity, Edwin Howard Armstong, Lippincott, 1956. Tom Osborne, Tom Osborne’s Story in His Own Words, a letter to Dave Packard explaining his development of the HP 9100 and the HP 35. The vast resource of the Internet.

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Fundamentals of Audio and Acoustics by Pat Brown 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Loudness and Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Surface Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Human Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Monitoring Audio Program Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Sound Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11.1 The Point Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11.2 The Line Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 39

23 23 26 26 27 29 30 32 34 35 36 36 37 38

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Fundamentals of Audio and Acoustics 2.1 Introduction Many people get involved in the audio trade prior to experiencing technical training. Those serious about practicing audio dig in to the books later to learn the physical principles underlying their craft. This chapter is devoted to establishing a baseline of information that will prove invaluable to anyone working in the audio field. Numerous tools exist for those who work on sound systems. The most important are the mathematical tools. Their application is independent of the type of system or its use, plus, they are timeless and not subject to obsolescence like audio products. Of course, one must always balance the mathematical approach with real-world experience to gain an understanding of the shortcomings and limitations of the formulas. Once the basics have been mastered, sound system work becomes largely intuitive. Audio practitioners must have a general understanding of many subjects. The information in this chapter has been carefully selected to give the reader the big picture of what is important in sound systems. Many of the topics are covered in greater detail in other chapters of this book. In this initial treatment of each subject, the language of mathematics has been kept to a minimum, opting instead for word explanations of the theories and concepts. This provides a solid foundation for further study of any of the subjects. Considering the almost endless number of topics that could be included here, I selected the following based on my own experience as a sound practitioner and instructor. They are: 1. 2. 3. 4. 5. 6. 7. 8. 9.

The Decibel and Levels. Frequency and Wavelength. The Principle of Superposition. Ohm’s Law and the Power Equation. Impedance, Resistance, and Reactance. Introduction to Human Hearing. Monitoring Audio Program Material. Sound Radiation Principles. Wave Interference.

A basic understanding in these areas will provide the foundation for further study in areas that are of particular interest to the reader. Most of the ideas and principles in this chapter have existed for many years. While I haven’t quoted any of the references verbatim, they get full credit for the bulk of the information presented here.

2.2 The Decibel Perhaps the most useful tool ever created for audio practitioners is the decibel (dB). It allows changes in system

parameters such as power, voltage, or distance to be related to level changes heard by a listener. In short, the decibel is a way to express “how much” in a way that is relevant to the human perception of loudness. We will not track its long evolution or specific origins here. Like most audio tools, it has been modified many times to stay current with the technological practices of the day. Excellent resources are available for that information. What follows is a short study on how to use the decibel for general audio work. Most of us tend to consider physical variables in linear terms. For instance, twice as much of a quantity produces twice the end result. Twice as much sand produces twice as much concrete. Twice as much flour produces twice as much bread. This linear relationship does not hold true for the human sense of hearing. Using that logic, twice the amplifier power should sound twice as loud. Unfortunately, this is not true. Perceived changes in the loudness and frequency of sound are based on the percentage change from some initial condition. This means that audio people are concerned with ratios. A given ratio always produces the same result. Subjective testing has shown that the power applied to a loudspeaker must be increased by about 26% to produce an audible change. Thus a ratio of 1.26:1 produces the minimum audible change, regardless of the initial power quantity. If the initial amount of power is 1 watt, then an increase to 1.26 watts (W) will produce a “just audible” increase. If the initial quantity is 100 W, then 126 W will be required to produce a just audible increase. A number scale can be linear with values like 1, 2, 3, 4, 5, etc. A number scale can be proportional with values like 1, 10, 100, 1000, etc. A scale that is calibrated proportionally is called a logarithmic scale. In fact, logarithm means “proportional numbers.” For simplicity, base 10 logarithms are used for audio work. Using amplifier power as an example, changes in level are determined by finding the ratio of change in the parameter of interest (e.g. wattage) and taking the base 10 logarithm. The resultant number is the level change between the two wattages expressed in Bels. The base 10 logarithm is determined using a look-up table or scientific calculator. The log conversion accomplishes two things: 1. It puts the ratio on a proportional number scale that better correlates with human hearing. 2. It allows very large numbers to be expressed in a more compact form, Fig. 2-1. The final step in the decibel conversion is to scale the Bel quantity by a factor of ten. This step converts Bels to decibels and completes the conversion process,

Chapter 2

Linear scale 01 k

10 k

20 k

100

30 k

40 k

50 k

10 K

100 K

Log scale 1

Figure 2-1. A logarithmic scale has its increments marked by a fixed ratio, in this case 10 to 1, forming a more compact representation than a linear scale. Courtesy Syn-Aud-Con.

Figure 2-2. The steps to performing a decibel conversion are outlined. Courtesy Syn-Aud-Con.

Fig. 2-2. The decibel scale is more resolute than the Bel scale. The decibel is always a power-related ratio. Electrical and acoustical power changes can be converted exactly in the manner described. Quantities that are not powers must be made proportional to power—a relationship established by the power equation. 2

E W = -----R where, W is power in watts, E is voltage in volts, R is resistance in ohms.

(2-1)

This requires voltage, distance, and pressure to be squared prior to taking the ratio. Some practitioners

prefer to omit the squaring of the initial quantities and simply change the log multiplier from ten to twenty. This produces the same end result. Fig. 2-3 provides a list of some dB changes along with the ratio of voltage, pressure, distance, and power required to produce the indicated dB change. It is a worthwhile endeavor to memorize the changes indicated in bold type and be able to recognize them by listening. A decibel conversion requires two quantities that are in the same unit, i.e., watts, volts, meters, feet. The unit cancels during the initial division process, leaving the ratio between the two quantities. For this reason, the decibel is without dimension and is therefore technically not a unit in the classical sense. If two arbitrary quantities of the same unit are compared, the result is a relative level change. If a standard reference quantity is used in the denominator of the ratio, the result is an absolute level and the unit is dB relative to the original

Fundamentals of Audio and Acoustics Subjective Change Voltage, % of PowerRatio dB Distance, Original Change Pressure Ratio

20log Barely perceptible Noticeable to most

Goal for system changes

Twice as loud or soft

Limits of audibility

10log 1 dB

and is dependent on the voltage change only, not the resistance that it is developed across or the power transfer. Since open-circuit conditions exist almost universally in modern analog systems, the practice of using the decibel with a voltage reference is widespread and well-accepted.

1.12:1

1.26:1

1.58:1

2 dB

1.41:1

2:1

3 dB

1.58:1

2.51:1

4 dB

1.78:1

3.16:1

5 dB

2:1

4:1

6 dB

Acoustical Power dB-PWL or Lw

2.24:1

5:1

7 dB

2.51:1

6.3:1

8 dB

2.8:1

8:1

9 dB

3.16:1

10:1 10 dB

10:1

100:1 20 dB

31.6:1

1000:1 30 dB

100:1

10,000:1 40 dB

316:1

0.3

100,000:1 50 dB

1000:1

0.1

1,000,000:1 60 dB

Figure 2-3. Some important decibel changes and the ratios of power, voltage, pressure, and distance that produce them. Courtesy Syn-Aud-Con.

unit. Relative levels are useful for live work. Absolute levels are useful for equipment specifications and calibration. Fig. 2-4 lists some references used for determining absolute levels. The decibel was originally used in impedance-matched interfaces and always with a power reference. Power requires knowledge of the resistance that a voltage is developed across. If the resistance value is fixed, changes in applied voltage can be expressed in dB, since the power developed will be directly proportional to the applied voltage. In modern sound systems, few device interfaces are impedance matched. They are actually mismatched to optimize the voltage transfer between components. While the same impedance does not exist at each device interface, the same impedance condition may. If a minimum 1:10 ratio exists between the output impedance and input impedance, then the voltage transfer is essentially independent of the actual output or input impedance values. Such an interface is termed constant voltage, and the signal source is said to be operating open circuit or un-terminated. In constant voltage interfaces, open circuit conditions are assumed when using the decibel. This means that the level change at the output of the system is caused by changing the voltage somewhere in the processing chain

Electrical Power dBW

1 Watt

dBm

0.001 Watt

1012 Watt

Electrical Voltage dBV

1 Volt

dBu

0.775 Volts

Acoustical Pressure dB SPL or Lp

0.00002 Pascals

Figure 2-4. Some common decibel references used by the audio industry.

One of the major utilities of the decibel is that it provides a common denominator when considering level changes that occur due to voltage changes at various points in the signal chain. By using the decibel, changes in sound level at a listener position can be determined from changes in the output voltage of any device ahead of the loudspeaker. For instance, a doubling of the microphone output voltage produces a 6 dB increase in output level from the microphone, mixer, signal processor, power amplifier, and ultimately the sound level at the listener. This relationship assumes linear operating conditions in each device. The 6 dB increase in level from the microphone could be caused by the talker speaking 6 dB louder or by simply reducing the miking distance by one-half (a 2:1 distance ratio). The level controls on audio devices are normally calibrated in relative dB. Moving a fader by 6 dB causes the output voltage of the device (and system) to increase by a factor of 2 and the output power from the device (and system) to be increased by a factor of four. Absolute levels are useful for rating audio equipment. A power amplifier that can produce 100 watts of continuous power is rated at L out = 10 log W = 10 log 100 = 20 dBW

(2-2)

Chapter 2

This means that the amplifier can be 20 dB louder than a 1 watt amplifier. A mixer that can output 10 volts prior to clipping can be rated at L out = 20 log E = 20 log 10

(2-3)

= 20 dBV If the same mixer outputs 1 volt rms at meter zero, then the mixer has 20 dB of peak room above meter zero. If a loudspeaker can produce a sound level at 1 meter of 90 dB ref. 20 μPa (micro-Pascals), then at 10 meters its level will be 1L p = 90 + 20 log ----10 = 90 + – 20

2.3 Loudness and Level The perceived loudness of a sound event is related to its acoustical level, which is in turn related to the electrical level driving the loudspeaker. Levels are electrical or acoustical pressures or powers expressed in decibels. In its linear range of operation, the human hearing system will perceive an increase in level as an increase in loudness. Since the eardrum is a pressure sensitive mechanism, there exists a threshold below which the signal is distinguishable from the noise floor. This threshold is about 20 μPa of pressure deviation from ambient at midrange frequencies. Using this number as a reference and converting to decibels yields L p = 20 log 0.00002 ------------------0.00002

(2-4)

= 70 dB In short, the decibel says, “The level difference caused by changing a quantity will depend upon the initial value of the quantity and the percentage that it is changed.” The applications of the decibel are endless, and the utility of the decibel is self-evident. It forms a bridge between the amount of change of a physical parameter and the loudness change that is perceived by the human listener. The decibel is the language of audio, Fig. 2-5.

(2-5)

= 0 dB (or 0 dB SPL) This is widely accepted as the threshold of hearing for humans at mid-frequencies. Acoustic pressure levels are always stated in dB ref. 0.00002 Pa. Acoustic power levels are always stated in dB ref. 1 pW (picowatt or 1012 W). Since it is usually the pressure level that is of interest, we must square the Pascals term in the decibel conversion to make it proportional to power. Sound pressure levels are measured using sound level meters with appropriate ballistics and weighting to emulate human hearing. Fig. 2-6 shows some typical sound pressure levels that are of interest to audio practitioners.

2.4 Frequency

Figure 2-5. Summary of decibel formulas for general audio work. Courtesy Syn-Aud-Con.

Audio practitioners are in the wave business. A wave is produced when a medium is disturbed. The medium can be air, water, steel, the earth, etc. The disturbance produces a fluctuation in the ambient condition of the medium that propagates as a wave that radiates outward from the source of the disturbance. If one second is used as a reference time span, the number of fluctuations above and below the ambient condition per second is the frequency of the event, and is expressed in cycles per second, or Hertz. Humans can hear frequencies as low as 20 Hz and as high as 20,000 Hz (20 kHz). In an audio circuit the quantity of interest is usually the electrical voltage. In an acoustical circuit it is the air pressure deviation from ambient atmospheric pressure. When the air pressure fluctuations have a frequency between 20 Hz and 20 kHz they are audible to humans. As stated in the decibel section, humans are sensitive to proportional changes in power, voltage, pressure, and distance. This is also true for frequency. If we start at

Fundamentals of Audio and Acoustics

dB A Sound source

110 100 90

The spectral or frequency response of a system describes the frequencies that can pass through that system. It must always be stated with an appropriate tolerance, such as ±3 dB. This range of frequencies is the bandwidth of the system. All system components have a finite bandwidth. Sound systems are usually bandwidth limited for reasons of stability and loudspeaker protection. A spectrum analyzer can be used to observe the spectral response of a system or system component.

Appropriate levels Leave the building! (A-weighted slow) Max music level using sound system (A-weighted slow)

Max speech level using sound system (A-weighted slow)

Face-to-face communication

60 50

2.5 Wavelength

Maximum allowable noise floor

If the frequency f of a vibration is known, the time period T for one cycle of vibration can be found by the simple relationship

40 30

Background noise from HVAC

1 T = --f

(2-6)

10 Threshold of hearing 0 Figure 2-6. Sound levels of interest to system designers and operators. Courtesy Syn-Aud-Con.

the lowest audible frequency of 20 Hz and increase it by a 2:1 ratio, the result is 40 Hz, an interval of one octave. Doubling 40 Hz yields 80 Hz. This is also a one-octave span, yet it contains twice the frequencies of the previous octave. Each successive frequency doubling yields another octave increase and each higher octave will have twice the spectral content of the one below it. This makes the logarithmic scale suitable for displaying frequency. Figs. 2-7 and 2-8 show a logarithmic frequency scale and some useful divisions. The perceived midpoint of the spectrum for a human listener is about 1 kHz. Some key frequency ratios exist: • 10:1 ratio—decade. • 2:1 ratio—octave.

The time period T is the inverse of the frequency of vibration. The period of a waveform is the time length of one complete cycle, Fig. 2-9. Since most waves propagate or travel, if the period of the wave is known, its physical size can be determined with the following equation if the speed of propagation is known: O = Tc

(2-7)

O = c-f

(2-8)

Waves propagate at a speed that is dependent on the nature of the wave and the medium that it is passing through. The speed of the wave determines the physical size of the wave, called its wavelength. The speed of light in a vacuum is approximately 300,000,000 meters per second (m/s). The speed of an electromagnetic wave in copper wire is somewhat less, usually 90% to 95% of the speed of light. The fast propagation speed of electromagnetic waves makes their wavelengths extremely long at audio frequencies, Fig. 2-10.

Log Scale 1

100

10K

100K

Audible Range Low

Mid

High

Voice Range

Figure 2-7. The audible spectrum divided into decades (a 10 to 1 frequency ratio). Courtesy Syn-Aud-Con.

Chapter 2

Octave Band Center Frequency

Band Limits

One-third Octave Centers

Band Limits

Voice range Articulation center

Figure 2-8. The audible spectrum divided into octaves (a 2 to 1 ratio) and one-third octaves. Courtesy Syn-Aud-Con.

At the higher radio frequencies (VHF and UHF), the wavelengths become very short—1 meter or less. Antennas to receive such waves must be of comparable physical size, usually one-quarter to one-half wavelength. When waves become too short for practical antennae, concave dishes can be used to collect the waves. It should be pointed out that the highest frequency that humans can hear (about 20 kHz) is a very low frequency when considering the entire electromagnetic spectrum. An acoustic wave is one that is propagating by means of vibrating a medium such as steel, water, or air. The propagation speeds through these media are relatively slow, resulting in waves that are long in length compared to an electromagnetic wave of the same frequency. The wavelengths of audio frequencies in air range from about 17 m (20 Hz) to 17 mm (20 kHz). The

wavelength of 1 kHz in air is about 0.334 m (about 1.13 ft). When physically short acoustic waves are radiated into large rooms, there can be adverse effects from reflections. Acoustic reflections occur when a wave encounters a change in acoustic impedance, usually from a rigid surface, the edge of a surface or some other obstruction. The reflection angle equals the incidence angle in the ideal case. Architectural acoustics is the study of the behavior of sound waves in enclosed spaces. Acousticians specialize in creating spaces with reflected sound fields that enhance rather than detract from the listening experience. When sound encounters a room surface, a complex interaction takes place. If the surface is much larger than the wavelength, a reflection occurs and an acoustic shadow is formed behind the boundary.

Fundamentals of Audio and Acoustics

1 wavelength

Increasing time

Phase angle (deg)

T = 1/f f = 1/T = Tc where, T is the time in seconds, f is frequency in hertz, c is propagation speed in feet or meters.

Figure 2-9. The wavelength of an event determines how it interacts with the medium that it is passing through. Courtesy Syn-Aud-Con.

If the obstruction is smaller than the wavelength of the wave striking it, the wave diffracts around the obstruction and continues to propagate. Both effects are complex and frequency (wavelength) dependent, making them difficult to calculate, Fig. 2-11. The reflected wave will be strong if the surface is large and has low absorption. As absorption is increased, the level of the reflection is reduced. If the surface is random, the wave can be scattered depending on the size relationship between the wave and the surface relief. Commercially available diffusors can be used to achieve uniform scattering in critical listening spaces, Fig. 2-12.

2.6 Surface Shapes The geometry of a boundary can have a profound affect on the behavior of the sound that strikes it. From a

sound reinforcement perspective, it is usually better to scatter sound than to focus it. A concave room boundary should be avoided for this reason, Fig. 2-13. Many auditoriums have concave rear walls and balcony faces that require extensive acoustical treatment for reflection control. A convex surface is more desirable, since it scatters sound waves whose wavelengths are small relative to the radius of curvature. Room corners can provide useful directivity control at low frequencies, but at high frequencies can produce problematic reflections. Electrical reflections can occur when an electromagnetic wave encounters a change in impedance. For such waves traveling down a wire, the reflection is back towards the source of the wave. Such reflections are not usually a problem for analog waves unless there is a phase offset between the outgoing and reflected waves. Note that an audio cable would need to be very long for its length to cause a significant time offset between the

Chapter 2

Figure 2-10. Acoustic wavelengths are relatively short and interact dramatically with their environment. Audio wavelengths are extremely long, and phase interaction on audio cables is not usually of concern. Courtesy Syn-Aud-Con.

Figure 2-12. Sound waves will interact with a large boundary in a complex way. Courtesy Syn-Aud-Con.

2.7 Superposition

Figure 2-11. Sound diffracts around objects that are small relative to the length of the sound wave. Courtesy Syn-Aud-Con.

incident and reflected wave (many thousands of meters). At radio frequencies, reflected waves pose a huge problem, and cables are normally terminated (operated into a matched impedance) to absorb the incident wave at the receiving device and reduce the level of the reflection. The same is true for digital signals due to their very high frequency content.

Sine waves and cosine waves are periodic and singular in frequency. These simple waveforms are the building blocks of the complex waveforms that we listen to every day. The amplitude of a sine wave can be displayed as a function of time or as a function of phase rotation, Fig. 2-14. The sine wave will serve as an example for the following discussion about superposition. Once the size (wavelength) of a wave is known, it is useful to subdivide it into smaller increments for the purpose of tracking its progression through a cycle or comparing its progression with that of another wave. Since the sine wave describes a cyclic (circular) event, one full cycle is represented by 360°, at which point the wave repeats. When multiple sound pressure waves pass by a point of observation, their responses sum to form a composite wave. The composite wave is the complex combination of two or more individual waves. The amplitude of the

Fundamentals of Audio and Acoustics

Concave surfaces focus sound

Convex surfaces scatter sound

Corners return sound to its source

Figure 2-13. Some surfaces produce focused reflections. Courtesy Syn-Aud-Con.

Figure 2-14. Simple harmonic motion can be represented with a sine or cosine wave. Both are viewpoints of the same event from different angles. Courtesy Syn-Aud-Con.

summation is determined by the relative phase of the individual waves. Let’s consider how two waves might combine at a point of observation. This point might be a listener seat or microphone position. Two extremes exist. If there is no phase offset between two waves of the same amplitude and frequency, the result is a coherent summation that is twice the amplitude of either individual wave (+6 dB). The other extreme is a 180° phase offset between the waves. This results in the complete cancellation of the pressure response at the point of observation. An infinite number of intermediate conditions occur between these two extremes. The phase interaction of waves is not a severe problem for analog audio signals in the electromagnetic domain for sound systems, where the wavelengths at audio frequencies are typically much longer than the interconnect cables. Waves reflected from receiver to source are in phase and no cancellation occurs. This is not the case for video, radio frequency, and digital signals. The shorter wavelengths of these signals can be dramatically affected by wave superposition on interconnect cables. As such, great attention must be given to the length and terminating impedance of the interconnect cables to assure efficient signal transfer between source and receiver. The practice of impedance matching between source, cable, and load is usually employed. In sound reinforcement systems, phase interactions are typically more problematic for acoustical waves than electromagnetic waves. Phase summations and cancellations are the source of many acoustical problems experienced in auditoriums. Acoustic wavelengths are often short relative to the room size (at least at high frequency), so the waves tend to bounce around the room before decaying to inaudibility. At a listener position, the reflected waves “superpose” to form a complex waveform that is heard by the listener. The sound radiated from multiple loudspeakers will interact in the same manner, producing severe modifications in the radiated sound pattern and frequency response. Antenna designers have historically paid more attention to these interactions than loudspeaker designers, since there are laws that govern the control of radio frequency emissions. Unlike antennas, loudspeakers are usually broadband devices that cover one decade or more of the audible spectrum. For this reason, phase interactions between multiple loudspeakers never result in the complete cancellation of sound pressure, but rather cancellation at some frequencies and coherent summation at others. The subjective result is tonal coloration and image shift of the sound source heard by the listener. The significance of this phenomenon is application-dependent. People having dinner in a restaurant

Chapter 2

would not be concerned with the effects of such interactions since they came for the food and not the music. Concert-goers or church attendees would be more concerned, because their seat might be in a dead spot, and the interactions disrupt their listening experience, possibly to the point of reducing the information conveyed via the sound system. A venue owner may make a significant investment in good quality loudspeakers, only to have their response impaired by such interactions with an adjacent loudspeaker or room surface, Fig. 2-16.

Figure 2-15. Phase interference occurs when waves from multiple sources arrive at different times. Courtesy Syn-Aud-Con.

Phase interactions are most disruptive in critical listening environments, such as recording studio control rooms or high quality home entertainment systems. Users of these types of systems often make a large investment to maintain sonic accuracy by purchasing phase coherent loudspeakers and appropriate acoustical treatments for the listening space. The tonal coloration caused by wave interference may be unacceptable for a recording studio control room but may be artistically pleasing in a home audio system. Loudspeaker designers can use wave interaction to their advantage by choosing loudspeaker spacings that form useful radiation patterns. Almost all pattern control in the low frequency decade is achieved in this manner. Uninformed system designers create undesirable radiation patterns by accident in the way that they place and stack loudspeakers. The results are poor coverage and reduced acoustic gain. The proper way to view the loudspeaker and room are as filters that the sound energy must pass through en route to the listener. Some aspects of these filters can be

compensated with electronic filters—a process known as equalization. Other aspects cannot, and electronic equalization merely aggravates or masks the problem.

2.8 Ohm’s Law In acoustics, the sound that we hear is nature restoring an equilibrium condition after an atmospheric disturbance. The disturbance produces waves that cause the atmospheric pressure to oscillate above and below ambient pressure as they propagate past a point of observation. The air always settles to its ambient state upon cessation of the disturbance. In an electrical circuit, a potential difference in electrical pressure between two points causes current to flow. Electrical current results from electrons flowing to a point of lower potential. The electrical potential difference is called an electromotive force (EMF) and the unit is the volt (V). The rate of electron flow is called current and the unit is the ampere (A). The ratio between voltage and current is called the resistance and the unit is the ohm (:). The product of voltage and current is the apparent power, W, that is produced by the source and consumed by the load. Power is the rate of doing work and power ratings must always include a reference to time. A power source can produce a rated voltage at a rated flow of current into a specified load for a specified period of time. The ratio of voltage to current can be manipulated to optimize a source for a specific task. For instance, current flow can be sacrificed to maximize voltage transfer. When a device is called upon to deliver appreciable current, it is said to be operating under load. The load on an automobile increases when it must maintain speed on an uphill grade, and greater power transfer between the engine and drive train is required. Care must be taken when loading audio components to prevent distortion or even damage. Ohm’s Law describes the ratios that exist between voltage, current, and resistance in an electrical circuit. R = E --I

(2-9)

E = IR

(2-10)

I = E --R where, E is in volts, I is in amperes, R is in ohms.

(2-11)

Fundamentals of Audio and Acoustics Direct current (dc) flows in one direction only. In ac (alternating current) the direction of current flow is alternating at the frequency of the waveform. Voltage and current are not always in sync so the phase relationship between them must be considered. Power flow is reduced when they are not in relative phase (synchronization). Voltage and current are in phase in resistive circuits. Phase shifts between voltage and current are produced by reactive elements in a circuit. Reactance reduces the power transferred to the load by storing energy and reflecting it back to the source. Loudspeakers and transformers are examples of sound system components that can have significant reactive characteristics. The combined opposition to current flow caused by resistance and reactance is termed the impedance (Z) of the circuit. The unit for impedance is also the ohm (: . An impedance can be purely resistive, purely reactive, or most often some combination of the two. This is referred to as a complex impedance. Impedance is a function of frequency, and impedance measurements must state the frequency at which the measurement was made. Sound system technicians should be able to measure impedance to verify proper component loading, such as at the amplifier/loudspeaker interface. 2

R + XT

In mechanics, a moving mass is analogous to an inductive reactance in an electrical circuit. The mass tends to keep moving when the driving force is removed. It has therefore stored some of the applied energy. In electrical circuits, an inductor opposes a change in the current flowing through it. As with capacitors, this property can be used to create useful filters in audio systems. Parasitic inductances can occur due to the ways that wires are constructed and routed. (2-14)

X L = 2SfL where, XL is the inductive reactance in ohms.

Inductive and capacitive reactance produce the opposite effect, so one can be used to compensate for the other. The total reactance XT is the sum of the inductive and capacitive reactance. (2-15)

XT = XL – XC (2-12)

where, Z is the impedance in ohms, R is the resistance in ohms, XT is the total reactance in ohms. Reactance comes is two forms. Capacitive reactance causes the voltage to lag the current in phase. Inductive reactance causes the current to lag the voltage in phase. The total reactance is the sum of the inductive and capacitive reactance. Since they are different in sign one can cancel the other, and the resultant phase angle between voltage and current will be determined by the dominant reactance. In mechanics, a spring is a good analogy for capacitive reactance. It stores energy when it is compressed and returns it to the source. In an electrical circuit, a capacitor opposes changes in the applied voltage. Capacitors are often used as filters for passing or rejecting certain frequencies or smoothing ripples in power supply voltages. Parasitic capacitances can occur when conductors are placed in close proximity. 1 X C = -----------2SfC

where, f is frequency in hertz, C is capacitance in farads, XC is the capacitive reactance in ohms.

(2-13)

Note that the equations for capacitive and inductive reactance both include a frequency term. Impedance is therefore frequency dependent, meaning that it changes with frequency. Loudspeaker manufacturers often publish impedance plots of their loudspeakers. The impedance of interest from this plot is usually the nominal or rated impedance. Several standards exist for determining the rated impedance from the impedance plot, Fig. 2-16. 20

Zmin

Impedance

Z =

0 20

200

20K

Frequency

Figure 2-16. An impedance magnitude plot displays impedance as a function of the applied frequency. Courtesy Syn-Aud-Con.

Chapter 2

An impedance phase plot often accompanies an impedance magnitude plot to show whether the loudspeaker load is resistive, capacitive, or inductive at a given frequency. A resistive load will convert the applied power into heat. A reactive load will store and reflect the applied power. Complex loads, such as loudspeakers, do both. When considering the power delivered to the loudspeaker, the impedance Z is used in the power equation. When considering the power dissipated by the load, the resistive portion of the impedance must be used in the power equation. The power factor describes the reduction in power transfer caused by the phase angle between voltage and current in a reactive load. Some definitions are useful. 2

-----Apparent Power Total Power = E Z

(2-16) 2

-----Active Power Absorbed Power = E R

(2-17) 2

E Reactive Power Reflected Power = -------------(2-18) Z cos T where, T is the phase angle between the voltage and current. Ohm’s Law and the power equation in its various forms are foundation stones of the audio field. One can use these important tools for a lifetime and not exhaust their application to the electrical and acoustical aspects of the sound reinforcement system.

2.9 Human Hearing It is beneficial for sound practitioners to have a basic understanding of the way that people hear and perceive sound. The human auditory system is an amazing device, and it is quite complex. Its job is to transduce fluctuations in the ambient atmospheric pressure into electrical signals that will be processed by the brain and perceived as sound by the listener. We will look at a few characteristics of the human auditory system that are of significance to audio practitioners. The dynamic range of a system describes the difference between the highest level that can pass through the system and its noise floor. The threshold of human hearing is about 0.00002 Pascals (Pa) at mid frequencies. The human auditory system can withstand peaks of up to 200 Pa at these same frequencies. This makes the dynamic range of the human auditory system approximately

200 DR = 20 log ------------------0.00002

(2-19)

= 140 dB The hearing system can not take much exposure at this level before damage occurs. Speech systems are often designed for 80 dB ref. 20 μPa and music systems about 90 dB ref. 20 μPa for the mid-range part of the spectrum. Audio practitioners give much attention to achieving a flat spectral response. The human auditory system is not flat and its response varies with level. At low levels, its sensitivity to low frequencies is much less than its sensitivity to mid-frequencies. As level increases, the difference between low- and mid-frequency sensitivity is less, producing a more uniform spectral response. The classic equal loudness contours, Fig. 2-17, describe this phenomenon and have given us the weighting curves, Fig. 2-18, used to measure sound levels. Modern sound systems are capable of producing very high sound pressure levels over large distances. Great care must be taken to avoid damaging the hearing of the audience. The time response of the hearing system is slow compared to the number of audible events that can occur in a given time span. As such, our hearing system integrates closely spaced sound arrivals (within about 35 ms) with regard to level. This is what makes sound indoors appear louder than sound outdoors. While reflected sound increases the perceived level of a sound source, it also adds colorations. This is the heart of how we perceive acoustic instruments and auditoriums. A good recording studio or concert hall produces a musically pleasing reflected sound field to a listener position. In general, secondary energy arrivals pose problems if they arrive earlier than 10 ms (severe tonal coloration) after the first arrival or later than 50 ms (potential echo), Fig. 2-19. The integration properties of the hearing system make it less sensitive to impulsive sound events with regard to level. Peaks in audio program material are often 20 dB or more higher in level than the perceived loudness of the signal. Program material that measures 90 dBA (slow response) may contain short term events at 110 dBA or more, so care must be taken when exposing musicians and audiences to high powered sound systems. The eardrum is a pressure sensitive diaphragm that responds to fluctuations in the ambient atmospheric pressure. Like a loudspeaker and microphone, it has an overload point at which it distorts and can be damaged.

Fundamentals of Audio and Acoustics

130 120

120

Loudness level (Phon)

110

Sound Pressure Level—dB ref. 20 MPa

100

10 MAF

10 20

100

200

500

10K

Frequency—Hz

Figure 2-17. The equal-loudness contours. Illustration courtesy Syn-Aud-Con.

Audible Effects of Delayed Signals of Equal Level

Relative response—dB

C B

50 20

50 100 200 500 1k 2k Frequency—Hz

5k 10k

Figure 2-18. Weighting scales for measuring sound levels. Illustration courtesy Syn-Aud-Con.

The Occupational Safety and Health Administration (OSHA) is responsible for assuring that public spaces remain in compliance regarding sound exposure. Sound systems are a major source of high level sounds and should work within OSHA guidelines. Tinnitus, or ringing in the ears, is one symptom of excessive sound exposure.

Figure 2-19. The time offset between sound arrivals will determine if the secondary arrival is useful or harmful in conveying information to the listener. The direction of arrival is also important and is considered by acousticians when designing auditoriums. Courtesy Syn-Aud-Con.

2.10 Monitoring Audio Program Material The complex nature of the audio waveform necessitates specialized instrumentation for visual monitoring. Typical voltmeters are not suitable for anything but the simplest waveforms, such as sine waves. There are two aspects of the audio signal that are of interest to the system operator. The peaks of the program material

Chapter 2

must not exceed the peak output capability of any component in the system. Ironically the peaks have little to do with the perceived loudness of the signal or the electrical or acoustic power generated by it. Both of these parameters are more closely tied to the rms (root-mean-square) value of the signal. Measurement of the true rms value of a waveform requires specialized equipment that integrates energy over a time span, much like the hearing system does. This integrated data will better correlate with the perceived loudness of the sound event. So audio practitioners need to monitor at least two aspects of the audio signal—its relative loudness (related to the rms level) and peak levels. Due to the complexity of true rms monitoring, most meters display an average value that is an approximation of the rms value of the program material. Many audio processors have instrumentation to monitor either peak or average levels, but few can track both simultaneously. Most mixers have a VI (volume indicator) meter that reads in VU (volume units). Such meters are designed with ballistic properties that emulate the human hearing system and are useful for tracking the perceived loudness of the signal. Meters of this type all but ignore the peaks in the program material, making them unable to display the available headroom in the system or clipping in a component. Signal processors usually have a peak LED that responds fast enough to indicate peaks that are at or near the component’s clipping point. Many recording systems have PPM (peak program meters) that track the peaks but reveal little about the relative loudness of the waveform. Fig. 2-20 shows an instrument that monitors both peak and relative loudness of the audio program material. Both values are displayed in relative dB, and the difference between them is the approximate crest factor of the program material. Meters of this type yield a more complete picture of the audio event, allowing both loudness and available headroom to be observed simultaneously.

Average

Peak

Figure 2-20. A meter that can display both average and peak levels simultaneously. Courtesy Dorrough Electronics.

2.11 Sound Propagation Sound waves are emitted from acoustic sources— devices that move to modulate the ambient atmospheric pressure. Loudspeakers become intentional acoustic sources when they are driven with waveforms that cause them to vibrate at frequencies within the bandwidth of the human listener. A point source is a device that radiates sound from one point in space. A true point source is an abstract idea and is not physically realizable, as it would be of infinitesimal size. This does not prevent the use of the concept to describe the characteristics of devices that are physically realizable. Let us consider the properties of some idealized acoustic sources—not ideal in that they would be desirable for sound reinforcement use, but ideal in respect to their behavior as predictable radiators of acoustic energy. 2.11.1 The Point Source A point source with 100% efficiency would produce 1 watt of acoustical power from one watt of applied electrical power. No heat would result, since all of the electrical power is converted. The energy radiated from the source would travel equally in all directions from the source. Directional energy radiation is accomplished by interfering with the emerging wave. Since interference would require a finite size, a true infinitesimal point source would be omnidirectional. We will introduce the effects of interference later. Using 1 pW (picowatt) as a power reference, the sound power level produced by 1 acoustic watt will be 1W L W = 10 log -----------------– 12 10 W

(2-20)

= 120 dB Note that the sound power is not dependent on the distance from the source. A sound power level of LW = 120 dB would represent the highest continuous sound power level that could result from 1 W of continuous electrical power. All real-world devices will fall short of this ideal, requiring that they be rated for efficiency and power dissipation. Let us now select an observation point at a distance 0.282 m from the sound source. As the sound energy propagates, it forms a spherical wave front. At 0.282 m this wave front will have a surface area of one square meter. As such, the one watt of radiated sound power is passing through a surface area of 1 m2.

Fundamentals of Audio and Acoustics 2

1W/m L I = 10 log ---------------------------– 12 2 10 W/m

(2-21)

= 120 dB This is the sound intensity level LI of the source and represents the amount of power flowing through the surface of a sphere of 1 square meter. Again, this is the highest intensity level that could be achieved by an omnidirectional device of 100% efficiency. LI can be manipulated by confining the radiated energy to a smaller area. The level benefit gained at a point of observation by doing such is called the directivity index (DI) and is expressed in decibels. All loudspeakers suitable for sound reinforcement should exploit the benefits of directivity control. For the ideal device described, the sound pressure level LP (or commonly SPL) at the surface of the sphere will be numerically the same as the L W an d L I (L P = 120 dB) since the sound pressure produced by 1 W will be 20 Pa. This LP is only for one point on the sphere, but since the source is omnidirectional, all points on the sphere will be the same. To summarize, at a distance of 0.282 m from a point source, the sound power level, sound intensity level, and sound pressure level will be numerically the same. This important relationship is useful for converting between these quantities, Fig. 2-21.

Source

1 m2

dB 1W W 1 W m2 W m2 20 Pa 0.00002 Pa

This behavior is known as the inverse-square law (ISL), Fig. 2-22. The ISL describes the level attenuation versus distance for a point source radiator due to the spherical spreading of the emerging waves. Frequency dependent losses will be incurred from atmospheric absorption, but those will not be considered here. Most loudspeakers will roughly follow the inverse square law level change with distance at points remote from the source, Fig. 2-23.

4 m2

source

1 m2

0.282 m

10log

0.282 m

4 6 dB 1

Figure 2-22. When the distance to the source is doubled, the radiated sound energy will be spread over twice the area. Both LI and LP will drop by 6 dB. Courtesy Syn-Aud-Con.

dB dB dB

Figure 2-21. This condition forms the basis of the standard terminology and relationships used to describe sound radiation from loudspeakers. Courtesy Syn-Aud-Con.

Let us now consider a point of observation that is twice as far from the source. As the wave continues to spread, its total area at a radius of 0.564 m will be four times the area at 0.282 m. When the sound travels twice as far, it spreads to cover four times the area. In decibels, the sound level change from point one to point two is 0.564 'L p = 20 log ------------0.282 = 6 dB

Figure 2-23. The ISL is also true for directional devices in their far field (remote locations from the device). Courtesy Syn-Aud-Con.

2.11.2 The Line Source Successful sound radiators have been constructed that radiate sound from a line rather than a point. The infinite line source emits a wave that is approximately cylindrical in shape. Since the diverging wave is not

Chapter 2

expanding in two dimensions, the level change with increasing distance is half that of the point source radiator. The sound level from an ideal line source will decrease at 3 dB per distance doubling rather than 6 dB, Fig. 2-24. It should be pointed out that these relationships are both frequency and line length dependent, and what is being described here is the ideal case. Few commercially available line arrays exhibit this cylindrical behavior over their full bandwidth. Even so, it is useful to allow a mental image of the characteristics of such a device to be formed.

processing has produced well-behaved line arrays that can project sound to great distances. Some incorporate an adjustable delay for each element to allow steering of the radiation lobe. Useful designs for auditoriums are at least 2 meters in vertical length. While it is possible to construct a continuous line source using ribbon drivers, etc., most commercially available designs are made up of closely spaced discrete loudspeakers or loudspeaker systems and are more properly referred to as line arrays, Fig. 2-25.

End of array

10log

2A Pressure maximum due to phase summation

3 dB

10log A = 3 dB 2A

2Dx

Pressure minimum due to phase summation

End of array

2Dx Dx

Figure 2-25. The finite line array has gained wide acceptance among system designers, allowing wide audience coverage with minimal energy radiation to room surfaces. Courtesy Syn-Aud-Con.

2.12 Conclusion Figure 2-24. Line sources radiate a cylindrical wave (ideal case). The level drop versus distance is less than for a point source. Courtesy Syn-Aud-Con.

If the line source is finite in length (as all real-world sources will be), then there will be a phase differential between the sound radiated from different points on the source to a specific point in space. All of the points will be the most in phase on a plane perpendicular from the array and equidistant from the end points of the array. As the point of observation moves away from the midpoint, phase interaction will produce lobes in the radiated energy pattern. The lobes can be suppressed by clever design, allowing the wave front to be confined to a very narrow vertical angle, yet with wide horizontal coverage. Such a radiation pattern is ideal for some applications, such as a broad, flat audience plane that must be covered from ear height. Digital signal

The material in this chapter was carefully selected to expose the reader to a broad spectrum of principles regarding sound reinforcement systems. As a colleague once put it, “Sound theory is like an onion. Every time you peel off a layer another lies beneath it!” Each of these topics can be taken to higher levels, and many have been by other authors within this textbook. The reader is encouraged to use this information as a springboard into a life-long study of audio and acoustics. We are called upon to spend much of our time learning about new technologies. It must be remembered that new methods come from the mature body of principles and practices that have been handed down by those who came before us. Looking backward can have some huge rewards. If I can see farther than those who came before me, it is because I am standing on their shoulders. Sir Isaac Newton

Fundamentals of Audio and Acoustics Bibliography D. Davis and C. Davis, Sound System Engineering, Boston: Focal Press, 1997. Glen Ballou, Handbook for Sound Engineers, 2nd Edition, Boston: Focal Press, 1991. F. Alton Everest, Master Handbook of Acoustics, 3rd Edition, TAB Books, 1998. Leo Baranek, Acoustics, New York: McGraw-Hill, 1954. Harry Olson, Acoustical Engineering, Professional Audio Journals, Inc., Philadelphia, PA.

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Chapter

by Peter Xinya Zhang 3.1 Psychoacoustics and Subjective Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Ear Anatomy and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Pinna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Temporal Bones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Ear Canal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Middle Ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4.1 Acoustic Reflex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Inner Ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Frequency Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Frequency Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Masking and Its Application in Audio Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Auditory Filters and Critical Bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Nonlinearity of the Ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Perception of Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Auditory Area and Thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Hearing Over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Loudness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Equal Loudness Contours and Loudness Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.2 Level Measurements with A-, B-, and C-Weightings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.3 Loudness in Sones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.4 Loudness versus Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.5 Loudness of Impulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.6 Perception of Dynamic Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.1 The Unit of Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.2 Perception of Pure and Complex Tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.3 Phase-Locking and the Range of Pitch Sensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.4 Frequency Difference Limen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.5 Dependence of Pitch on Level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.6 Perfect Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.7 Other Pitch Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Timbre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Binaural and Spatial Hearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.1 Localization Cues for Left and Right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.2 Localization on Sagittal Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.3 Externalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.4 Precedence (Hass) Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.5 Franssen Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.6 Cocktail Party Effect and Improvement of Signal Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.7 Distance Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Psychoacoustics 3.1 Psychoacoustics and Subjective Quantities Unlike other senses, it is surprising how limited our vocabulary is when talking about hearing.1 Especially in the audio industry, we do not often discriminate between subjective and objective quantities. For instance, the quantities of frequency, level, spectrum, etc. are all objective, in a sense that they can be measured with a meter or an electronic device; whereas the concepts of pitch, loudness, timbre, etc. are subjective, and they are auditory perceptions in our heads. Psychoacoustics investigates these subjective quantities (i.e., our perception of hearing), and their relationship with the objective quantities in acoustics. Psychoacoustics got its name from a field within psychology—i.e., recognition science—which deals with all kinds of human perceptions, and it is an interdisciplinary field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology, computer science, etc. Although there are clear and strong relationships between certain subjective and objective quantities—e.g., pitch versus frequency—other objective quantities also have influences. For example, changes in sound level can affect pitch perception. Furthermore, because no two persons are identical, when dealing with perceptions as in psychoacoustics, there are large individual differences, which can be critical in areas such as sound localization. 2 In psychoacoustics, researchers have to consider both average performances among population and individual variations. Therefore, psychophysical experiments and statistical methods are widely used in this field. Compared with other fields in acoustics, psychoacoustics is relatively new, and has been developing greatly. Although many of the effects have been known for some time (e.g., Hass effect3), new discoveries have been found continuously. To account for these effects, models have been proposed. New experimental findings might invalidate or modify old models or make certain models more or less popular. This process is just one representation of how we develop our knowledge. For the purpose of this handbook, we will focus on summarizing the known psychoacoustic effects rather than discussing the developing models.

3.2 Ear Anatomy and Function Before discussing various psychoacoustic effects, it is necessary to introduce the physiological bases of those effects, namely the structure and function of our auditory system. The human ear is commonly consid-

ered in three parts: the outer ear, the middle ear, and the inner ear. The sound is gathered (and as we shall see later, modified) by the external ear called the pinna and directed down the ear canal (auditory meatus). This canal is terminated by the tympanic membrane (eardrum). These parts constitute the outer ear, as shown in Figs. 3-1 and 3-2. The other side of the eardrum faces the middle ear. The middle ear is air filled, and pressure equalization takes place through the eustachian tube opening into the pharynx so normal atmospheric pressure is maintained on both sides of the eardrum. Fastened to the eardrum is one of the three ossicles, the malleus which, in turn, is connected to the incus and stapes. Through the rocking action of these three tiny bones the vibrations of the eardrum are transmitted to the oval window of the cochlea with admirable efficiency. The sound pressure in the liquid of the cochlea is increased some 30–40 dB over the air pressure acting on the eardrum through the mechanical action of this remarkable middle ear system. The clear liquid filling the cochlea is incompressible, like water. The round window is a relatively flexible pressure release allowing sound energy to be transmitted to the fluid of the cochlea via the oval window. In the inner ear the traveling waves set up on the basilar membrane by vibrations of the oval window stimulate hair cells that send nerve impulses to the brain. Pinna

Ossicles

Cochlea

Auditory nerve Eustachian tube

Eardrum

Oval Round window window

Figure 3-1. A cross-section of the human ear showing the relationship of the various parts.

3.2.1 Pinna The pinna, or the human auricle, is the most lateral (i.e., outside) portion of our auditory system. The beauty of these flaps on either side of our head may be questioned, but not the importance of the acoustical function they serve. Fig. 3-3 shows an illustration of various parts of the human pinna. The entrance to the ear canal, or concha, is most important acoustically for filtering because it contains the largest air volume in a pinna. Let

Chapter 3

Ossicles

Cochlea

Basilar membrane

Helix Fossa Scapha

Ear drum Ear canal Oval window

Eustachian tube

Round window Outer ear

Middle ear

Concha

Inner ear

Figure 3-2. Highly idealized portrayal of the outer ear, middle ear, and inner ear.

Lobule

Figure 3-3. The human outer ear, the pinna, with identification of some of the folds, cavities, and ridges that have significant acoustical effect.

Acoustic gain components–dB

us assume for the moment that we have no pinnae, just holes in the head, which is actually a simplest model for human hearing, called the spherical head model. Cupping our hands around the holes would make sounds louder as more sound energy is directed into the opening. How much does the pinna help in directing sound energy into the ear canal? We can get some idea of this by measuring the sound pressure at the opening of the ear canal with and without the hand behind the ear. Wiener and Ross4 did this and found a gain of 3 to 5 dB at most frequencies, but a peak of about 20 dB in the vicinity of 1500 Hz. Fig. 3-4 shows the transfer function measured by Shaw,5 and the curves numbered 3 and 4 are for concha and pinna flange, respectively. The irregular and asymmetric shape of a pinna is not just for aesthetic reasons. In Section 3.11, we will see that it is actually important for our ability to localize sounds and to aid in spatial-filtering of unwanted conversations.

Intertragic notch

20 15 10

On each of the left and right sides of our skull, behind the pinna, there is a thin, fanlike bone—namely, the temporal bone—covering the entire human ear, except for the pinna. This bone can be further divided into four portions—i.e., the squamous, mastoid, tympanic and petrous portions. The obvious function for the temporal bone is to protect our auditory system. Other than cochlear implant patients, whose temporal bone has to be partly removed during a surgery, people might not pay much attention to it, especially regarding acoustics. However the sound energy that propagates through the bone into our inner ear, as opposed to through the ear canal and middle ear, is actually fairly significant. For

Total: 45o Spherical head Torso and neck, etc. Concha Pinna flange Ear canal and eardrum

5 3 1

5 4

0 2

10 0.2

3.2.2 Temporal Bones

T 1 2 3 4 5

0.5

1.0 2 Frequency–Hz

Figure 3-4. The average pressure gain contributed by the different components of the outer ear in humans. The sound source is in the horizontal plane, 45q from straight ahead. (After Shaw, Reference 5.)

patients with conductive hearing loss—e.g., damage of middle ear—there are currently commercially available devices, which look something like headphones and are placed on the temporal bone. People with normal hearing can test it by plugging their ears while wearing the device. Although the timbres sound quite different from normal hearing, the filtered speech is clear enough to understand. Also because of this bone conduction, along with other effects such as acoustic reflex, which will be discussed in Section 3.2.4.1, one hears his or her own

Psychoacoustics voice differently from how other people hear the voice. While not receiving much attention in everyday life, it might be sometimes very important. For example, an experienced voice teacher often asks a student singer to record his or her own singing and playback with an audio system. The recording will sound unnatural to the singer but will be a more accurate representation of what the audience hears. 3.2.3 Ear Canal The ear canal has a diameter about 5 to 9 mm and is about 2.5 cm long. It is open to the outside environment at the concha, and is closed at the tympanic membrane. Acoustically, it can be considered as a closed pipe whose cross-sectional shape and area vary along its length. Although being bended and irregular in shape, the ear canal does demonstrate the modal characteristic of a closed pipe. It has a fundamental frequency of about 3 kHz, corresponding to a quarter wavelength close to the length of the ear canal. Because of this resonant frequency, our hearing is most sensitive to a frequency band around 3 kHz, which is, not just by coincidence, the most important frequency band of human speech. On Fig. 3-4, the number 5 curve shows the effect of the ear canal, taking the eardrum into account as well. As can be seen, there is an approximately 11 dB of gain at around 2.5 kHz. After combining all the effects of head, torso and neck, pinna, ear canal and eardrum, the total transfer function is the curve marked with a letter T on Fig. 3-4. It is relatively broadly tuned between 2 and 7 kHz, with as much as 20 dB of gain. Unfortunately, because of this resonance, in very loud noisy environments with broadband sound, hearing damage usually first happens around 4 kHz. 3.2.4 Middle Ear The outer ear, including the pinna and the ear canal, ends at the eardrum. It is an air environment with low impedance. On the other hand, the inner ear, where the sensory cells are, is a fluid environment with high impedance. When sound (or any wave) travels from one medium to another, if the impedances of the two media do not match, much of the energy would be reflected at the surface, without propagating into the second medium. For the same reason, we use microphones to record in the air and hydrophones to record under water. To make our auditory system efficient, the most important function of the middle ear is to match the impedances of outer and inner ears. Without the middle ear,

we would suffer a hearing loss of about 30 dB (by mechanical analysis6 and experiments on cats7). A healthy middle ear (without middle ear infection) is an air-filled space. When swallowing, the eustachian tube is open to balance the air pressure inside the middle ear and that of the outside world. Most of the time, however, the middle ear is sealed from the outside environment. The main components of the middle ear are the three ossicles, which are the smallest bones in our body: the malleus, incus, and stapes. These ossicles form an ossiclar chain, which is firmly fixed on the eardrum and the oval window on each side. Through mostly three types of mechanical motions—namely piston motion, lever motion and buckling motion8—the acoustic energy is transferred into the inner ear effectively. The middle ear can be damaged temporarily by middle ear infection, or permanently by genetic disease. Fortunately, with current technology, doctors can rebuild the ossicles with titanium, the result being a total recovering of hearing.9 Alternatively one can use devices that rely on bone conduction.10 3.2.4.1 Acoustic Reflex There are two muscles in the middle ear: the tensor tympani that is attached to the malleus, and the stapedius muscle that is attached to the stapes. Unlike other muscles in our bodies, these muscles form an angle with respect to the bone, instead of along the bone, which makes them very ineffective for motion. Actually the function of these muscles is for changing the stiffness of the ossicular chain. When we hear a very loud sound—i.e., at least 75 dB higher than the hearing threshold—when we talk or sing, when the head is touched, or when the body moves,11 these middle ear muscles will contract to increase the stiffness of the ossicular chain, which makes it less effective, so that our inner ear is protected from exposure to the loud sound. However, because this process involves a higher stage of signal processing, and because of the filtering features, this protection works only for slow onset and low-frequency sound (up to 1.2 kHz12) and is not effective for noises such as an impulse or noise with high frequencies (e.g., most of the music recordings today). 3.2.5 Inner Ear The inner ear, or the labyrinth, is composed of two systems: the vestibular system, which is critical to our sense of balance, and the auditory system which is used for hearing. The two systems share fluid, which is separated from the air-filled space in the middle ear by

Chapter 3

the oval window and the round window. The auditory portion of the inner ear is the snail-shaped cochlea. It is a mechanical-to-electrical transducer and a frequency-selective analyzer, sending coded nerve impulses to the brain. This is represented crudely in Fig. 3-5. A rough sketch of the cross section of the cochlea is shown in Fig. 3-6. The cochlea, throughout its length (about 35 mm if stretched out straight), is divided by Reissner’s membrane and the basilar membrane into three separate compartments—namely, the scala vestibuli, the scala media, and the scala tympani. The scala vestibuli and the scala tympani share the same fluid, perilymph, through a small hole, the helicotrema, at the apex; while the scala media contains another fluid, endolymph, which contains higher density of potassium ions facilitating the function of the hair cells. The basilar membrane supports the Organ of Corti, which contains the hair cells that convert the relative motion between the basilar membrane and the tectorial membrane into nerve pulses to the auditory nerve.

100 Hz

Obstacles

Brain

1 kHz

80 mm2

4 kHz

10 kHz

Eardrum

Ratio 1.3 to3:1

3 mm2 window

Cochlea

Basilar membrane

Figure 3-5. The mechanical system of the middle ear. Reissner's membrane

Auditory nerve

Scala vestibuli

Tectorial membrane

Scala media

Outer hair cells

Scala tympani

Inner hair cells

Basilar membrane

Figure 3-6. Cross-sectional sketch of the cochlea.

When an incident sound arrives at the inner ear, the vibration of the stapes is transported into the scala

vestibuli through the oval window. Because the cochlear fluid is incompressible, the round window connected to the scala tympani vibrates accordingly. Thus, the vibration starts from the base of the cochlea, travels along the scala vestimbuli, all the way to the apex, and then through the helicotrema into the scala tympani, back to the base, and eventually ends at the round window. This establishes a traveling wave on the basilar membrane for frequency analysis. Each location at the basilar membrane is most sensitive to a particular frequency—i.e., the characteristic frequency—although it also responds to a relatively broad frequency band at smaller amplitude. The basilar membrane is narrower (0.04 mm) and stiffer near the base, and wider (0.5 mm) and looser near the apex. (By contrast, when observed from outside, the cochlea is wider at the base and smaller at the apex.) Therefore, the characteristic frequency decreases gradually and monotonically from the base to the apex, as indicated in Fig. 3-5. The traveling-wave phenomenon illustrated in Figs. 3-7 and 3-8 shows the vibration patterns—i.e., amplitude versus location—for incident pure tones of different frequencies. An interesting point in Fig. 3-8 is that the vibration pattern is asymmetric, with a slow tail close to the base (for high frequencies) and a steep edge close to the apex (for low frequencies). Because of this asymmetry, it is easier for the low frequencies to mask the high frequencies than vice versa. Within the Organ of Corti on the basilar membrane, there are a row of inner hair cells (IHC), and three to five rows of outer hair cells (OHC), depending on location. There are about 1500 IHCs and about 3500 OHCs. Each hair cell contains stereociliae (hairs) that vibrate corresponding to the mechanical vibration in the fluid around them. Because each location on the basilar membrane is most sensitive to its own characteristic frequency, the hair cells at the location also respond most to its characteristic frequency. The IHCs are sensory cells, like microphones, which convert mechanical vibration into electrical signal—i.e., neural firings. The OHCs, on the other hand, change their shapes according to the control signal received from efferent nerves. Their function is to give an extra gain or attenuation, so that the output of the IHC is tuned to the characteristic frequency much more sharply than the IHC itself. Fig. 3-9 shows the tuning curve (output level vs. frequency) for a particular location on the basilar membrane with and without functioning OHCs. The tuning curve is much broader with poor frequency selectivity when the OHCs do not function. The OHCs make our auditory system an active device, instead of a passive microphone. Because the OHCs are active and

Amplitude

Psychoacoustics

25 Hz

Amplitude

1.25 ms

100 Hz

22 24 26 28 30 Distance from oval window—mm

Figure 3-7. A traveling wave on the basilar membrane of the inner ear. (After von Békésy, Reference 13.) The exaggerated amplitude of the basilar membrane for a 200 Hz wave traveling from left to right is shown at A. The same wave 1.25 ms later is shown at B. These traveling 200 Hz waves all fall within the envelope at C.

consume a lot of energy and nutrition, they are usually damaged first due to loud sound or ototoxic medicines (i.e., medicine that is harmful to the auditory system). Not only does this kind of hearing loss make our hearing less sensitive, it also makes our hearing less sharp. Thus, as is easily confirmed with hearing-loss patients, simply adding an extra gain with hearing aids would not totally solve the problem.

3.3 Frequency Selectivity 3.3.1 Frequency Tuning As discussed in Section 3.2.5, the inner hair cells are sharply tuned to the characteristic frequencies with help from the outer hair cells. This tuning character is also conserved by the auditory neurons connecting to the inner hair cells. However, this tuning feature varies with level. Fig. 3-10 shows a characteristic diagram of tuning curves from a particular location on the basilar mem-

10 20 30 Distance from oval window}mm 400 Hz

Amplitude

0 C.

10 20 30 Distance from oval window}mm

10 20 30 Distance from oval window}mm 1600 Hz

10 20 30 Distance from oval window}mm

Figure 3-8. An illustration of vibration patterns of the hair cells on the basilar membrane for various incident pure tones. There is a localized peak response for each audible frequency. (After von Békésy, Reference 13.)

brane at various levels. As can be seen in this graph, as level increases, the tuning curve becomes broader, indicating less frequency selectivity. Thus, in order to hear music more sharply, one should play back at a relatively low level. Moreover, above 60 dB, as level increases, the characteristic frequency decreases. Therefore when one hears a tone at a high level, a neuron that is normally tuned at a higher characteristic frequency is now best tuned to the tone. Because eventually the brain perceives pitch based on neuron input, at high levels, without knowing that the characteristic frequency has decreased, the brain hears the pitch to be sharp. Armed with this knowledge, one would think that someone who was engaged in critical listening—a recording engineer, for example—would choose to listen at moderate to low levels. Why then do so many

Chapter 3 hearing already, and in order to pick up certain frequency bands they keep on boosting the level, which unfortunately further damages their hearing.

100

Treshold—dB SPL

3.3.2 Masking and Its Application in Audio Encoding

0 0.1

1.0 Frequency—kHz

4.0

Basilar Membrane velocity—dB

Figure 3-9. Tuning curve with (solid) and without (dashed) functioning outer hair cells. (Liberman and Dodds, Reference 14.)

20 dB SPL 40 dB SPL 60 dB SPL 80 dB SPL

90 80 70 60 50 40 30 20 10 0 2

8 10 12 Frequency—Hz

30 dB SPL 50 dB SPL 70 dB SPL 90 dB SPL

Figure 3-10. Tuning curve at various levels at a particular location of the basilar membrane of a chinchilla. (Plack, Reference 15, p90, Ruggero et al., Reference 16.)

audio professionals choose to monitor at very high levels? There could be many reasons. Loud levels may be more exciting. It may simply be a matter of habit. For instance, an audio engineer normally turns the volume to his or her customary level fairly accurately. Moreover, because frequency selectivity is different at different levels, an audio engineer might choose to make a recording while listening at a “realistic” or “performance” level rather than monitoring at a level that is demonstratedly more accurate. Finally, of course, there are some audio professionals who have lost some

Suppose a listener can barely hear a given acoustical signal under quiet conditions. When the signal is playing in presence of another sound (called “a masker”), the signal usually has to be stronger so that the listener can hear it.17 The masker does not have to include the frequency components of the original signal for the masking effect to take place, and a masked signal can already be heard when it is still weaker than the masker.18 Masking can happen when a signal and a masker are played simultaneously (simultaneous masking), but it can also happen when a masker starts and ends before a signal is played. This is known as forward masking. Although it is hard to believe, masking can also happen when a masker starts after a signal stops playing! In general, the effect of this backward masking is much weaker than forward masking. Forward masking can happen even when the signal starts more than 100 ms after the masker stops,19 but backward masking disappears when the masker starts 20 ms after the signal.20 The masking effect has been widely used in psychoacoustical research. For example, Fig. 3-10 shows the tuning curve for a chinchilla. For safety reasons, performing such experiments on human subjects is not permitted. However, with masking effect, one can vary the level of a masker, measure the threshold (i.e., the minimum sound that the listener can hear), and create a diagram of a psychophysical tuning curve that reveals similar features. Besides scientific research, masking effects are also widely used in areas such as audio encoding. Now, with distribution of digital recordings, it is desirable to reduce the sizes of audio files. There are lossless encoders, which is an algorithm to encode the audio file into a smaller file that can be completely reconstructed with another algorithm (decoder). However, the file sizes of the lossless encoders are still relatively large. To further reduce the size, some less important information has to be eliminated. For example, one might eliminate high frequencies, which is not too bad for speech communication. However, for music, some important quality might be lost. Fortunately, because of the masking effect, one can eliminate some weak sounds that are masked so that listeners hardly notice the difference. This technique has been widely used in audio encoders, such as MP3.

Psychoacoustics 3.3.3 Auditory Filters and Critical Bands Experiments show that our ability to detect a signal depends on the bandwidth of the signal. Fletcher (1940)18 found that, when playing a tone in the presence of a bandpass masker, as the masker bandwidth was increased while keeping the overall level of the masker unchanged, the threshold increased as bandwidth increased up to a certain limit, beyond which the threshold remained constant. One can easily confirm that, when listening to a bandpass noise with broadening bandwidth and constant overall level, the loudness is unchanged, until a certain bandwidth is reached, and beyond that bandwidth the loudness increases as bandwidth increases, although the reading of an SPL meter is constant. An explanation to account for these effects is the concept of auditory filters. Fletcher proposed that, instead of directly listening to each hair cell, we hear through a set of auditory filters, whose center frequencies can vary or overlap, and whose bandwidth is varying according to the center frequency. These bands are referred to as critical bands (CB). Since then, the shape and bandwidth of the auditory filters have been carefully studied. Because the shape of the auditory filters is not simply rectangular, it is more convenient to use the equivalent rectangular bandwidth (ERB), which is the bandwidth of a rectangular filter that gives the same transmission power as the actual auditory filter. Recent study by Glasberg and Moore (1990) gives a formula for ERB for young listeners with normal hearing under moderate sound pressure levels21: ERB = 24.7 4.37F + 1 where, the center frequency of the filter F is in kHz, ERB is in Hz. Sometimes, it is more convenient to use an ERB number as in Eq. 3-1, 21 similar to the Bark scale proposed by Zwicker et al.22: ERB Number = 21.4 log 4.37F + 1 where, the center frequency of the filter F is in kHz.

filters which are popular in audio and have been widely used in acoustical measurements ultimately have their roots in the study of human auditory response. However, as Fig. 3-11 shows, the ERB is wider than 1 » 3 octave for frequencies below 200 Hz; is smaller than 1 » 3 octave for frequencies above 200 Hz; and, above 1 kHz, it approaches 1 / 6 octave. Table 3-1. Critical Bandwidths of the Human Ear Critical Band No

Center Frequency Hz

Bark Scale (Hz)

Equivalent Rectangular Band (ERB), Hz

100

200

150

100

250

100

350

100

450

110

570

120

700

140

840

150

111

1000

160

130

1170

190

150

1370

210

170

1600

240

200

1850

280

220

2150

320

260

2500

380

300

2900

450

350

3400

550

420

4000

700

500

4800

900

620

5800

1100

780

7000

1300

990

8500

1800

1300

10,500

2500

1700

13,500

3500

2400

(3-1)

Table 3-1 shows the ERB and Bark scale as a function of the center frequency of the auditory filter. The Bark scale is also listed as a percentage of center frequency, which can then be compared to filters commonly used in acoustical measurements: octave (70.7%), half octave (34.8%), one-third octave (23.2%), and one-sixth octave (11.6%) filters. The ERB is shown in Fig. 3-11 as a function of frequency. One-third octave

3.4 Nonlinearity of the Ear When a set of frequencies are input into a linear system, the output will contain only the same set of frequencies, although the relative amplitudes and phases can be adjusted due to filtering. However, for a nonlinear system, the output will include new frequencies that are not present in the input. Because our auditory system has developed mechanisms such as acoustic reflex in the middle ear and the active processes in the inner ear, it is n o n l i n e a r. T h e r e a r e t w o t y p e s o f n o n l i n e a r-

Chapter 3 3.5 Perception of Phase RB

)

1000

ic al Cr it

oc t ta ve

200

100

1 /3

Bandwidth—Hz

av e

ba n

500

1 /6

20 10 100

200

500 1k 2k Center frequency—Hz

10k

Figure 3-11. A plot of critical bandwidths (calculated ERBs) of the human auditory system compared to constant percentage bandwidths of filter sets commonly used in acoustical measurements.

ity—namely, harmonic distortion and combination tones. Harmonic distortion can be easily achieved by simply distorting a sine-tone. The added new components are harmonics of the original signal. A combination tone happens when there are at least two frequencies in the input. The output might include combination tones according to fc = n u f1 r m u f2

(3-2)

The complete description of a given sound includes both an amplitude spectrum and a phase spectrum. People normally pay a lot of attention to the amplitude spectrum, while caring less for the phase spectrum. Yet academic researchers, hi-fi enthusiasts, and audio engineers all have asked, “Is the ear able to detect phase differences?” About the middle of the last century, G. S. Ohm wrote, “Aural perception depends only on the amplitude spectrum of a sound and is independent of the phase angles of the various components contained in the spectrum.” Many apparent confirmations of Ohm’s law of acoustics have later been traced to crude measuring techniques and equipment. Actually, the phase spectrum sometimes can be very important for the perception of timbre. For example, an impulse and white noise sound quite different, but they have identical amplitude spectrum. The only difference occurs in the phase spectrum. Another common example is speech: if one scrambles the relative phases in the spectrum of a speech signal, it will not be intelligible. Now, with experimental evidence, we can confirm that our ear is capable of detecting phase information. For example, the neural firing of the auditory nerve happens at a certain phase, which is called the phase-locking, up to about 5 kHz.24 The phase-locking is important for pitch perception. In the brainstem, the information from left and right ears is integrated, and the interaural phase difference can be detected, which is important for spatial hearing. These phenomena will be discussed in more detail in Sections 3.9 and 3.11.

where, fc is the frequency of a combination tone,

3.6 Auditory Area and Thresholds

f1 and f2 are the two input frequencies, and n and m are any integer numbers.

The auditory area depicted in Fig. 3-12 describes, in a technical sense, the limits of our aural perception. This area is bounded at low sound levels by our threshold of hearing. The softest sounds that can be heard fall on the threshold of hearing curve. Above this line the air molecule movement is sufficient to elicit a response. If, at any given frequency, the sound pressure level is increased sufficiently, a point is reached at which a tickling sensation is felt in the ears. If the level is increased substantially above this threshold of feeling, it becomes painful. These are the lower and upper boundaries of the auditory area. There are also frequency limitations below about 20 Hz and above about 16 kHz, limitations that (like the two thresholds) vary considerably from individual to individual. We are less concerned here about specific numbers than we are about principles. On the auditory area of Fig. 3-12, all the sounds of life are

For example, when two tones at 600 and 700 Hz are input, the output might have frequencies such as 100 Hz (= 700 600 Hz), 500 Hz (= 2 × 600 700 Hz), and 400 Hz (= 3 × 600 2 × 700 Hz), etc. Because the harmonic distortion does not change the perception of pitch, it would not be surprising if we are less tolerant of the combination tones. Furthermore, because the auditory system is active, even in a completely quiet environment, the inner ear might generate tones. These otoacoustic emissions23 are a sign of a healthy and functioning inner ear, and quite different from the tinnitus resulting from exposure to dangerously high sound pressure levels.

Psychoacoustics played out—low frequency or high, very soft or very intense. Speech does not utilize the entire auditory area. Its dynamic range and frequency range are quite limited. Music has both a greater dynamic range than speech and a greater frequency range. But even music does not utilize the entire auditory area. Threshold of feeling

Sound pressure level—dB

120 100 80

Music

60 Speech 40 20 0 20

Threshold of hearing 50 100

500

10k 20k

Frequency—Hz

Figure 3-12. All sounds perceived by humans of average hearing acuity fall within the auditory area. This area is defined by the threshold of hearing and the threshold of feeling (pain) and by the low and high frequency limits of hearing. Music and speech do not utilize the entire auditory area available, but music has the greater dynamic range (vertical) and frequency demands (horizontal).

3.7 Hearing Over Time If our ear was like an ideal Fourier analyzer, in order to translate a waveform into a spectrum, the ear would have to integrate over the entire time domain, which is not practical and, of course, not the case. Actually, our ear only integrates over a limited time window (i.e., a filter on the time axis), and thus we can hear changes of pitch, timbre, and dynamics over time, which can be shown on a spectrogram instead of a simple spectrum. Mathematically, it is a wavelet analysis instead of a Fourier analysis. Experiments on gap detection between tones at different frequencies indicate that our temporal resolution is on the order of 100 ms,25 which is a good estimate of the time window of our auditory system. For many perspectives (e.g., perceptions on loudness, pitch, timbre), our auditory system integrates acoustical information within this time window.

3.8 Loudness Unlike level or intensity, which are physical or objective quantities, loudness is a listener’s subjective perception. As the example in Section 3.3, even if the SPL meter reads the same level, a sound with a wider bandwidth might sound much louder than a sound with a smaller bandwidth. Even for a pure tone, although loudness follows somewhat with level, it is actually a quite complicated function, depending on frequency. A tone at 40 dB SPL is not necessarily twice as loud as another sound at 20 dB SPL. Furthermore, loudness also varies among listeners. For example, a listener who has lost some sensitivity in a certain critical band will perceive any signal in that band to be at a lower level relative to someone with normal hearing. Although there is no meter to directly measure a subjective quantity such as loudness, psycho-physical scaling can be used to investigate loudness across subjects. Subjects can be given matching tasks, where they are asked to adjust the level of signals until they match, or comparative tasks, where they are asked to compare two signals and estimate the scales for loudness. 3.8.1 Equal Loudness Contours and Loudness Level By conducting experiments using pure tones with a large population, Fletcher and Munson at Bell Labs (1933) derived equal loudness contours, also known as the Fletcher-Munson curves. Fig. 3-13 shows the equal loudness contours later refined by Robinson and Dadson, which have been recognized as an international standard. On the figure, the points on each curve correspond to pure tones, giving the same loudness to an average listener. For example, a pure tone at 50 Hz at 60 dB SPL is on the same curve as a tone at 1 kHz at 30 dB. This means that these two tones have identical loudness to an average listener. Obviously, the level for the 50 Hz tone is 30 dB higher than the level of the 60 Hz tone, which means that we are much less sensitive to the 50 Hz tone. Based on the equal loudness contours, loudness level, in phons, is introduced. It is always referenced to a pure tone at 1 kHz. The loudness level of a pure tone (at any frequency) is defined as the level of a 1 kHz tone that has identical loudness to the given tone for an average listener. For the above example, the loudness of the 50 Hz pure tone is 30 phons, which means it is as loud as a 30 dB pure tone at 1 kHz. The lowest curve marked with “minimum audible” is the hearing threshold. Although many normal listeners can hear tones weaker than this threshold at some fre-

Chapter 3

quencies, on average, it is a good estimate of a minimum audible limit. The tones louder than the curve of 120 phons will cause pain and hearing damage. Loudness level–phons 120 Sound pressure level–dB

100 80 60 40 20 Minimum audible

0 50

100

300 500 1k Frequency–Hz

3k 5k 10k 20k

Figure 3-13. Equal loudness contours for pure tones in a frontal sound field for humans of average hearing acuity determined by Robinson and Dadson. The loudness levels in phons correspond to the sound pressure levels at 1000 Hz. (ISO Recommendation 226).

The equal loudness contours also show that human hearing is most sensitive around 4 kHz (which is where the hearing damage due to loud soundsfirst happens), less sensitive to high frequencies, and much less sensitive for very low frequencies (which is why a subwoofer has to be very powerful to produce strong bass, the price of which is the masking of mid-and high-frequencies and potential hearing damage). A study of this family of curves tells us why treble and bass frequencies seem to be missing or down in level when favorite recordings are played back at low levels.26 One might notice that for high frequencies above 10 kHz, the curves are nonmonotonic for low levels. This is due to the second resonant mode of the ear canal. Moreover, at low frequencies below 100 Hz, the curves are close to each other, and the change of a few dB can give you the feeling of more than 10 dB of dynamic change at 1 kHz. Furthermore, the curves are much flatter at high levels, which unfortunately encouraged many to listen to reproduced music at abnormally high levels, again causing hearing damage. Actually, even if one wanted to have flat or linear hearing, listening at abnormally high levels might not be wise, because the frequency selectivity of our auditory system will be much poorer, leading to much greater interaction

between various frequencies. Of course, one limitation of listening at a lower level is that, if some frequency components fall below the hearing threshold, then they are not audible. This problem is especially important for people who have already lost some acuity at a certain frequency, where his or her hearing threshold is much higher than normal. However, in order to avoid further damage of hearing, and in order to avoid unnecessary masking effect, one still might consider listening at moderate levels. The loudness level considers the frequency response of our auditory system, and therefore is a better scale than the sound pressure level to account for loudness. However, just like the sound pressure level is not a scale for loudness, the loudness level does not directly represent loudness, either. It simply references the sound pressure level of pure tones at other frequencies to that of a 1 kHz pure tone. Moreover, the equal loudness contours were achieved with pure tones only, without consideration of the interaction between frequency components—e.g., the compression within each auditory filter. One should be aware of this limit when dealing with broadband signals, such as music. 3.8.2 Level Measurements with A-, B-, and C-Weightings Although psychoacoustical experiments give better results on loudness, practically, level measurement is more convenient. Because the equal loudness contours are flatter at high levels, in order to make level measurements somewhat representing our loudness perception, it is necessary to weight frequencies differently for measurements at different levels. Fig. 3-14 shows the three widely used weighting functions. 27 The A-weighting level is similar to our hearing at 40 dB, and is used at low levels; the B-weighting level represents our hearing at about 70 dB; and the C-weighting level is more flat, representing our hearing at 100 dB, and thus is used at high levels. For concerns on hearing loss, the A-weighting level is a good indicator, although hearing loss often happens at high levels. 3.8.3 Loudness in Sones Our hearing for loudness is definitely a compressed function (less sensitive for higher levels), giving us both sensitivity for weak sounds and large dynamic range for loud sounds. However, unlike the logarithmic scale (dB) that is widely used in sound pressure level, experimental evidence shows that loudness is actually a power law function of intensity and pressure as shown in Eq. 3-3.

Gain—dB

Loudness—sones

Psychoacoustics

A-weighting B-weighting C-weighting

Level—dB SPL Frequency—Hz

Figure 3-14. Levels with A-, B-, and C-weightings. (Reference 27.)

Loudness = k u I

3.8.4 Loudness versus Bandwidth

= kc u p

Figure 3-15. Comparison between loudness in sones and loudness level in phons for a 1 kHz tone. (Plack, Reference 15, p118, data from Hellman, Reference 28.)

(3-3)

where, k and kc are constants accounting for individuality of listeners, I is the sound intensity, p is the sound pressure, D varies with level and frequency. The unit for loudness is sones. By definition, one sone is the loudness of a 1 kHz tone at a loudness level of 40 phons, the only point where phons and SPL meet. If another sound sounds twice as loud as the 1 kHz tone at 40 phons, it is classified as 2 sones, etc. The loudness of pure tones in sones is compared with the SPL in dB in Fig. 3-15. The figure shows that above 40 dB, the curve is a straight line, corresponding to an exponent of about 0.3 for sound intensity and an exponent of 0.6 for sound pressure as in Eq. 3-3. The exponent is much greater for levels below 40 dB, and for frequencies below 200 Hz (which can be confirmed by the fact that the equal loudness contours are compact for frequencies below 200 Hz on Fig. 3-13). One should note that Eq. 3-3 holds for not only pure tones, but also bandpass signals within an auditory filter (critical band). The exponent of 0.3 (11% >20% (limit value 15%)

Long reverberation times entail an increased articulation loss. With the corresponding duration, this reverberation acts like noise on the following signals and thus reduces the intelligibility. Fig. 7-10 shows the articulation loss, Alcons, as a function of the SNR and the reverberation time RT60 . The top diagram allows us to ascertain the influence of the difference LR (diffuse sound level) – LN (noise level) and of the reverberation time RT60 on the Alcons value, which gives ALconsR/N. Depending on how large the SNR (L D LRN) is, this value is then corrected in the bottom diagram in order to obtain Alcons D/R/N . The noise and the signal level have to be entered as dBA values. The illustration shows also that with an increase of the SNR to more than 25 dB, it is practically no longer possible to achieve an improved intelligibility. (In praxis, this value is often even considerably lower, since with high volumes, for example above 90 dB, and due to the heavy impedance changes in the middle ear that set on here as well as through the strong bass emphasis that occurs owing to the frequency-dependent ear sensitivity.) 7.2.2.9 Subjective Intelligibility Tests A subjective evaluation method for speech intelligibility consists in the recognizability of clearly spoken pronounced words (so-called test words) chosen on the

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157

Table 7-3. Examples of English Words Used in Intelligibility Tests aisle

done

jam

ram

tame

barb

dub

law

ring

toil

barge

feed

lawn

rip

ton

bark

feet

lisle

rub

trill tub

baste

file

live

run

bead

five

loon

sale

vouch

beige

foil

loop

same

vow

boil

fume

mess

shod

whack

choke

fuse

met

shop

wham

chore

get

neat

should

woe

cod

good

need

shrill

woke

coil

guess

oil

sip

would

coon

hews

ouch

skill

yaw

coop

hive

paw

soil

yawn

cop

hod

pawn

soon

yes

couch

hood

pews

soot

yet

could

hop

poke

soup

zing

cow

how

pour

spill

zip

dale

huge

pure

still

dame

jack

rack

tale

basis of the word-frequency dictionary and a language-relevant phoneme distribution. In German intelligibility test logatoms (monosyllable consonant-vowel-groups that do not readily make sense, so that a logical supplementation of logatoms that were not clearly understood during the test is not possible—e.g., grirk, spres) are used for exciting the room. In English-speaking countries, however, test words as shown in Table 7-3 are used.19 There are between 200 and 1000 words to be used per test. The ratio between correctly understood words (or logatoms or sentences) and the total number read yields the word or syllable or sentence intelligibility V rated in percentages. The intelligibility of words VW and the intelligibility of sentences VS can be derived from Fig. 7-11.

Syllable intelligibiliy VL–% unsatifactory

poor satisfactory

good

excellent

Figure 7-10. Articulation loss Alcons as a function of the level ratio between diffuse sound LR and direct-sound level LD, reverberation time RT60 and noise level LN.

Figure 7-11. Assessment of the quality of speech intelligibility as a function of syllable intelligibility VL, word intelligibility VW, and sentence intelligibility VS.

Table 7-4 shows the correlation between the intelligibility values and the ratings.

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Table 7-4. Correlation between the Intelligibility Values and the Ratings Rating

Syllable Intelligibility VL in %

Sentence Intelligibility VS in %

Word Intelligibility VW in %

Excellent

90–96

94 –96

Good

67–90

95–96

87–94

Satisfactory

48–67

92–95

78–87

Poor

34–48

89–92

67 –78

Unsatisfactory

0–34

0–89

0–67

The results of the subjective intelligibility test are greatly influenced by speech velocity which includes the number of spoken syllables or words within the articulation time (articulation velocity) and the break time. Therefore so-called predictor sentences are often used to precede the words or logatoms that are not part of the test. These sentences consist of three to four syllables each, for example: “Mark the word...”, “Please write down…,” “We’re going to write….” Additionally to providing a continuous flow of speech, this also serves for guaranteeing that the evaluation takes place in an approximately steady-state condition of the room. There is a close correlation between the subjectively ascertained syllable intelligibility and room-acoustical criteria. For example, a long reverberation time reduces the syllable intelligibility 20 Fig. 7-12 owing to the occurrence of masking effects, despite an increase in loudness, see Eq. 7-8. Quite recently, comprehensive examinations concerning the frequency dependence of speechweighting room-acoustical criteria were conducted in order to find the influence of spatial sound coloration.12 It was ascertained that with broadband frequency weighting between 20 Hz and 20 kHz the definition measure C50 (see Section 7.2.2.6) correlates very insufficiently with the syllable intelligibility. Through a frequency evaluation across three to four octaves around a center frequency of 1000 Hz, however, the influence of the sound coloration can sufficiently be taken into account. Even better results regarding the subjective weightings are provided by the frequency analysis, if the following frequency responses occur, Fig. 7-13. As the definition declines with rising frequency due to sound coloration, the intelligibility of speech is also low (bad intelligibility o 3). This includes also the definition responses versus frequency with a maximum value at 1000 Hz, poor intelligibility o 4 in Fig. 7-13. The definition responses versus rising frequency to

Figure 7-12. Syllable intelligibility factor as a function of reverberation time.

Figure 7-13. Correlation between attainable intelligibility and frequency dependence of the definition measure C50.

be aimed at for room-acoustical planning should either be constant (good intelligibility o 1) or increasing (very good intelligibility o 2). With regard to auditory psychology, this result is supported by the importance for speech intelligibility of the consonants situated in this higher-frequency range. The determination of speech intelligibility through the definition measure C 50 can easily lead to faulty results as the mathematical integration limit of 50 ms is not a jump function with regards to intelligibility without knowledge of the surrounding sound reflection distribution. The best correlation with the influence of the spatial sound coloration exists between the subjective speech intelligibility and the center time tS (see Section 7.2.2.4) with a frequency weighting between the octave of 500 Hz to the octave of 4000 Hz. According to Hoffmeier,12 the syllable intelligibility V measured at the point of detection is then calculated as V = 0.96 u V sp u V SNR u V R

(7-34)

where, Vsp is the influence factor of the sound source (trained speaker Vsp = 1, untrained speaker Vsp | 0.9),

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159

VSNR is the influence factor of the useful level (speech level) Lx and of the disturbance level Lst according to Fig. 7-14,6 2 ts –6 t s V R = – 6 u 10 § ------- · – 0.0012 § ------- · + 1.0488 © ms ¹ © ms ¹

Figure 7-15. Syllable intelligibility IS as a function of the articulation loss Alcons. Parameter: reverberation time RT60. Preconditions: approximate statistical reverberation behavior; signal-to-noise ratio (SNR) t 25 dB.

Figure 7-14. Syllable intelligibility factor VS/N as a function of speech sound pressure level LS and noise pressure level LN.

The correlation shown in Fig. 7-15 can also be derived between articulation loss and syllable intelligibility. For low reverberation times, syllable intelligibility is almost independent of the articulation loss. An inverse correlation behavior sets in only with increasing reverberation time. It is evident that with the usual Alcons values between 1% and 50%, syllable intelligibility can take on values between 68% and 93% (meaning a variation of 25%) and that for an articulation loss 4 dB. This correlation can also be seen in Fig. 7-16, which shows the correlation between measured RASTI-values and articulation loss Alcons. One sees that acceptable articulation losses of Alcons 6 dB) from the idealized spherical pattern above 20 kHz. Using smaller capsules (1e4 in or even 1e8 in) can improve the omnidirectivity of the microphone but it also reduces its sensitivity and yields a lower SNR during the measurements. 9.2.1.5 Surface Materials and Absorption Considerations in Physical Models Ideally, the surface materials used in a scale physical model should have absorption coefficients that closely match those of real materials planned for the full-size environment at the equivalent frequencies. For example, if a 1:20 scale model is used to investigate sound absorption from a surface at 1 kHz in the model (or 50 Hz in the real room) then the absorption coefficient a of the material used in the model at 1 kHz should match that of the planned full-size material at 50 Hz. In practice this requirement is never met since materials that have similar absorption coefficients over an extended range of frequencies are usually limited to hard reflectors where a < 0.02 and even under these condition, the absorption in the model will increase with frequency and deviate substantially from the desired value. The minimum value for the absorption coefficient of any surface in a model can be found from

D min = 1.8 u 10

–4

219

(9-8)

where, f is the frequency of the sound wave at which the absorption is measured. Thus at frequencies of 100 kHz, an acoustically hard surface like glass in a 1:20 scale model will have an absorption coefficient of D min = 0.06, a value that is clearly greater than D < 0.03 or what can be expected of glass at the corresponding 5 kHz frequency in the full-size space. The difference in level between the energy of the nth reflected wave to that of the direct wave after n reflections on surfaces with an absorption coefficient a is given by ' Level = 10 log 1 – D

(9-9)

Considering glass wherein the model D = D mi n = 0.06, the application of Eq. 9-9 above shows that after two reflections the energy of the wave will have dropped by 0.54 dB. If the reflection coefficient is now changed to D = 0.03 then the reduction in level is 0.26 dB or a relative error of less than 0.3 dB. Even after five reflections, the relative error due to the discrepancies between a and a min is still less than 0.7 dB, a very small amount indeed. On the other hand, in the case of acoustically absorptive materials (D > 0.1) the issue of closely matching the absorption coefficients in the models to those used in the real environment becomes very important. The application of Eq. 9-9 to absorption coefficients D in excess of 0.6 shows that even a slight mismatch of 10% in the absorption coefficients can result in differences of 1.5 dB after only two reflections. If the mismatch is increased to 20% then errors in the predicted level in excess of 10 dB can take place in the model. Due to the difficulty in finding materials that are suitable for use in both the scaled physical model and in the real-size environment, different materials are used to match the absorption coefficient in the model (at the scaled frequencies) to that of the real-size environment at the expected frequencies. For example, a 10 mm layer of wool in a 1:20 scale model can be used to model rows of seats in the actual room, or a thin layer of polyurethane foam in a 1:10 scale model can be used to represent a 50 mm coating of acoustical plaster in the real space. Another physical parameter that is difficult to account for in scale physical model is stiffness, thus the evaluation of effects such as diaphragmatic

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absorption and associated construction techniques is difficult to model accurately.

9.2.2 Computational Models This section presents models that create a mathematical representation of an acoustical environment by using assumptions that are based on either a geometrical, analytical, numerical, or statistical description of the physical phenomena (or parameters) to be considered, or on any combination of the afore- mentioned techniques, In all instances, the final output of the modeling phase is the result of extensive mathematical operations that are usually performed by computers. With the development of powerful and affordable computers and of graphical interfaces these modeling tools have become increasingly popular with acoustical designers. To various degrees, the aim of computational models is to ultimately yield a form of the impulse response of the room at a specific receiver location from which data pertaining to time, frequency, and direction of the sound energy reaching the receiver can be derived. This information can then be used to yield specific quantifiers such as reverberation time, lateral reflection ratios, intelligibility, and so on. The inherent advantage of computational models is flexibility: changes to variables can be made very rapidly and the effects of the changes are available at no hard cost, save for that of computer time. Issues related to source or receiver placement, changes in materials and/or in room geometry can be analyzed to an infinite extent. Another advantage of computational models is that scaling is not an issue since the models exist in a virtual world as opposed to a physical one. Computational models are themselves divided into subgroups that are fundamentally based on issues of adequacy, accuracy, and efficiency. An adequate model uses a set of assumptions based on a valid (true) description of the physical reality that is to be modeled. An accurate model will further the cause of adequacy by providing data that is eminently useful because of the high confidence associated with it. An efficient model will aim at providing fast and adequate results but maybe to a lesser—yet justified—extent in accuracy. Although issues of accuracy and of efficiency will be considered in this portion of the chapter, the discussion of the various classes of computational models will be primarily based on their adequacy.

9.2.2.1 Geometrical Models The primary assumption that is being made in all geometrical models2 applied to acoustics is that the wave can be seen as propagating in one or more specific directions, and that its reflection(s) as it strikes a surface is (are) also predictable in terms of direction; this is a very valid assumption when the wavelength can be considered small compared to the size of the surface and the condition ka > 5 presented in Table 9-1 quantifies the limit above which the assumption is valid. Under this condition, the propagating sound waves can be represented as straight lines emanating from the sources and striking the surfaces (or objects) in the room at specific points. The laws of optics involving angles of incidence and angles of reflection will apply and the term geometrical acoustics is used to describe the modeling technique. The second assumption of relevance to geometrical acoustics models is that the wavelength of the sound waves impinging on the surfaces must be large compared to the irregularities in the surface, in other words the surface has to appear smooth to the wave and in this instance the irregularities in the surface will become invisible since the wave will diffract around them. If the characteristic dimension of the irregularities is denoted by b, then the condition kb < 1 is required using the criteria outlined in Table 9-1. This is a necessary condition to assume that the reflection is specular, that is that all of its energy is concentrated in the new direction of propagation. Unless this condition is met in the actual room the energy of the reflected wave will be spread out in a diffuse fashion and the geometrical acoustics assumption of the model will rapidly become invalid, especially if many reflections are to be considered. Image Models. In this class of geometrical acoustics models, the assumption that is being made is that the only sound reflections that the model should be concerned about are those reaching the receiver, so the methodology aims at computing such reflections within time and order constraints selected by the user of the model while ignoring the reflections that will not reach the receiver. To find the path of a first-order reflection a source of sound S0 is assumed to have an image—a virtual source S1—located across the surface upon which the sound waves are impinging as presented in Fig. 9-5. As long as the surface can be considered to be rigid, the image method allows for the prediction of the angles of reflections from the surface and can find all of the paths that may exist between a source and a receiver.3 It

Acoustical Modeling and Auralization also satisfies the boundary conditions that must take place at the surface, that is, the acoustical pressures have to be equal on both sides of the surface at the reflection point, and the velocity of the wave has to be zero at the interface. The image from the virtual source S1 can also be used to determine where the second-order reflections from a second surface will be directed to since as far as the second surface is concerned, the wave that is impinging upon it emanated from S1. A second order source S2 can thus be created as shown in Fig. 9-6 and the process can be repeated as needed to investigate any order of reflections that constitutes a path between source and receiver.

221

tions inside a space that reach a receiver at a specific location. A sample of a reflectogram is shown in Fig. 9-9.. S1 (image of the source) Convex surface Reflection point

Tangential plane

Receiver S0 (source)

S1 (image of the source)

Figure 9-7. Image construction from a convex plane. Adapted from Reference 1. Reflection point

Surface (boundary)

S1 (image of the source)

Receiver

Reflection point

S0 (source)

Tangential plane

Figure 9-5. A source and its virtual image located across a boundary define the direction of the first-order reflection. Boundary 1 S1 (image of the source across boundary 1)

Receiver S0 (source) 1st order reflection

2nd order reflection

Concave surface

S0 (source) Receiver

Figure 9-8. Image construction from a concave plane Adapted from Reference 1.

Boundary 2

90 dB 70 dB

Figure 9-6. Higher-order reflections can be created by adding virtual images of the source.

It is thus possible to collect the amplitude and the direction of all of the reflections at a specific location as well as a map of where the reflections emanate from. Even the reflection paths from curved surfaces can be modeled by using tangential planes as shown in Fig. 9-7 and Fig. 9-8. Since the speed of sound can be assumed to be a constant inside the room, the distance information pertaining to the travel of the reflections can be translated into time-domain information; the result is called a reflectogram (or sometimes an echogram) and it provides for a very detailed investigation of the reflec-

50 dB

Direct sound

S2 (2nd order image of the source across boundary 2)

30 dB 10 dB 0 ms

100 ms

200 ms

Figure 9-9. A reflectogram (or echogram) display of reflections at a specific point inside a room.

Although it was originally developed solely for the determination of the low-order specular reflections taking place in rectangular rooms due to the geometric increase in the complexity of the computations required, the technique was expanded to predict the directions of the specular reflections from a wide range of shapes. 4 In the image method, the boundaries of the room are effectively

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being replaced by sources and there is no theoretical limit to the order of reflection that can be handled by the image methodology. From a practical standpoint, the number of the computations that are required tends to grow exponentially with the order of the reflections and the number of surfaces as shown in Eq. 9-10, where NIS represents the number of images, NW is the number of surfaces that define the room, and i is the order of the reflections.5 NW i N IS = ---------------- > N W – 1 – 1 @ NW – 2

(9-10)

S2 (2nd order image of the source across boundary 2) S3 (invalid image of the source)

Boundary 2 S0 (source)

S1 (image of the source across boundary 1) Boundary 1

Furthermore reflections must be analyzed properly in terms of their visibility to the receiver in the case of complicated room shapes where some elements may block the reflections from the receiver as shown in Fig. 9-10.

Reflection

Balcony Listener

Figure 9-10. The reflection is not visible to the listener due to the balcony obstruction.

The model must also constantly check for the validity of the virtual sources to insure that they actually contribute to the real reflectogram by emulating reflections taking place inside the room and not outside its physical boundaries. Fig. 9-11 illustrates such a situation. In Fig. 9-11 a real source S 0 creates a first-order image S 1 across boundary 1. This is a valid virtual source that can be used to determine the magnitude and the direction of first-order specular reflections on the boundary surface 1. If one attempts to create a second-order virtual source S2 from S1 with respect to boundary surface 2 to find the second order reflection, the image of this virtual source S 2 with respect to boundary 1 is called S3 but it is contained outside the boundary used to create it and it cannot represent a physical reflection. Once the map of all the images corresponding to the reflection paths has been stored, the intensity of each individual reflection can be computed by applying Eq. 9-9 introduced earlier. Since the virtual sources do

Figure 9-11. Invalid images can be created when a virtual source is reflected across the boundary used to create it. Adapted from Reference 4.

represent the effect of the boundaries on the sound waves, the frequency dependence of the absorption coefficients of the surfaces is modeled by changing the power radiated by the virtual sources; thus, once the image map is obtained the model can be used to rapidly simulate an unlimited number of “what if” simulations pertaining to material changes as long as the locations of the sources and the receiver remain unchanged. A further correction for the air absorption resulting from the wave traveling over extended distances can also be incorporated at this time in the simulation. The same reasoning applies to the frequency distribution of the source: since the image map (and the resulting location of the reflections in the time domain) is a sole function of source and receiver position, the image model can rapidly perform “what if ” simulations to yield reflectograms at various frequencies. The image methodology does not readily account for variations in the absorption coefficient of the surfaces as a function of the angle of incidence of the wave. When taking into account all of the properties in the transmission medium, it can be shown that many materials will exhibit a substantial dependence of their absorption coefficient on the incidence angle of the wave, and in its most basic implementation the image method can misestimate the intensity of the reflections. It is however, possible to incorporate the relationship between angle of incidence and absorption coefficient into a suitable image algorithm in order to yield more accurate results, although at the expense of computational time. In an image model the user can control the length of the reflection path as well as the number of segments (i.e., the order of the reflections) that comprise it. This allows for a reduction in the computational time of the

Acoustical Modeling and Auralization process since virtual sources located beyond a certain distance from the receiver location can be eliminated while not compromising the fact that all of the reflections within a specific time frame are being recorded, and the image method can lead to very accurate results in the modeling of the arrival time of reflections at a specific location. Efficient computer implementations of the image methodology have been developed4 to allow for a fast output of the reflections while also checking for the validity of the images and for the presence of obstacles. Still the method is best suited to the generation of very accurate reflectograms of short durations (500 ms or less) and limited number of reflections (fifth order maximum for typical applications). These factors do not negatively affect the application of the image method in acoustical modeling since in a typical large space—like an auditorium or a theater—the sound field will become substantially diffuse after only a few reflections and some of the most relevant perceived attributes of the acoustics of the space are correlated to information contained in the first 200 ms of the reflectogram. Ray-Tracing Models. The ray-tracing methodology follows the assumptions of geometrical acoustics presented at the onset of this section, but in this instance the source is modeled to emit a finite number of rays representing the sound waves in either an omnidirectional pattern for the most general case of a point source, or in a specific pattern if the directivity of the source is known. Fig. 9-12 shows an example of a source S generating rays inside a space and how some of the rays are reflected and reach the receiver location R.

Source

Receiver

Figure 9-12. Rays are generated by a source, S. Some of the rays reach the receiver, R.

In this instance, the goal is not to compute all of the reflection paths reaching the receiver within a given time frame but to yield a high probability that a speci-

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fied density of reflections will reach the receiver (or detector usually modeled as a sphere with a diameter selected by the user) over a specific time window. In the case of the image method, the boundaries of the room are replaced by virtual sources that dictate the angle of the reflections of the sound waves. In a similar fashion, the ray-tracing technique creates a virtual environment in which the rays emitted by the source can be viewed as traveling in straight paths across virtual rooms until they reach a virtual listener as presented in Fig. 9-13. This ray found a virtual receiver but missed the three neighbors that were closer to the source

Source This ray found a virtual receiver in the virtual room nearest to the source

Receiver This ray did not find any receiver in any of the virtual rooms

Figure 9-13. The rays can be seen as traveling in straight paths across virtual images of the room until they intercept a receiver. Adapted from Reference 4.

The time of travel and location of the ray are then recorded and can yield a reflectogram similar to that presented earlier in Fig. 9-9. The main advantage of the ray-tracing technique is that since the model is not trying to find all of the reflection paths between source and receiver, the computational time is greatly reduced when compared to an image technique; for a standard ray-tracing algorithm, the computational time is found to be proportional to the number of rays and to the desired order of the reflections. Another advantage inherent to the technique is that multiple receiver locations may be investigated simultaneously since the source is emitting energy in all directions and the model is returning the number and the directions of rays that are being detected without trying to complete a specific path between source and receiver. On the other hand, since the source is emitting energy in many directions and one cannot dictate what the frequency content of a specific ray is versus that of another, the simulations pertaining to the assessment of frequency-dependent absorption must be performed independently and in their entirety for each frequency of interest.

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One problem associated with the ray-tracing technique is that the accuracy of the detection is strongly influenced by size of the detector. A large spherical detector will record a larger number of hits from the rays than another spherical detector of smaller diameter, even if the respective centers of the spheres are located at the exact same point in space. Furthermore, the ray-tracing method may lead to an underestimation of the energy reaching the detector (even if its size is considered adequate) unless large numbers of rays are used since the energy is sampled via rays that diverge as they spread from the source thus increasing the possibility that low-order reflections may miss the detector. Techniques combining the image methodology and the ray-tracing approach have been developed. 5 The algorithms aim at reducing the number of images to be considered by using the more computationally efficient ray-tracing technique to conduct the visibility test required by the image method. Beam-Tracing Models. The triangular area that is defined between two adjacent rays emanating from a source is called a 2D ray; more than two rays can also be used to define a 3D pyramidal or conical region of space in which the acoustical energy is traveling away from the source. In these instances, the source is viewed at emitting beams of energy, and the associated modeling techniques are known as beam-tracing methods. Figure 9-14 shows an example of a beam and its reflection path from a surface. Reflected beam

S (source) Incident beam

Surface Reflection area S1 (image of the source)

Figure 9-14. A 3D beam is emitted by a source S and reflects at a surface.

The beam-tracing technique offers the advantage of guaranteeing that the entire space defining the model will receive energy since the directions of propagations are not sampled as in the case of the traditional ray-tracing approach. Virtual source techniques are used to locate the points that define the reflection zones across the boundaries of the room. On the other hand,

the technique requires very complex computations to determine the reflection patterns from the surfaces since the reflection cannot be viewed as a single point as in the case of the ray-tracing technique: when 2D beams are used, the reflections from the surfaces must be considered as lines, while 3D beams define their reflections as areas. Care must also be taken to account for overlapping of the beams by each other or truncation of the beams by obstacles in the room. Although the computational complexity of the model is substantially increased when it comes to assessing the direction of the reflections, the departure from the single point reflection model presents numerous advantages over the traditional image and/or ray-tracing technique. The issues associated with the divergence of the reflections as a function of increased distance from the source are naturally handled by the beam-tracing approach. Furthermore, the effects of acoustical diffusio n can be mo deled— at least in an esti mat ed fashion—since the energy contained in the beams can be defined as having a certain distribution over either the length of the intersecting lines (for 2D beams) or areas (for 3D beams). For example, an adaptive beam-tracing model6 that controls the cross-sectional shape of the reflecting beam as a function of the shape of the reflecting surfaces also allows for an evaluation of the diffuse and specular energy contained inside a reflecting beam. If the energy contained inside the incident beam is EB and the energy reflected from a surface is ER, then one can write ER = EB 1 – D 1 – G

(9-11)

where, Dis the surface’s absorption coefficient, Gis the surface’s diffusion coefficient. The energy E D that is diffused by the surface is found to be proportional to the area of illumination A and inversely proportional to the square of an equivalent distance L between the source and the reflection area E B AG 1 – D E D v ------------------------------2 4SL

(9-12)

The adaptive algorithm allows for a separate assessment of the specular and of the diffuse reflections from the same geometrical data set that represents the travel map of the beams inside the space. In this instance the diffused energy from a given surface is redirected to other surfaces in a recursive fashion via radiant exchange, a technique also used in light rendering applications. The diffuse and the specular portions of the

Acoustical Modeling and Auralization response can then be recombined to yield a reflectogram that presents a high degree of accuracy, especially when compared to traditional ray-tracing techniques. Fig. 9-15 shows a comparative set of impulse response reflectograms obtained by the adaptive beam tracing, the image, the ray-tracing, and the nonadaptive beam-tracing techniques in a model of a simple performance space containing a stage and a balcony. 5

Adaptive Beam Tracing

0 SPL(dB) –5 –10 5

0.1

Time—s 0.2

0.3

0.2

0.3

0 0.1 Time—s 0.2 Nonadaptive Beam Tracing

0.3

Image Method

0 SPL(dB) –5 –10 5

0.1

Time—s

Ray-Tracing

0 SPL(dB) –5 –10 5 0 SPL(dB) –5 –10

0.1

Time—s

0.2

Figure 9-15. Comparative reflectograms for a simple room model. From Reference 6.

The adaptive model is able to yield a reflectogram that is extremely close to that obtained with an image method—i.e., it is able to generate all of the possible reflections paths at a single point in space. From the perspective of computing efficiency, the adaptive-beam tracing methodology compares favorably with the image methodology especially when the complexity of the room and/or the order of the reflections is increased. Other variants of the beam-tracing approach have been developed. In the priority-driven approach,7 the algorithms are optimized to generate a series of the

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most relevant beams from a psychoacoustics perspective so that the reflectogram can be generated very rapidly, ideally in real time and the model can be used in an interactive fashion. The beams are ranked in order of importance based on a priority function that aims at accurately reproducing the early portion of the reflectogram since it is by far the most relevant to the perception of the space from the perspective of psychoacoustics. The late portion of the reflectogram (the late reverberation) is then modeled by using a smooth and dense energy profile that emulates the statistical decay of the energy in a large space. A note on diffusion: The issue of diffusion has been of prime interest to the developers of computer models since commercially available or custom-made diffusers are often integrated into room designs, sometimes at a high cost. Although diffusion is an essential qualitative part of the definition of a sound field, the quantitative question of “how much diffusion is needed?” is often answered using considerations that have little foundation in scatter theory and/or general acoustics. A concept as elementary as reverberation finds its classical quantitative representation (the Sabine/Eyring equation and associated variants) rooted into the notion that the sound field is assumed to be diffuse, and unless this condition is met in reality, one will encounter substantial errors in predicting the reverberation time. Today’s advanced large room computer acoustic simulation software products incorporate the ability to model diffused reflections using either a frequency dependence function or an adaptive geometry that spreads out the incident energy of the sound ray over a finite area. This allows for a much more accurate correlation between predicted and test data especially in rooms that have geometry involving shapes and aspect ratios that are out of the ordinary, noneven distribution of absorptive surfaces, and/or coupled volumes.8 Under these conditions the incorporation of diffusion parameters into the model is necessary and a specular-only treatment of the reflections (even when using an efficient ray-tracing technique) will lead to errors. 9.2.2.2 Wave Equation Models Wave equation models are based on an evaluation of the fundamental wave equation, which in its simplest form relates the pressure p of a wave at any point in space to its environment via the use of the 3D Laplacian operator 2 and the wave number k: 2

p+k p = 0

(9-13)

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Solving the fundamental wave equation allows for an exact definition of the acoustic pressure at any specific point since appropriate boundary conditions defining the physical properties of the environment (surfaces, medium) can be used whenever required. As an example, in a model based on the wave equation the materials that comprise the environment (like the room) can be defined in terms of their acoustical impedance z given by p z = ---U where, p refers to the pressure of the wave, U to its velocity in the medium.

(9-14)

When using the wave equation, issues having to do with diffraction, diffusion, and reflections are automatically handled since the phenomena are assessed from a fundamental perspective without using geometrical simplifications. The main difficulty associated with the method is found in the fact that the environment (surfaces and materials) must be described accurately in order for the wave equation to be applied: either an analytical or a numerical approach can be used to achieve this goal. 9.2.2.2.1 Analytical Model: Full-Wave Methodology. An analytical model aims at providing a mathematical expression that describes a specific phenomenon in an accurate fashion based on underlying principles and/or physical laws that the phenomenon must obey. Because of this requirement the analytical expression governing the behavior of a model must be free of correction terms obtained from experiments and of parameters that cannot be rigorously derived from—or encountered in—other analytical expressions. The complexity of the issues associated with sound propagation has prevented the development of a single and unified model that can be applied over the entire range of frequencies and surfaces that one may encounter in acoustics; most of the difficulties are found in trying to obtain a complete analytical description of the scattering effects that take place when sound waves impinge on a surface. In the words of J.S. Bradley,9 one of the seminal researchers in the field of architectural acoustics: Without the inclusion of the effects of diffraction and scattering, it is not possible to accurately predict values of conventional room acoustics parameters […]. Ideally, approxima-

tions to the scattering effects of surfaces, or of diffraction from finite size wall elements should be derived from more complete theoretical analyses. Much work is needed to develop room acoustics models in this area. In this section, we present the full-wave methodology,10 one analytical technique that can be used for the modeling of the behavior of sound waves as they interact with nonidealized surfaces, resulting in some of the energy being scattered, reflected, and/or absorbed as in the case of a real space. Due to the complexity of the mathematical foundation associated with this analytical technique, only the general approach is introduced here and the reader is referred to the bibliography and reference section for more details. The full-wave approach (originally developed for electromagnetic scattering problems) meets the important condition of acoustic reciprocity requiring that the position of the source and of the receiver can be interchanged without affecting the physical parameters of the environment like transmission and reflection coefficients of the room’s surfaces. In other words if the environment remains the same, interchanging the position of a source and of a receiver inside a room will result in the same sound fields being recorded at the receiver positions. The full-wave method also allows for exact boundary conditions to be applied at any point on the surfaces that define the environment, and it accounts for all scattering phenomena in a consistent and unified manner, regardless of the relative size of the wavelength of the sound wave with that of the objects in its path. Thus the surfaces do not have to be defined by general (and less than accurate) coefficients to represent absorption or diffusion, but they can be represented in terms of their inherent physical properties like density, bulk modulus, and internal sound velocity. The full-wave methodology computes the pressure at every point in the surface upon which the waves are impinging, and follows the shape of the surface. The coupled equations involving pressure and velocity are then converted into a set of equations that separate the forward (in the direction of the wave) and the backward components of the wave from each other, thus allowing for a detailed analysis of the sound field in every direction. Since the full-wave approach uses the fundamental wave equation for the derivation of the sound field, the model can return variables such as sound pressure or sound intensity as needed. The main difficulty associated with the full-wave method is that the surfaces must also be defined in an analytical fashion. This is possible for simple (i.e.,

Acoustical Modeling and Auralization planar, or curved) surfaces for which equations are readily available, but for more complicated surfaces— such as those found in certain shapes of diffusers—an analytical description is more difficult to achieve, and the methodology becomes restricted to receiver locations that are located at a minimum distance from the surfaces upon which the sound waves are impinging. Still for many problems the full-wave methodology is a very accurate and efficient way to model complicated scattering phenomena.

9.2.2.3 Numerical Model: Boundary Element Methodology The boundary element analysis (BEA) techniques are numerical methods that yield a quantitative value of the solution to the problem under investigation. BEA techniques11,12,13,14 can be used in solving a wide range of problems dealing with the interaction of energy (in various forms) with media such as air and complex physical surfaces, and they are well suited to the investigation of sound propagation in a room. Although the method is based on solving the fundamental differential wave equation presented earlier, the BEA methodology makes use of an equivalent set of much simpler algebraic equations valid over a small part of the geometry, and then expands the solution to the entire geometry by solving the resulting set of algebraic equations simultaneously. In essence, the BEA technique replaces the task of solving one very complex equation over a single complicated surface by that of solving a large quantity of very simple equations over a large quantity of very simple surfaces. In a BEA implementation the surface is described using a meshing approach as shown in Fig. 9-16. In the BEA method the analytical form of the solution over the small domain (area) of investigation is not directly accessible for modification. The use exercises control over the solution by properly specifying the domain (geometry) of the problem, its class (radiation or scattering), the parameters of the source (power, directivity, location), and, of course, the set of boundary conditions that must be applied at each area defined by the mesh. It is thus possible to assign individual material properties at every location in the mesh of the model in order to handle complex scattering and absorption scenarios, if needed. Although it can be adapted to solving acoustical problems in the time domain the BEA technique is better suited to providing solutions in the frequency domain since the characteristics of the

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Room

Mesh around surface (boundary)

Boundary element operator

Figure 9-16. A mesh describes a boundary in the BEA method.

materials are considered to be time-invariant but frequency dependent. The main issue that is associated with the use of BEA methodology for the investigation of acoustical spaces is that the size of the elements comprising the mesh representing the surfaces dictates the accuracy of the solution. A small mesh size will, of course, allow for a very accurate description of the surfaces, both geometrically and in terms of its materials, but it will also drastically affect the computational time required to yield a solution. On the other hand, a large mesh size will yield very fast results that may be inaccurate because the algebraic equations that are used in lieu of the fundamental wave equation improperly being applied over large surfaces. A comparison of the accuracy yielded by BEA techniques over very simple geometries indicates that a minimum ratio of seven to one (7:1) must exist between the wavelength of the sound and the element size in order to bind the dependence of the BEA analysis on the size of its element to less than a ±0.5 dB resolution. In other words, the wavelengths considered for analysis must be at least seven times larger than the largest mesh element in order for the methodology to be accurate. For this reason the BEA methodology is very efficient and accurate to model sound propagation at low frequencies (below 1000 Hz), but it becomes tedious and cumbersome at higher frequencies since in this instance the mesh must be modeled with better than a 50 mm resolution. Still the technique can be shown to yield excellent results when correlating modeled projection and actual test data from complicated surfaces such as diffusers.13

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Numeric Model: Finite Difference Time-Domain Methodology. As mentioned earlier, the BEA techniques are best suited to yielding data in the frequency domain, although they can be adapted to provide time-domain information albeit at a cost in computing efficiency. Another numerical methodology that uses a discrete representation of the acoustical environment is known as Finite-Difference Time-Domain (FDTD) and it is very efficient in terms of computational speed and storage while also offering excellent resolution in the time domain. It has been demonstrated15 that the technique can be used to effectively model low-frequency problems in room acoustics simulations and the results are suitable for the generation of reflectograms. In the finite difference (FD) approach instead of describing the surface with a mesh (as with the BEA technique), a grid is used and the algebraic equations are solved at the points of the grid as shown in Fig. 9-17. Room

modal frequencies, modal density, and mode distributions are presented, along with the appropriate descriptive equations in Chapter 5—Small Room Acoustics. Another application of statistics in acoustical modeling can be found in situations where resonance effects take place at high frequencies, as opposed to the traditionally low frequencies associated with room modes. A technique known as Statistical Energy Analysis16 (SEA) can be used to accurately account for the effect of modal resonance effects that take place in systems such as partitions and walls, by analyzing the kinetic energy and the strain energy associated with vibrating structures. An SEA model will describe a vibrating system (such as a wall) with mass and spring equivalents and will allow for the analysis of the effect that adding damping materials will have on the vibration spectrum. SEA techniques are optimized for frequency-domain analysis and the output cannot be used for time-domain applications to add information to the impulse response of a room, or to yield a reflectogram; still, the main advantage of SEA is that real materials such as composite partitions with different degrees of stiffness, construction beams, and acoustical sprays can be modeled in a precise manner (i.e., not only in terms of a unique physical coefficient) over an extended range of frequency.

Grid around surface

9.2.2.5 Small Room Models

Finite difference operator

Figure 9-17. A grid describes a surface in the FD method.

In this instance the size of the grid can be made as small as needed to provide a high degree of resolution when needed and the grid points can be defined using the most effective coordinate system for the application. For example, a flat surface could be defined with a (x, y, z) Cartesian grid system while cylinders (for pillars) and spheres (for audience’s heads) could be expressed with cylindrical and spherical systems respectively. 9.2.2.4 Statistical Models The use of statistics in acoustical modeling is primarily reserved for the study of the behavior of sound in rectangular and rigid rooms where the dominant phenomena that are taking place are related to modes. The issues of

A room that is acoustically small can be defined as one in which classically defined reverberation phenomena (using the assumption of a diffuse sound field) do not take place, but rather that the sound decays in a nonuniform manner that is a function of where the measurement is taken. The use of diffusion algorithms in large room models that rely on either ray-tracing, image source, or adaptive algorithms has vastly improve the reliability of the prediction models in a wide range of spaces, however accurate predictions of the sound field can be made in small rooms considering the interference patterns that result from modal effects. Figs. 9-18 and 9-19 shows the mapping17 of the interference patterns resulting from modal effects in an 8 m × 6 m room where two loudspeakers are located at B1 and B2. In the first instance, a modal effect at 34.3 Hz creates a large dip in the response at about 5.5 m, while the second case shows a very different pattern at 54.4 Hz. Such models are very useful to determine the placement of low-frequency absorbers into a room in order to minimize the impact of modal effects at a specific listening location, and they are a good complement to the large

Acoustical Modeling and Auralization room models that typically do not investigate the distribution of the sound field at the very low frequencies.

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propagation in a complicated environment, and this section will present only a couple of examples. 9.2.3.1 Gypsum Cavity Wall Absorption

Figure 9-18. A mapping of the sound field resulting from modal interference patterns at 34.3 Hz. From CARA.

There is numerous test data available pertaining to the sound transmission class (STC) of various wall constructions, but little has been investigated regarding the sound absorption of walls constructed of gypsum (drywall) panels. The absorption of a composite wall panel is partly diaphragmatic (due to the mounting), partly adiabatic (due to the porosity of the material and the air), and some energy is lost inside the cavity via resonance. The complicated absorption behavior of gypsum walls has been described18 using an empirical model that takes into account absorption data acquired in reverberation chamber experiments. The mathematical model is fitted to the measured data to account for the resonant absorption of the cavity by assuming that the mechanical behavior of the wall can be modeled by a simple mechanical system. In this model, the resonance frequency at which the maximum cavity absorption takes place is given by m1 + m2 f MAM = P --------------------d m1 m2

(9-15)

where, m1 and m2 are the mass of the gypsum panels comprising the sides of the wall in kg/m2, d is the width of the cavity expressed in millimeters, P is a constant with the following values: If the cavity is empty (air), P = 1900, If the cavity contains porous or fibrous sound-absorptive materials, P = 1362. Figure 9-19. A mapping of the sound field resulting from modal interference patterns at 54.4 Hz. From CARA.

9.2.3 Empirical Models Empirical models are derived from experiments and are described by equations that typically follow curve-fitting procedures of the data obtained in the observations. No analytical, geometrical, and/or statistical expression is developed to fully explain the interdependence of variables and parameters in the model, but a general form of a descriptive expression may be constructed from underlying theories. Empirical models have been extensively used for many years in acoustical modeling due to the large quantity of variables and parameters that are often present when dealing with issues of sound

The empirical model combines the maximum absorption DMAM taking place at the resonant frequency given by Eq. 9-15 with the high-frequency absorption DS into a form that fits data obtained experimentally, to give an equation that allows for the prediction of the absorption coefficient of the wall as a function of frequency: f MAM 2 D f = D MAM § ------------· + D MAM © f ¹

(9-16)

Although it does not take into account all of the construction variables (stud spacing, bonding between layers) the model still provides accurate prediction of the sound absorption parameters of various gypsum wall constructions.

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9.2.3.2 Absorption from Trees and Shrubs When dealing with issues related to outdoor noise propagation one may need to predict the anticipated noise reduction that can be expected from vegetation. In this instance, some of the general attributes of a tree-barrier such as height and width can be modeled from geometry, but others like leaf density, wind resistance, or diffraction effects from trunks may prove very difficult to describe either analytically or geometrically. In this instance an empirical model that fits experimental data to polynomial equations based on statistical regression is the most appropriate19 to yield the sound pressure level at various distances from a sound source while taking into account tree height, width of the tree barrier, wind velocity, and tree type. An example of such an equation is presented below, and it is shown to give excellent (±1 dB) accuracy between predicted and observed levels for distances extending 150 ft to 400 ft from the source that is assumed to be truck noise on an interstate highway. The receiver is shielded from the traffic by a belt of conifer trees planted along the interstate. L dB = 81.65 – 0.2257H – 0.0229W + 0.728V – 0.0576D

(9-17)

where, LdB is the predicted sound level behind the tree belt, H is the height of the tree belt, expressed in feet, W is the width of the tree belt, expressed in feet, V is the wind velocity component in the direction of the sound propagation, expressed in mph, D is the distance from the receiver to the tree belt. Other equations are available for different sources and different types of trees. In this class of empirical models, no attempt is made to support the equation by analytical expressions but this does not affect the usefulness or the accuracy of the model. 9.2.4 Hybrid Models As the name implies hybrid models use a combination of techniques to yield results and the choice of the technique may be based on a specific need such as fast output, accuracy, range of applicability, etc. A hybrid model can combine the inherent accuracy of the image method for the determination of reflection arrival time in the specular case, with an adaptive beam-tracing approach when diffusion is required, and may also incorporate some BEM computations for complicated

materials wherever required. A hybrid model can also rely on empirical approaches to provide a confidence factor for results obtained from physical scale models or from statistical approaches. An example of hybrid techniques can be found in models that are aimed at assessing outdoor noise propagation.20 In this instance, the objects that are in the path of the sound waves are typically buildings or large natural obstacles and can be considered to be much larger than the wavelength, except for the lowest frequencies, and as such, the geometrical acoustics assumptions apply very well; as such, the image method is very appropriate to compute reflection paths between obstacles. On the other hand one cannot ignore the fact that outdoor noise may contain a lot of low frequencies and that diffraction effects will take place; in this instance the model must use an appropriate description of diffraction such as the one presented in Chapter 4—Acoustical Treatment of Rooms and the model may also be refined from empirical data table to represent complicated sources such as car traffic, aircraft, and trains since point source assumptions become invalid and the sources are also moving. Figs. 9-20 and 9-21 shows the type of noise prediction maps that can be obtained from such a model; in the first instance the noise sources are a combination of street traffic and large mechanical systems, and the model takes into account the diffraction effects of various buildings. In the second instance, the model is used to assess the difference in expected noise levels between different types of pavements (asphalt vs. concrete) based on traffic data on a segment of road that is surrounded by residences. Hybrid models are also found in construction applications, where they combine analytical techniques based on specific equations with databases of test results obtained in the laboratory and in the field. As an example, a simple model could be developed using the Mass Law in order to predict the sound transmission between two spaces and yield an estimate of the Sound Transmission Class (STC) of the partition, however, the results would not be very useful because they would extensively be influenced by the construction technique and the presence of flanking paths. With a model that takes into account the construction techniques of the partition, 21 the results are much more accurate and provide the designer with valuable insight on the weak links of the construction as they pertains to noise transmission.

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Noise map at 10 m (All levels in dB-A)

Traffic noise map using Average Daily Volumes/day

Figure 9-20. A noise map from an outdoor propagation model. CadnaA by DataKustik GmbH.

Difference Map Weekday

Figure 9-21. Difference maps for noise generated by different types of road pavements. Courtesy SoundPLAN, by SoundPLAN LLC.

9.3 Auralization Auralization is the process of rendering audible, by physical or mathematical modeling, the sound field of a source in a space, in such a way

as to simulate the binaural listening experience at a given position in the modeled space.22 Auralization systems have been in existence since the 1950s.23 During the early experiments, researchers used a physical 1:10 scale model in which a tape containing speech and music samples was played back at scaled-up speed through a scaled omnidirectional source while also taking into account the air absorption and scaling the reverberation time of the model. A recording of the sound was made at the desired receiver locations using a scaled dummy head and the results were played back at a scaled-down speed under anechoic conditions using two speakers. The sound of the model was then subjectively assessed and compared to that perceived in the real room. The technique—or variants of it—was used for the prediction of the acoustics of both large and small rooms throughout the 1970s, however, with computer systems becoming increasingly faster and more affordable auralization techniques based on computational models have been developed to yield an audible repre-

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sentation of the sound field at any specified receiver location by using the results of the acoustical modeling phase. Various implementations of auralization have been put into place24,25,26,27 at the time of this writing but because of the tremendous developments that are taking place in the field of auralization this section will only explore the general concepts associated with the topic of auralization since it is safe to say that specific implementations of auralization techniques will be subject to changes and additions dictated by new technological advances and/or by market demands. 9.3.1 The Basic Auralization Process The basic auralization process associated with an acoustical model is illustrated in Fig. 9-22. The process starts with the reflectograms representing the impulse response (IR) of the model obtained at a specific receiver location for various frequencies. The reflectograms contain the information pertaining to the intensity and the direction of arrival of the reflections over a period of time that is deemed suitable to record the desired order and length of the reflections, and they are obtained from any of the methodologies presented in the modeling portion of this chapter. The reflectograms are then convolved—or mixed—with a dry (anechoic) recording of speech or music that can be played back under controlled conditions, using either headphones or loudspeakers, for the purpose of subjective evaluation.

Since the reflectogram typically represents the impulse response at a single point (or within a small volume) in the modeled space, it must be modified in order to represent the binaural sound that would be reaching the eardrums of a listener by and at this point, two separate approaches are available.

9.3.2.1 Binaural Reproduction Using Loudspeakers The impulse response is divided into its left and right components corresponding to the vertical left and right planes crossing the receiver location, and thus yielding the binaural impulse response (BIR) of the room for a listener at the receiver location. The anechoic signal is convolved separately for the left and the right channel, and the result is presented under anechoic and/or near field conditions to a listener using loudspeakers as shown in Fig. 9-24. This technique has the advantage of being efficient from a computational standpoint since the process is limited to the separation of the IR into the BIR and the resulting convolution into left and right channels for the playback system. The drawback of the technique is that the playback requires a controlled environment where the listener has to maintain a fixed position with respect to the playback system and the crosstalk between the loudspeakers must be very small in order to yield the proper sense of spatial impression. 9.3.2.2 Binaural Reproduction Using Headphones

9.3.2 Implementation The energy reaching the listener is comprised of the direct sound, of the early reflections, and of the late reflections as shown in Fig. 9-23. The direct sound is easily found and modeled accurately in the reflectogram since it represents the energy traveling from source to receiver in a direct line of sight. The only concern for the accurate auralization of the direct sound is to insure that the attenuation follows the inverse-distance spreading law as dictated by the source configuration and directivity. The early reflections are also obtained from the modeling phase but the reflectogram must be limited in length—or in the order of the reflections—because of computational constraints. The late portion of the reflectogram is usually modeled from a dense and random pattern of reflections with a smooth decay and a frequency content patterned after the reverberation time of the room estimated at various frequencies.

In this approach, the BIR is further modified by the application of head-related transfer functions (HRTF) that represent the effects that the head, torso, shoulders, and ears will have on the sound that reaches the eardrums of the listener. It has been shown28,29 that these parameters have a drastic influence on the localization of the sound and on its overall subjective assessment. As shown in Fig. 9-25, the reproduction system must now use headphones since the effects of the body and head shape of the listener have already been taken into account. The advantage of this approach is that the playback system is very simple; good quality headphones are readily available and no special setup is required. The drawback is that the implementation of the modified BIR takes time due to the computational requirements for the application of the HRTF. It must also be noted that the HRTF may not accurately describe the specific parameters that a given listener experiences, although current HRTF research has yielded accurate

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Reflectogram at 16 kHz dB

Impulse response reflectograms

Reflectogram at 2 kHz Reflectogram at 1 kHz Reflectogram at 500 Hz Reflectogram at 250 Hz

Time

Reflectogram at 125 Hz dB

Time

Convolution engine (software and/or hardware)

Playback system

Anechoic music sample

Figure 9-22. The basic auralization process. Direct sound Discrete reflections (early and late) 80 dB Late reverberation

60 dB 40 dB 20 dB

0 ms

200 ms

Time

Figure 9-23. An example of a complete reflectogram at 1000 Hz.

composite data for a wide segment of the test results. Another issue of concern when using headphone reproduction is that the apparent source location will move with the listener’s head movements, something that does not take place in the real world. 9.3.2.3 Multichannel Reproduction Using Loudspeakers In this instance, the impulse response of the room is divided into components that correspond to the general locations in space from where the reflections originate as shown in Fig. 9-26. Various systems have been developed30,31 throughout the years ranging from just a few speakers to hundreds of units driven by dozens of

separate channels. The advantage of the technique is that the system relies on the listener’s own HRTF while also allowing for head tracking effects. From the perspective of efficiency the approach can be implemented with minimal hardware and software since the reflections can be categorized in terms of their direction of arrival while the IR is being generated. The multichannel reproduction technique can actually be implemented from a physical scale model without the need for computer tools by using delay lines and an analog matrix system.1 The reproduction system is, of course, rather complicated since it requires substantial hardware and an anechoic environment. 9.3.3 Real-Time Auralization and Virtual Reality A real-time auralization system allows the user to actually move within the room and to hear the resulting changes in the sound as they actually happen. This approach requires the near-instantaneous computation of the impulse response so that all parameters pertaining to the direct sound and to the reflections can be computed. In a recent implementation32 the space is modeled using an enhanced image method approach in which a fast ray-tracing preprocessing step is taken to check the visibility of the reflections at the receiver location. The air absorption and the properties of the surface materials are modeled using efficient digital filters, and the late reverberation is described using techniques that give a smooth and dense reflection pattern

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Convolution engine (software and/or hardware) Left plane impulse response

Left playback system (loudspeaker)

Impulse response reflectograms

Reflectogram at 16 kHz dB Reflectogram at 2 kHz Reflectogram at 1 kHz Reflectogram at 500 Hz Reflectogram at 250 Hz Time Reflectogram at 125 Hz dB

Anechoic music sample

Right playback system (loudspeaker)

Time

Right plane impulse response

Convolution engine (software and/or hardware)

Figure 9-24. Auralization with a binaural impulse response and speaker presentation.

Left HRTF

Convolution engine (software and/or hardware)

Left plane impulse response

Impulse response reflectograms

Reflectogram at 16 kHz dB Reflectogram at 2 kHz Reflectogram at 1 kHz Reflectogram at 500 Hz Reflectogram at 250 Hz Time Reflectogram at 125 Hz dB

Anechoic music sample

Left channel headphones

Right channel headphones Time

Right HRTF Right plane impulse response

Convolution engine (software and/or hardware)

Figure 9-25. Auralization with a HRTF binaural impulse response and headphone presentation.

that follows the statistical behavior of sound in a bounded space. The technique yields a parametric room

impulse response (PRIR) in which a combination of real-time and nonreal-time processes performs a model-

Acoustical Modeling and Auralization

Full range loudspeaker one per channel

Anechoic environment

Figure 9-26. Speaker arrangement for multichannel presentation. Adapted from Reference 29.

ing of the physical parameters that define the space. A diagram of the modeling and auralization process of this system is presented in Fig. 9-27. Room Geometry and Material Data

Nonreal-time analysis Difference Ray-tracing Measurements method

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account for the early portion of the reflections with a simpler static impulse response that provides the foundation for the calculation of the late part of the sound field. This approach is moderately efficient in terms of computational time and memory consumption and recent developments33 have been aimed at making use of an efficient means to process the impulse response of a space. Using an approach known as Ambisonics B-format34 the sound information is encoded into four separate channels labeled W, X, Y and Z. The W channel would be equivalent to the mono output from an omnidirectional microphone while the X, Y and Z channels are the directional components of the sound in front-back (X), left-right (Y), and up-down (Z) directions. This allows a single B-format file to be stored for each location to account for all head motions at this specific location and to produce a realistic and fast auralization as the user can move from one receiver location to the other and experience a near-seamless simulation even while turning his/her head in the virtual model.

9.4 Conclusion

Real-time synthesis Image-source method

Acoustical attributes of the room

Direct sound and early reflections

Artificial late reverberation

Auralization

Figure 9-27. A real-time interactive modeling and auralization system. Adapted from Reference 32.

In this approach, known as dynamic auralization, the presentation of the sound field can be done either via binaural headphones or by multi-channel speaker techniques and the auralization parameters must be updated at a fast rate (typically more than ten times per second) in order for the rendering to be of high quality. The impulse response that is used for the convolutions can be a combination of an accurate set of binaural responses (that map head-tracking movements) to

Acoustical modeling and auralization are topics of ongoing research and development. Originally planned for the evaluation of large rooms, the techniques have also been used in small spaces35 and in outdoor noise propagation studies36 and one can expect to witness the standard use of these representation tools in a wide range of applications aimed at assessing complex acoustical quantifiers. Even simple digital processing systems such as those offered as plug-ins for audio workstations can be used to illustrate the effect of frequency-dependent transmission loss from various materials using simple equalization and level settings corresponding to octave or third-octave band reduction data. Further work is needed in the representation and modeling of complicated sources such as musical instruments, automobiles, trains, and other forms of transportation; work is also ongoing in the definition of materials and surfaces so that the effect of vibrations and stiffness is accounted for. Still, the models are rapidly becoming both very accurate and very efficient and they are demonstrating their adequacy at illustrating the complicated issues that are associated with sound propagation and, eventually, sound perception.

236

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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Makrinenko, Leonid I. “Acoustics of Auditoriums in Public Buildings.” First Publication: 1986 (Russian). Acoustical Society of America (1994) Translated by R.S. Ratner. J.S. Bradley, Editor. Pierce, Allan D. Acoustics. “An Introduction to Its Physical Principles and Applications.” Acoustical Society of America, 1991, 2nd printing. Allen, J. B. and Berkley, D. A. “Image Method for Efficiently Simulating Small-Room Acoustics.” Journal of the Acoustical Society of America, 65 (4). 943-950, 1979. Barish, J. “Extension of the Image Method to Arbitrary Polyhedra.” Journal of the Acoustical Society of America, 75 (6). 1827-1836, 1984. Vorländer, M. “Simulation of the Transient and Steady-State Sound Propagation in Rooms Using a New Combined Ray-Tracing/Image Source Algorithm.” Journal of the Acoustical Society of America, 86 (1). 172-178, 1989. Drumm, I. A., and Lam, Y. M. “The Adaptive Beam Tracing Algorithm.”Journal of the Acoustical Society of America, 107 (3). 1405-1412, 2000. Min, P., and Funkhouser, T. “Priority-Driven Acoustic Modeling for Virtual Environments.” Eurographics 2000, 19 (3), 2000. Dalenbäck Bengt-Inge. “The rediscovery of diffuse reflection in room acoustics prediction.” A presentation to the 144th Meeting of the Acoustical Society of America, Cancun, 2002. Bradley, J. S. “Architectural research today.” Bahar, E. “Acoustic Scattering by Two-Dimensionally Rough Interfaces between Dissipative Acoustic Media. Full-Wave, Physical Acoustics, and Perturbation Solutions.” Journal of the Acoustical Society of America, 89 (1). 19-26, 1991. Kane, J. Boundary Elements Analysis, Prentice Hall, 1994. COMET/Acoustics, User Document V.2.1. Automated Analysis Corporation, 1994. Cox, T. J. “Predicting the Scattering from Diffusers Using 2-D Boundary Element Methods.” Journal of the Acoustical Society of America, 96 (1). 874-878, 1994. D’Antonio, P., and Cox, T. “Two Decades of Sound Diffusor Design and Development. Part 2: Prediction, Measurements, and Characterization.” Journal of the Audio Engineering Society, 46 (12) 1075-1091, 1998. Botteldooren, D. “Finite-Difference Time-Domain Simulations of Low-Frequency Room Acoustics Problems.” Journal of the Acoustical Society of America, 8 (6). 3302-3309, 1995. Lalor, N. “Statistical Energy Analysis and Its Use as an NVH Analysis Tool.” Sound & Vibration,30 (1). 16-20, 1996. CARA (Computer-Aided-Room-Acoustics) software, from www.cara.de, Version 2.2. Bradley, J. S. “Sound Absorption of Gypsum Board Cavity Walls.” Journal of the Audio Engineering Society, 45 (4), 253-259, 1997. Cook, D., and Van Haverbeke, D. “Trees and Shrubs for Noise Abatement.” Research Bulletin 246. The Forest Service, U.S. Department of Agriculture cooperating with the University of Nebraska College of Agriculture, 1971. Probst, W., and Huber, B. “Calculation and Assessment of Traffic Noise Exposure.” Sound and Vibration, 07/00 pp.16-20, 2000. BASTIAN software, from DataKustic, Germany. Kleiner, M., Dalenbäck, B.-I., and Svensson, P. “Auralization — An Overview.” Journal of the Audio Engineering Society, 41 (11): 861-875, 1993. Adapted from reference 1, Chapter 4, section 4, pp. 106, endnote [43]. CATT-Acoustics, from B.I. Dalenbäck ODEON, from Ørsted DTU EARS, from ADA (Acoustic Design Ahnert) DIVA, from the DIVA Group Wightman, F. L., and Kistler, D. J. “Headphone Simulation of Free-Field Listening. I: Stimulus Synthesis.” Journal of the Audio Engineering Society, 85 (2). 858-867, 1989.

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29. Wightman, F. L., and Kistler, D. J. “Headphone Simulation of Free-Field Listening. II: Psychological Validation.” Journal of the Audio Engineering Society, 85 (2). 868-878, 1989. 30. Camras, M. “Approach to Recreating a Sound Field.” Journal of the Acoustical Society of America, 43 (6). 1425-1431, 1968. 31. Ono, K., Komiyama, S., and Nakabayashi, K. “A Method of Reproducing Concert Hall Sounds by Loudspeaker Walls.” Journal of the Acoustical Society of America, 46 (11). 988-995, 1998. 32. Savioja, L. Modeling Techniques for Virtual Acoustics. Ph.D. Dissertation, 2000. 33. Dalenbäck Bengt-Inge and Strömberg, M. “Real time walkthrough auralization – The first year.” Proceedings of the Institute of Acoustics, 28 (2), 2007. 34. From Wikipedia reference on Ambisonics 35. Granier, E., Kleiner, M., Dalenbäck, B.-I., and Svensson, P. “Experimental Auralization of Car Audio Installations.” Journal of the Audio Engineering Society, 44 (10): 835-849, 1996. 36. Cadna A. “Computer Program for the Calculation and Assessment of Outdoor Noise Immissions.” User Document, DataKustic GmbH, 2000.

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Part 2

Electronic Components

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Chapter

Resistors, Capacitors, and Inductors by Glen Ballou 10.1 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.1 Resistor Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Combining Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.3 Types of Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Network Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.3 Characteristics of Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4 Types of Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.1 Film Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.2 Paper Foil-Filled Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.3 Mica Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.4 Ceramic Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.5 Electrolytic Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.6 Suppression Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.4.7 Supercapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Types of Inductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.1 Air Core Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.2 Axial Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.3 Bobbin Core Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.4 Ceramic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.5 Epoxy-Coated Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.6 Ferrite Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.7 Laminated Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.8 Molded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.9 MPP Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.10 Multilayer Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.11 Phenolic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.12 Powdered Iron Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.13 Radial Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.14 Shielded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.15 Slug Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.16 Tape Wound Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.17 Toroidal Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 Impedance Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

241

243 243 246 247 251 253 253 253 255 256 257 257 257 257 261 262 263 263 263 263 263 263 264 264 264 264 264 264 264 264 265 265 265 265 265 265

10.3.3 Ferrite Beads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.4 Skin Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.5 Shielded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Resonant Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

242

268 268 268 268 270 272

Resistors, Capacitors, and Inductors 10.1 Resistors Resistance is associated with the phenomenon of energy dissipation. In its simplest form, it is a measure of the opposition to the flow of current by a piece of electric material. Resistance dissipates energy in the form of heat; the best conductors have low resistance and produce little heat, whereas the poorest conductors have high resistance and produce the most heat. For example, if a current of 10 A flowed through a resistance of 1 :, the heat would be 100 W. If the same current flowed through 100 : , the heat would be 10,000 W, which is found with the equation

P = I R where, P is the power in watts, I is the current in amperes, R is the resistance in ohms.

(10-1)

In a pure resistance—i.e. one without inductance or capacitance—the voltage and current phase relationship remains the same. In this case the voltage drop across the resistor is V = IR where, V is the voltage in volts, I is the current in amperes, R is the resistance in ohms.

(10-2)

All resistors have one by-product in common when put into a circuit, they produce heat because power is dissipated any time a voltage, V, is impressed across a resistance R. This power is calculated from Eq. 10-1 or 2

VP = ----R where, P is the power in watts, V is the voltage in volts, R is the resistance in ohms.

(10-3)

Changing the voltage, while holding the resistance constant, changes the power by the square of the voltage. For instance, a voltage change from 10 V to 12 V increases the power 44%. Changing the voltage from 10 V to 20 V increases the power 400%. Changing the current while holding the resistance constant has the same effect as a voltage change. Changing the current from 1 A to 1.2 A increases the

243

power 44%, whereas changing from 1 A to 2 A increases the power 400%. Changing the resistance while holding the voltage constant changes the power linearly. If the resistance is decreased from 1 k: to 800 : and the voltage remains the same, the power will increase 20%. If the resistance is increased from 500 : to 1 k:, the power will decrease 50%. Note that an increase in resistance causes a decrease in power. Changing the resistance while holding the current constant is also a linear power change. In this example, increasing the resistance from 1 k: to 1.2 k: increases the power 20%, whereas increasing the resistance from 1 k: to 2 k: increases the power 100%. It is important in sizing resistors to take into account changes in voltage or current. If the resistor remains constant and voltage is increased, current also increases linearly. This is determined by using Ohm’s Law, Eq. 10-1 or 10-3. Resistors can be fixed or variable, have tolerances from 0.5% to 20%, and power ranges from 0.1 W to hundreds of watts 10.1.1 Resistor Characteristics Resistors will change value as a result of applied voltage, power, ambient temperature, frequency change, mechanical shock, or humidity. The values of the resistor are either printed on the resistor, as in power resistors, or are color coded on the resistor, Fig. 10-1. While many of the resistors in Fig. 10-1 are obsolete, they are still found in grandma’s old radio you are asked to repair. Voltage Coefficient. The voltage coefficient is the rate of change of resistance due to an applied voltage, given in percent parts per million per volt (%ppm/V). For most resistors the voltage coefficient is negative—that is, the resistance decreases as the voltage increases. However, some semiconductor devices increase in resistance with applied voltage. The voltage coefficient of very high valued carbon-film resistors is rather large and for wirewound resistors is usually negligible. Varistors are resistive devices designed to have a large voltage coefficient. Temperature Coefficient of Resistance. The temperature coefficient of resistance (TCR) is the rate of change in resistance with ambient temperature, usually stated as parts per million per degree Celsius (ppm/°C). Many types of resistors increase in value as the temperature increases, while others, particularly hot-molded carbon types, have a maximum or minimum in their resistance

244

Chapter 10

Miniature Resistor System 1st significant figure 2nd significant figure

Multiplier

Dot Band System Tolerance Multiplier

Tolerance

1st significant figure 1st significant figure 2nd significant figure 2 significant figure Body Dot System nd

Multiplier 2nd significant figure 1st significant figure Body-End-Dot System Tolerance Multiplier

2nd significant figure 1st significant figure Body-End Band System Tolerance Multiplier

2nd significant figure 1st significant figure Color Band System Carbon composition Carbon film Multiplier Tolerance Multiplier Tolerance

3rd significant figure 2nd significant figure 1st significant figure Resistors with black body are composition, noninsulated. Resistors with colored body are composition, insulated. Wirewound resistors have the 1st color band double width. Color Digit Multiplier Tolerance Failure Rate

1 0 Black 1.0 ±1% 10 1 Brown 0.1 ±2% 100 2 Red 0.01 ±3% 1000 3 Orange 0.001 ±4% 10,000 4 Yellow

100,000 5 Green

1,000,000 6 Blue

10,000,000 7 Violet

8 100,000,000 Gray Solderable*

9 White

±5% 0.1 Gold

±10% 0.01 Silver ±20% No Color 2nd significant figure 1st significant figure

Figure 10-1. Color codes for resistors.

curves that gives a zero temperature coefficient at some temperature. Metal film and wirewound types have temperature coefficient values of less than 100 ppm/°C. Thermistors are resistance devices designed to have a large temperature coefficient. The percent temperature coefficient of resistance is R – r 100TCR = ------------------------- T R – T T R

(10-4)

where, TCR is the temperature coefficient in percent per °C, R is the resistance at reference temperature, r is the resistance at test temperature, TR is the reference temperature in °C, TT is the test temperature in °C. It is better to operate critical resistors with a limited temperature rise. Noise. Noise is an unwanted voltage fluctuation generated within the resistor. The total noise of a resistor always includes Johnson noise, which depends only on resistance value and the temperature of the resistance element. Depending on the type of element and its construction, total noise may also include noise caused by current flow and by cracked bodies and loose end caps or leads. For adjustable resistors, noise is also caused by the jumping of the contact over turns of wire and by an imperfect electrical path between the contact and resistance element. Hot-Spot Temperature. The hot-spot temperature is the maximum temperature measured on the resistor due to both internal heating and the ambient operating temperature. The maximum allowable hot-spot temperature is predicated on the thermal limits of the materials and the resistor design. The maximum hot-spot temperature may not be exceeded under normal operating conditions, so the wattage rating of the resistor must be lowered if it is operated at an ambient temperature higher than that at which the wattage rating was established. At zero dissipation, the maximum ambient temperature around the resistor may be its maximum hot-spot temperature. The ambient temperature for a resistor is affected by surrounding heat-producing devices. Resistors stacked together do not experience the actual ambient temperature surrounding the outside of the stack except under forced cooling conditions. Carbon resistors should, at most, be warm to touch, 40°C (140°F), while wirewound or ceramic resistors are designed to operate at temperatures up to 140°C (284°F). Wherever power is dissipated, it is imperative that adequate ventilation is provided to eliminate

Resistors, Capacitors, and Inductors

Power Coefficient. T h e p o w e r c o e f f i c i e n t i s t h e product of the temperature coefficient of resistance and the temperature rise per watt. It is given in percent per watt (%/W), and is the change in value resulting from applied power. Ac Resistance. The ac resistance value changes with frequency because of the inherent inductance and capacitance of the resistor plus the skin effect, eddy current losses, and dielectric loss. Ambient Temperature Effect. W h e n o p e r a t i n g a resistor in free air at high ambient temperature, the power capabilities must be derated, Fig. 10-2. Free air is operation of a resistor suspended by its terminals in free space and still air with a minimum clearance of one foot in all directions to the nearest object.

12 1 inch space 11 2 inch space

10 9 Number of resistors in group

thermal destruction of the resistor and surrounding components.

245

8 3/ 4

inch space

6 5 4 3

2 100

1 40

U.L. - NEMA - Industrial Standard

Figure 10-3. Power derating for grouping resistors. Courtesy Ohmite Mfg. Co.

material and ventilation. Fig. 10-4 indicates the effects on a resistor enclosed in an unpainted steel sheet metal box, 0.32 inches thick without vents. Determining the derating is often by trial and error.

40 Mil R-26

300

500 A

20 Temperature rise—oC

400

200

0 40 80 120 160 200 240 280 320 360 400 Ambient temperature rise—oC

Figure 10-2. Resistor derating for elevated ambient temperature. Courtesy Ohmite Mfg. Co.

Grouping. Mounting a number of resistors in close proximity can cause excessive temperature rise requiring derating the power capabilities, Fig 10-3. The curves are for operation at maximum permissible hot spot temperature with spacing between the closest points of the resistors. Derating could be less if operated at less than permissible hot spot temperature. Enclosure. Enclosures create a rise in temperature due to the surface area, size, shape, orientation, thickness,

300 C 200

100 D

100

Temperature rise—oF

% rated wattage

60 65 70 75 80 85 90 95 100 % of single unit free air rating

E 0

50 75 100 0 % rated load A. Resistor in 33/8 inch × 33/8 inch × 8 inch box. B. Resistor in 513/16 inch × 513/16 inch × 123/4 inch box. C. Resistor in free air. D. Box temperature—small. E. Box temperature—large. F. Unpainted sheet metal box, 0.32 inch thick steel, no vents. 0

Figure 10-4. Effect of the size of an enclosure on a 500 W 3/ inch × 61/ inch resistor. Courtesy of Ohmite Mfg. Co. 4 2

246

Chapter 10

Forced Air Cooling. Resistors and components can be operated at higher than rated wattage with forced air cooling, Fig. 10-5. The volume of cooling air required to keep the resistor temperature within limits can be found with the equation 3170 Volume of air = ------------ KW (10-5) 'T where, Volume of air is in cubic feet per minute, 'T is the permissible temperature rise in degrees F, KW is the power dissipated inside the enclosure in kilowatts. 400

15 30 15 45 15 75 10 70 5 75 0

200

10 7 5 3 2 1 1

150 1500

Figure 10-5. Percent of free air rating for a typical resistor cooled by forced air. Courtesy of Ohmite Mfg. Co.

Air density at high altitudes causes less heat to be dissipated by convection so more forced air would be required. Pulse Operation. A resistor can usually be operated with a higher power in the pulse mode than in a continuous duty cycle. The actual increase allowed depends on the type of resistor. Fig. 10-6 is the percent of continuous duty rating for pulse operation for a wirewound resistor. Fig. 10-7 is the percent of continuous duty rating for pulse operation for typical NEMA duty cycles. Fig. 10-8 shows the percent of continuous duty rating for pulse operation of a 160 W vitreous enameled resistor. 10.1.2 Combining Resistors

200%

1000% 500% 2

5 710 20

50 100 200 500 1k 2k Off time—s

5k 10k

Figure 10-7. Percent of continuous duty rating for pulse operation of small and medium size vitreous enameled resistors. Courtesy of Ohmite Mfg. Co. 1000 700 500 300 200

125% 150%

On time—s

500 1000 Air velocity—ft/min

125%

10 W 50 W

100 70 50 30 20

250

300 400 500 600 700 800 % of rated load

Figure 10-6. Effect of pulse operation on wirewound resistors. Courtesy of Ohmite Mfg. Co.

On time—s

300

100 0

100 200

1000 700 500 300 200

350 % rated watts

Seconds On Off 15 15

100 70 50 30 20 10 7 5 3 2 1 1

200% 500% !000%

5 710 20

50 100 200 500 1k 2k Off time—s

5k 10k

Figure 10-8. Percent of continuous duty rating for pulse operation of a 160 W vitreous enameled resistor. Courtesy of Ohmite Mfg. Co.

Resistors can be combined is series or parallel or series/parallel.

R T = R 1 + R 2 + }R n

Resistors in series. The total resistance of resistors connected in series is the summation of the resistors.

The total resistance is always greater than the largest resistor.

(10-6)

Resistors, Capacitors, and Inductors Resistors in Parallel. The total resistance of resistors in parallel is 1 R T = ---------------------------------------1 1 1 ------ + ------ + } -----R R1 R2 n

(10-7)

If two resistors are in parallel use: R1 u R2 R T = ----------------R1 + R2

(10-8)

When all of the resistors are equal, divide the value of one resistor by the number of resistors to determine the total resistance. The total resistance is always less than the smallest resistor. To determine the value of one of the resistors when two are in parallel and the total resistance and one resistor in known, use RT u R1 R 2 = ----------------R1 – RT

(10-9)

10.1.3 Types of Resistors Every material that conducts electrical current has resistivity, which is defined as the resistance of a material to electric current. Resistivity is normally defined as the resistance, in ohms, of a 1 cm per side cube of the material measured from one surface of the cube to the opposite surface. The measurement is stated in ohms per centimeter cubed (:/cm3). The inverse of resistivity is conductivity. Good conductors have low resistivity, and good insulators have high resistivity. Resistivity is important because it shows the difference between materials and their opposition to current, making it possible for resistor manufacturers to offer products with the same resistance but differing electrical, physical, mechanical, or thermal features. Following is the resistivity of various materials: Material Aluminum Copper Nichrome Carbon (varies) Ceramic (typical)

Resistivity 0.0000028 0.0000017 0.0001080 0.0001850 100,000,000,000,000 or (1014)

Carbon-Composition Resistors. Carbon-composition resistors are the least expensive resistors and are widely

247

used in circuits that are not critical to input noise and do not require tolerances better than r5%. The carbon-composition, hot-molded version is basically the same product it was more than 50 years ago. Both the hot- and cold-molded versions are made from a mixture of carbon and a clay binder. In some versions, the composition is applied to a ceramic core or armature, while in the inexpensive version, the composition is a monolithic rigid structure. Carbon-composition resistors may be from 1 : to many megohms and 0.1–4 W. The most common power rating is ¼ W and ½ W with resistance values from 2 :–22 M: . Carbon-composition resistors can withstand higher surge currents than carbon-film resistors. Resistance values, however, are subject to change upon absorption of moisture and increase rapidly at temperatures much above 60°C (140°F). Noise also becomes a factor when carbon-composition resistors are used in audio and communication applications. A carbon-core resistor, for example, generates electrical noise that can reduce the readability of a signal or even mask it completely. Carbon-Film Resistors. Carbon-film resistors are leaded ceramic cores with thin films of carbon applied. Carbon film resistors offer closer tolerances and better temperature coefficients than carbon composition resistors. Most characteristics are virtually identical for many general purpose, noncritical applications where high reliability, surge currents, or noise are not crucial factors. Metal Film Resistors. Metal film resistors are discrete devices formed by depositing metal or metal oxide films on an insulated core. The metals are usually either nichrome sputtered on ceramic or tin oxide on ceramic or glass. Another method of production is to screen or paint powdered metal and powdered glass that is mixed in an ink or pastelike substance on a porous ceramic substrate. Firing or heating in an oven bonds the materials together. This type of resistor technology is called cermet technology. Metal film resistors are most common in the 10 :to 1 M: range and 1e8 W to 1 W with tolerances of r1%. The TCR is in the r100 ppm/°C range for all three technologies. Yet there are subtle differences: • Cermet covers a wider resistance range and handles higher power than nichrome deposition. • Nichrome is generally preferred over tin oxide in the upper and lower resistance ranges and can provide TCRs that are lower than 50 ppm/°C. • Tin oxide is better able to stand higher power dissipation than nichrome.

248

Chapter 10

Wirewound Resistors. Wire wound re sistor s h av e resistive wire wound on a central ceramic core. One of the oldest technologies, wirewounds provide the best known characteristics of high temperature stability and power handling ability. Nichrome, Manganin, and Evanohm are the three most widely used wires for wirewound resistors. Wi r e w o u n d r e s i s t o r s a r e u s u a l l y i n t h e 0.1 :–250 k: range. Tolerance is r2% and TCR is r10 ppm/°C. Wirewound resistors are generally classed as power or instrument-grade products. Power wirewounds, capable of handling as much as 1500 W, are wound from uninsulated coarse wire to provide better heat dissipation. Common power ratings are 1.5 W, 3 W, 5 W, 8 W, 10 W, 20 W, 25 W, 50 W, 100 W, and 200 W. Instrument-grade precision wirewound resistors are made from long lengths of finely insulated wire. After winding, they are usually coated with a ceramic material. All wirewound resistors are classed as air-core inductors and the inductive reactance alters the high frequency resistive value. This problem is directly proportional with frequency. Special windings are useful to cancel reactance at audio frequencies. Because of the severity of the problem, these resistors cannot be used at high frequencies. Noninductive Resistors. Non-inductive resistors are used for high frequency applications. This is accomplished by utilizing the Ayrton-Perry type of wiring, i.e. two windings connected in parallel and wound in opposite directions. This keeps the inductance and distributed capacitance at a minimum. Table 10-1 is a comparison of MEMCOR-TRUOHM type FR10, FR50, VL3 and VL5 resistors. Resistor Networks. With the advent of printed circuit boards and integrated circuits, resistor networks became popular. The resistive network may be mounted in a single-in-line package (SIP) socket or a dual-in-line package (DIP) socket—the same as the ones used for integrated circuits. The most common resistor network has 14 or 16 pins and includes 7 or 8 individual resistors or 12 to 15 resistors with a common terminal. In most resistor networks the value of the resistors are the same. Networks may also have special value resistors and interconnections for a specific use, as shown in Fig. 10-9. The individual resistors in a thick-film network can have a resistance value ranging from 10 : to 2.2 M: and are normally rated at 0.125 W per resistor. They have normal tolerances of r2% or better and a tempera-

Table 10-1. Inductance Comparison of Standard and Non-Inductive Windings. Approximate Frequency Effect Stock inductive winding Type

FR10 (10 W)

FR50 (50 W)

VL3 (3 W)

VL5 (5 W)

Resistance (:)

LS (H)

Non-inductive winding LS (H)

CP (F)

5.8

0.01

–

100

11.0

0.16

–

500

18.7

0.02

–

1000

20.8

–

0.75

5000

43.0

–

1.00

6.8

0.05

–

100

>100.0

0.40

–

500

>100.0

0.31

–

1000

>100.0

–

1.10

5000

>100.0

–

1.93

1.2

0.02

–

100

1.6

0.07

–

500

4.9

–

0.47

1000

4.5

–

0.70

5000

3.0

–

1.00

2.5

0.08

–

100

5.6

0.14

–

500

6.4

–

0.03

1000

16.7

–

0.65

5000

37.0

–

0.95

Courtesy Ohmite Mfg. Co.

ture coefficient of resistance r100 ppm/°C from 55°C to +125°C (67°F to +257°F). Thin-film resistors are almost always specialized units and are packaged as DIPs or flatpacks. (Flatpacks are soldered into the circuit.) Thin-film networks use nickel chromium, tantalum nitride, and chromium cobalt vacuum depositions. Variable Resistors. Variable resistors are ones whose value changes with light, temperature, or voltage or through mechanical means. Photocells (Light-Sensitive Resistors). Photocells are used as off–on devices when a light beam is broken or as audio pickups for optical film tracks. In the latter, the sound track is either a variable density or variable area. Whichever, the film is between a focused light source and the photocell. As the light intensity on the photocell varies, the resistance varies.

Resistors, Capacitors, and Inductors

Figure 10-9. Various types of resistor networks.

Photocells are rated by specifying their resistance at low and high light levels. These typically vary from 600 :–110 k: (bright), and from 100 k:–200 M: (dark). Photocell power dissipation is between 0.005 W and 0.75 W. Thermistors. Thermistors, thermal-sensitive resistors, may increase or decrease their resistance as temperature rises. If the coefficient of resistance is negative, the resistance decreases as the temperature increases; if positive, the resistance increases with an increase in temperature. Thermistors are specified by how their resistance changes for a 1°C change in temperature. They are also rated by their resistance at 25°C and by the ratio of resistance at 0°C and 50°C. Values vary from 2.5 :–1 M: at room temperature with power ratings from 0.1–1 W. Thermistors are normally used as temperature-sensing devices or transducers. When used with a transistor, they can be used to control transistor current with a change in temperature. As the transistor heats up, the emitter-to-collector current increases. If the power supply voltage remains the same, the power dissipation in the transistor increases until it destroys itself through thermal runaway. The change in resistance due to temperature

249

change of the thermistor placed in the base circuit of a transistor can be used to reduce base voltage and, therefore, reduce the transistor emitter to collector current. By properly matching the temperature coefficients of the two devices, the output current of the transistor can be held fairly constant with temperature change. Varistors. Varistors (voltage-sensitive resistors) are voltage-dependent, nonlinear resistors which have symmetrical, sharp breakdown characteristics similar to back-to-back Zener diodes. They are designed for transient suppression in electrical circuits. The transients can result from the sudden release of previously stored energy—i.e., electromagnetic pulse (EMP)—or from extraneous sources beyond the control of the circuit designer, such as lightning surges. Certain semiconductors are most susceptible to transients. For example, LSI and VLSI circuits, which may have as many as 20,000 components in a 0.25 inch × 0.25 inch area, have damage thresholds below 100 μJ. The varistor is mostly used to protect equipment from power-line surges by limiting the peak voltage across its terminals to a certain value. Above this voltage, the resistance drops, which in turn tends to reduce the terminal voltage. Voltage-variable resistors or varistors are specified by power dissipation (0.25 –1.5 W) and peak voltage (30–300 V). Thermocouples. While not truly a resistor, thermocouples are used for temperature measurement. They operate via the Seebeck Effect which states that two dissimilar metals joined together at one end produce a voltage at the open ends that varies as the temperature at the junction varies. The voltage output increases as the temperature increases. Thermocouples are rugged, accurate, and have a wide temperature range. They don’t require a exitation source and are highly responsive. Thermoouples are tip sensitive so they measure the temperature at a very small spot. Their output is very small (tens to hundreds of microvolts, and is nonlinear, requiring external linearization in the form of cold-junction compensation. Never use copper wire to connect a thermocouple to the measureing device as that constitutes another thermocouple. Resistance Temperature Detectors. RT D s a r e v e r y accurate and stable. Most are made of platinum wire wound around a small ceramic tube. They can be thermally shocked by going from 100qC to 195qC 50 times with a resulting error less than 0.02qC. RTDs feature a low resistance-value change to temperature (0.1 :1qC. RTDs can self heat, causing

Chapter 10

inaccurate readings, therefore the current through the unit should be kept to 1 mA or less. Self heating can also be controlled by using a 10% duty cycle rather than constant bias or by using an extremely low bias which can reduce the SNR. The connection leads may cause errors if they are long due to the wire resistance. Potentiometers and Rheostats. T h e r e s i s t a n c e o f potentiometers (pots), and rheostats is varied by mechanically varying the size of the resistor. They are normally three terminal devices, two ends and one wiper, Fig. 10-10. By varying the position of the wiper, the resistance between either end and the wiper changes. Potentiometers may be wirewound or nonwirewound. The nonwirewound resistors usually have either a carbon or a conductive plastic coating. Potentiometers or pots may be 300° single turn or multiple turn, the most common being 1080° three turn and 3600° ten turn.

High Low Wiper

Wiper

High Low

Low

Rear view

100 90 100 % resistance

250

Percent counter-clockwise rotation 80 70 60 50 40 30 20

60 C3 40

C4 C2

20 0

0 10 20 Left terminal

80 90 100 Right terminal

Percent clockwise rotation

C1. Linear taper, general-purpose control for television picture adjustments. Resistance proportional to shaft rotation. C2. Left-hand semilog taper for volume and tone controls. 10% of resistance at 50% rotation. C3. Right-hand semilog taper, reverse of C2. 90% of resistance at 50% of rotation. C4. Modified left-hand semilog taper for volume and tone controls. 20% of resistance at 50% of rotation. C5. Modified right-hand semilog taper, reverse of C4. 80% of resistance at 50% of rotation. C6. Symmetrical straight-line taper with slow resistance change at either end. Used principally as tone control or balance control.

Figure 10-11. Tapers for six standard potentiometers in resistivity versus rotation.

Figure 10-10. Three terminal potentiometer.

Wirewound pots offer TCRs of r50 ppm/°C and tolerances of r5%. Resistive values are typically 10 :–100 k:, with power ratings from 1 W to 200 W. C a r b o n p o t s h a v e T C R s o f r 4 0 0 p p m / °C t o r800 ppm/°C and tolerances of r20%. The resistive range spans 50 :–2 M:, and power ratings are generally less than 0.5 W. Potentiometers may be either linear or nonlinear, as shown in Fig. 10-11. The most common nonlinear pots are counterclockwise semilog and clockwise semilog. The counterclockwise semilog pot is also called an audio taper pot because when used as a volume control, it follows the human hearing equal loudness curve. If a linear pot is used as a simple volume control, only about the first 20% of the pot rotation would control the usable volume of the sound system. By using an audio taper pot as in Fig. 10-11 curve C2, the entire pot is used. Note there is only a 10%–20% change in resistance value between the common and wiper when the pot is 50% rotated. Potentiometers are also produced with various taps that are often used in conjunction with loudness controls.

Potentiometers also come in combinations of two or more units controlled by a single control shaft or controlled individually by concentric shafts. Switches with various contact configurations can also be assembled to single or ganged potentiometers and arranged for actuation during the first few degrees of shaft rotation. A wirewound potentiometer is made by winding resistance wire around a thin insulated card, Fig. 10-12A. After winding, the card is formed into a circle and fitted around a form. The card may be tapered, Fig. 10-12B, to permit various rates of change of resistance as shown in Fig 10-11. The wiper presses along the wire on the edge of the card. Contact Resistance. Noisy potentiometers have been a problem that has plagued audio circuits for years. Although pots have become better in tolerance and construction, noise is still the culprit that forces pots to be replaced. Noise is usually caused by dirt or, in the case of wirewound potentiometers, oxidation. Many circuits have gone up in smoke because bias-adjusting resistors, which are wirewound for good TCR, oxidize and the contact resistance increases to a point where it is more than the value of the pot. This problem is most

Resistors, Capacitors, and Inductors

Wiper

251

RLeakage C1 C2

R1 Vin End view A. Fixed card wirewound resistor. Wiper

V1 R2

RW VW

RLoad VLoad

Figure 10-13. Effects of wiper noise on potentiometer output.

10.2 Capacitors B. Tapered card wirewound resistor.

Figure 10-12. Construction of a wirewound resistor.

noticeable when trying to adjust a bias voltage with an old oxidized pot. Sometimes the pot can be cleaned by spraying it with a contact cleaner or silicone and then vigorously rotating it. Usually, however, it is best to replace it because anything else is only temporary. Any dc voltage present on the pot is also a source of noise. Such voltage is often produced by leaky coupling capacitors at the input connector or output circuit of the wiper, allowing dc voltage to appear at the wiper contact. If there is a resistance between the resistor and the wiper, the dc current flowing through the wiper contact to the output stage will create a voltage drop. Because the wiper is moving, the contact resistance constantly changes creating what looks like a varying ac voltage. Using Fig. 10-13, the value at VLoad, whether ac or dc, can be calculated with Eqs. 10-10 and 10-11. If the wiper resistance is 0—i.e., a perfect pot—the output voltage VLoad is V Load

Ry = V 1 § ------------------· © R 1 + R y¹

(10-10)

where, R 2 R Load R y = ------------------------R 2 + R Load If a pot wiper has a high resistance, Rw, the output voltage VLoad is R Load · V Load = V w § -------------------------© R w + R Load¹ where, R 2 R w + R Load V w = V 1 § ---------------------------------------· . © R 2 + R w + R Load¹

(10-11)

Capacitors are used for both dc and ac applications. In dc circuits they are used to store and release energy such as filtering power supplies and for providing on demand, a single high voltage pulse of current. In ac circuits capacitors are used to block dc, allowing only ac to pass, bypassing ac frequencies, or discriminating between higher and lower ac frequencies. In a circuit with a pure capacitor, the current will lead the voltage by 90°. The value of a capacitor is normally written on the capacitor and the sound engineer is only required to determine their effect in the circuit. Where capacitors are connected in series with each other, the total capacitance is 1 C T = ---------------------------------------1 } 1 1 ------ + -----+ -----Cn C1 C2

(10-12)

and is always less than the value of the smallest capacitor. When connected in parallel, the total capacitance is CT = C1 + C2 } + Cn

(10-13)

and is always larger than the largest capacitor. When a dc voltage is applied across a group of capacitors connected in series, the voltage drop across the combination is equal to the applied voltage. The drop across each individual capacitor is inversely proportional to its capacitance, and assuming each capacitor has an infinitely large effective shunt resistance, can be calculated by the equation CX V C = V A § ------· © C T¹

(10-14)

where, VC is the voltage across the individual capacitor in the series (C1, C2, Cn) in volts,

252

Chapter 10

VA is the applied voltage in volts, CX is the capacitance of the individual capacitor under consideration in farads, CT is the sum of all of the capacitors in series. When used in an ac circuit, the capacitive reactance, or the impedance the capacitor injects into the circuit, is important to know and is found with the equation: 1 X C = -----------2SfC where, XC is the capacitive reactance in ohms, f is the frequency in hertz, C is the capacitance in farads.

(10-15)

To determine the impedance of circuits with resistance, capacitance, and inductance, see Section 10.4. Capacitance is the concept of energy storage in an electric field. If a potential difference is found between two points, an electric field exists. The electric field is the result of the separation of unlike charges, therefore, the strength of the field will depend on the amounts of the charges and their separator. The amount of work necessary to move an additional charge from one point to the other will depend on the force required and therefore upon the amount of charge previously moved. In a capacitor, the charge is restricted to the area, shape, and spacing of the capacitor electrodes, sometimes known as plates, as well as the property of the material separating the plates. When electrical current flows into a capacitor, a force is established between two parallel plates separated by a dielectric. This energy is stored and remains even after the input current flow ceases. Connecting a conductor across the capacitor provides a plate-to-plate path by which the charged capacitor can regain electron balance, that is, discharge its stored energy. This conductor can be a resistor, hard wire, or even air. The value of a parallel plate capacitor can be found with the equation > N – 1 A -@ u10– 13 (10-16) C = xH ------------------------------d where, C is the capacitance in farads, x is 0.0885 when A and d are in cm, and 0.225 when A and d are in inches, H is the dielectric constant of the insulation, N is the number of plates, A is the area of the plates, d is the spacing between the plates.

The work necessary to transport a unit charge from one plate to the other is (10-17) e = kg where, e is the volts expressing energy per unit charge, k is the proportionality factor between the work necessary to carry a unit charge between the two plates and the charge already transported and is equal to 1/C where C is the capacitance in farads, g is the coulombs of charge already transported. The value of a capacitor can now be calculated from the equation q C = --e where, q is the charge in coulombs, e is found with Eq. 10-17.

(10-18)

The energy stored in a capacitor is found with the equation 2

---------W = CV 2 where, W is the energy in joules, C is the capacitance in farads, V is the applied voltage in volts.

(10-19)

Dielectric Constant (K). The dielectric constant is the property of a given material that determines the amount of electrostatic energy that may be stored in that material per unit volume for a given voltage. The value of K expresses the ratio of a capacitor in a vacuum to one using a given dielectric. The K of air is 1 and is the reference unit employed for expressing K of other materials. If K of the capacitor is increased or decreased, the capacitance will increase or decrease respectively if other quantities and physical dimensions are kept constant. Table 10-2 is a listing of K for various materials. Table 10-2. Comparison of Capacitor Dielectric Constants Dielectric Air or vacuum Paper Plastic Mineral oil Silicone oil

K (Dielectric Constant) 1.0 2.0–6.0 2.1–6.0 2.2–2.3 2.7–2.8

Resistors, Capacitors, and Inductors Table 10-2. Comparison of Capacitor Dielectric Constants (Continued) K (Dielectric Constant)

Quartz Glass Porcelain Mica Aluminum oxide Tantalum pentoxide Ceramic

3.8–4.4 4.8–8.0 5.1–5.9 5.4–8.7 8.4 26.0 12.0–400,000

have passed. When the voltage is removed, the capacitor discharges and the current decays 63.2% per time constant to zero. These two factors are shown graphically in Fig. 10-14. Curve A shows the voltage across a capacitor when charging. Curve B shows the capacitor voltage when discharging. It is also the voltage across the resistor on charge or discharge. 100

The dielectric constant of materials is generally affected by both temperature and frequency, except for quartz, Styrofoam, and Teflon, whose dielectric constants remain essentially constant. Small differences in the composition of a given material will also affect the dielectric constant. Force. The equation for calculating the force of attraction between the two plates is

Percent of voltage or current

Dielectric

80 60 40 20

B 0 0

AV F = --------------------------(10-20) 2 K 1504S where, F is the attractive force in dynes, A is the area of one plate in square centimeters, V is the potential energy difference in volts, K is the dielectric constant, S is the separation between the plates in centimeters. 10.2.1 Time Constants When a dc voltage is impressed across a capacitor, a time (t) is required to charge the capacitor to a voltage. This is determined with the equation: t = RC where, t is the time in seconds, R is the resistance in ohms, C is the capacitance in farads.

253

(10-21)

In a circuit consisting of only resistance and capacitance, the time constant t is defined as the time it takes to charge the capacitor to 63.2% of the maximum voltage. During the next time constant, the capacitor is charged or the current builds up to 63.2% of the remaining difference of full value, or to 86.5% of the full value. Theoretically, the charge on a capacitor or the current through a coil can never actually reach 100% but is considered to be 100% after five time constants

2 3 4 5 Time—RC or L/R A. Voltage across C when charging. B. Voltage across C when discharging.

Figure 10-14. Universal time graph.

10.2.2 Network Transfer Function Network transfer functions are the ratio of the output to input voltage (generally a complex number) for a given type of network containing resistive and reactive elements. The transfer functions for networks consisting of resistance and capacitance are given in Fig. 10-15. The expressions for the transfer functions of the networks are: A is jZ or j2Sf, B is RC, C is R1C1, D is R2C2, n is a positive multiplier, f is the frequency in hertz, C is in farads, R is in ohms. 10.2.3 Characteristics of Capacitors The operating characteristics of a capacitor determine what it was designed for and therefore where it is best used. Capacitance (C). The capacitance of a capacitor is normally expressed in microfarads (μF or 106 farads)

254

Chapter 10

Network

R Input

Output

1 1 + AB

Input

Output

AB 1 + AB

Input

Output

1 1 + 3AB + A2B2

Input

C R

Input

R Input C

R1 Input

R2 C2

1 Output 1 + (C D + R1C2)A + CDA2

Output

C2 R2

Output

C1 Input R1

C R

1 3 + 2AB

CDA2 1 + (C D + R1C2)A + CDA2

Output

A3B3 1 + 5AB +6A2B2 + A3B3

Output

AB 1 + 3AB + A2B2

R C

C Input R

Output

(1 + AB)2 1 + 3AB + A2B2

Output

1 + AB 2 + AB

Output

n(1 + AB) (1 = n) + nAB

Output

1 + AB 2 + AB

C Input

Input

R C Input

Output

Input

AB 1 + 3AB + A2B2

Input

Output

AB 1 + 3AB

Output

1 + AB 3 + AB

Output

(1 + AB)2 2 + 5AB + A2B2

Output

1 + 3AB 2 + 5AB + A2B2

AB 1 + 3AB + A2B2

Input

R C

C C1

Input

1 + AB 1 + 2AB

Output

C Input

1 + AB 1 + 2AB

Input C

Output

C R

Transfer function

R Input C

C Input R

Network

Transfer function

Input R2

nR Output

n(3 + AB) 3(1 + n) + 2nAB

R2(1 + AC) Output (R + R ) + (R D + R C)A 1 2 1 2

Figure 10-15. Resistance-capacitance network transfer functions.

Resistors, Capacitors, and Inductors or picofarads (pF or 1012 farads) with a stated accuracy or tolerance. Tolerance is expressed as plus or minus a certain percentage of the nominal or nameplate value. Another tolerance rating is GMV (guaranteed minimum value), sometimes referred to as MRV (minimum rated value). The capacitance will never be less than the marked value when used under specified operating conditions but the capacitance could be more than the named value. Equivalent Series Resistance (ESR). All capacitors have an equivalent series resistance expressed in ohms or milliohms. This loss comes from lead resistance, termination losses, and dissipation in the dielectric material. Equivalent Series Inductance (ESL). The equivalent series inductance can be useful or detrimental. It does reduce the high-frequency performance of the capacitor. However, it can be used in conjunction with the capacitors capacitance to form a resonant circuit. Dielectric Absorption (DA). Dielectric absorption is a reluctance on the part of the dielectric to give up stored electrons when the capacitor is discharged. If a capacitor is discharged through a resistance, and the resistance is removed, the electrons that remained in the dielectric will reconvene on the electrode, causing a voltage to appear across the capacitor. This is also called memory. When an ac signal, such as sound, with its high rate of attack is impressed across the capacitor, time is required for the capacitor to follow the signal because the free electrons in the dielectric move slowly. The result is compressed signal. The procedure for testing DA calls for a 5 min capacitor charging time, a 5 s discharge, then a 1 min open circuit, after which the recovery voltage is read. The percentage of DA is defined as the ratio of recovery to charging voltage times 100. Insulation Resistance. Insulation resistance is basically the resistance of the dielectric material, and determines the period of time a capacitor, once charged with a dc voltage, will hold its charge by a specified percentage. The insulation resistance is generally very high. In electrolytic capacitors, the leakage current should not exceed I L = 0.04C + 0.30 where, IL is the leakage current in microamperes, C is the capacitance in microfarads.

(10-22)

255

Maximum Working Voltage. All capacitors have a maximum working voltage that should not be exceeded. The capacitors working voltage is a combination of the dc value plus the peak ac value that may be applied during operation. For instance, if a capacitor has 10 Vdc applied to it, and an ac voltage of 10 Vrms or 17 Vpeak is applied, the capacitor will have to be capable of withstanding 27 V. Quality Factor (Q). The quality factor of a capacitor is the ratio of the capacitors reactance to its resistance at a specified frequency. Q is found by the equation 1 Q = ---------------2SfCR where, f is the frequency in hertz, C is the value of capacitance in farads, R is the internal resistance in ohms.

(10-23)

Dissipation Factor (DF). The dissipation factor is the ratio of the effective series resistance of a capacitor to its reactance at a specified frequency and is given in percent. It is also the reciprocal of Q. It is, therefore, a similar indication of power loss within the capacitor and, in general, should be as low as possible. Power Factor (PF). The power factor represents the fraction of input volt-amperes or power dissipated in the capacitor dielectric and is virtually independent of the capacitance, applied voltage, and frequency. PF is the preferred measurement in describing capacitive losses in ac circuits. 10.2.4

Types of Capacitors

The uses made of capacitors become more varied and more specialized each year. They are used to filter, tune, couple, block dc, pass ac, shift phase, bypass, feed through, compensate, store energy, isolate, suppress noise, and start motors, among other things. While doing this, they frequently have to withstand adverse conditions such as shock, vibration, salt spray, extreme temperatures, high altitude, high humidity, and radiation. They must also be small, lightweight, and reliable. Capacitors are grouped according to their dielectric material and mechanical configuration. Because they may be hardwired or mounted on circuit boards, capacitors come with leads on one end, two ends, or they may be mounted in a dual-in-line (DIP) or single in-line (SIP) package. Figs. 10-16 and 10-17 show the various types of capacitors, their characteristics, and their color codes.

256

Chapter 10

Tubular Ceramic Capacitors Temperature coefficient 1st & 2nd significant digit Capacitance multiplier Tolerance

Six Dot System White EIA identifier indicates mica capacitor 1st significant figure 2nd significant figure Indicator style (optional)

Five dot color code radial lead

Multiplier Capacitance tolerance Characteristic

Temperature coefficient 1st & 2nd significant digit Capacitance multiplier Tolerance

Nine Dot System White EIA identifier indicates mica capacitor 1st significant figure 2nd significant figure

Five dot color code axial lead

Indicator style (optional)

Temperature coefficient Temperature coefficient multiplier 1st & 2nd significant digit Capacitance multiplier Tolerance

Multiplier Capacitance tolerance Characteristic dc working voltage Operating temperature Identifier (white)

Six dot color code radial lead Ceramic Disk Capacitor Temperature coefficient 1st & 2nd digits Multiplier Tolerance

Five dot color code

Multiplier

Characteristic B C D E F

Three dot color code

Ceramic Disk Capacitor 47 35 V

Positive Capacitance (MF) Rated dc voltage

Color Char.

Positive lead (longer) Capacitance in picofarads Temperature coefficient 5 dot 6 dot Color Digits Multiplier Tolerance 1st 2nd ¾10 pF >10 pF ppoC Sig. Fig. Multiplier Black Brown Red Orange Yellow Green Blue Violet Gray White Gold Silver

0 1 2 3 4 5 6 7 8 9 — —

0 1 1 10 2 100 3 1000 4 5 6 7 8 0.01 9 0.1 — —

±2.0 pF ±20% 0 ±0.1 pF ±1% 33 ±2% 75 ±3% 150

230 ±0.5 pF ±5% 300

470

750 ±0.25 pF 150 to 1500 ±1.0 pF 10% +100 to 75

0.0 1.0 1.5 2.0 3.3 4.7 7.5

100

1000

10,000 +1 +10 +100 +1000 +10,000

Figure 10-16. Color codes for tubular and disk ceramic capacitors.

Black Brown Red Orange Yellow Green Blue Violet Gray White Gold Silver

B C D E F

Mica Capacitor Characteristics Temperature coefficient Maximum of capacitance (ppm/oC) capacitance drift Not specified ±200 ±100

20–(+100) 0 to +70

Not specified ±0.5% +0.5pF ±0.3% +0.1pF ±0.3% +0.1pF ±0.5% +0.1pF

Digits Multiplier Tolerance dc Operating 1st 2nd working temperature voltage range 0 0 1 ±20% 100 1 1 10 ±1%

55oC to +85°C 2 2 100 ±2% 300 3 3 1000

55°C to +125°C 4 4 10,000 500 5 5 ±5% 6 6 7 7 8 8 9 9 – – 0.1 ±0.5% 1000 – – 0.01 ±10%

Figure 10-17. Color codes for mica capacitors.

10.2.4.1 Film Capacitors Film capacitors consist of alternate layers of metal foil, and one or more layers of a flexible plastic insulating

Resistors, Capacitors, and Inductors material (dielectric) in ribbon form rolled and encapsulated.

10.2.4.2 Paper Foil-Filled Capacitors Paper foil-filled capacitors consist of alternate layers of aluminum foil and paper rolled together. The paper may be saturated with oil and the assembly mounted in an oil-filled, hermetically sealed metal case. These capacitors are often used as motor capacitors and are rated at 60 Hz.

10.2.4.3 Mica Capacitors Two types of mica capacitors are in use. In one type, alternate layers of metal foil and mica insulation, are stacked together and encapsulated. In the silvered-mica type, a silver electrode is screened on the mica insulators that are then assembled and encapsulated. Mica capacitors have small capacitance values and are usually used in high frequency circuits.

10.2.4.4 Ceramic Capacitors Ceramic capacitors are the most popular capacitors for bypass and coupling applications because of their variety of sizes, shapes, and ratings. Ceramic capacitors also come with a variety of K values or dielectric constant. The higher the K value, the smaller the size of the capacitor. However, high K-value capacitors are less stable. High-K capacitors have a dielectric constant over 3000, are very small, and have values between 0.001 μF to several microfarads. When temperature stability is important, capacitors with a K in the 10–200 region are required. If a high Q capacitor is also required, the capacitor will be physically larger. Ceramic capacitors can be made with a zero capacitance/temperature change. These are called negative-positive-zero (NPO). They come in a capacitance range of 1.0 pF–0.033 μF. A temperature-compensated capacitor with a designation of N750 is used when temperature compensation is required. The 750 indicates that the capacitance will decrease at a rate of 750 ppm/°C with a temperature rise or the capacitance value will decrease 1.5% for a 20°C (68°F) temperature increase. N750 capacitors come in values between 4.0 pF and 680 pF.

257

10.2.4.5 Electrolytic Capacitors The first electrolytic capacitor was made in Germany in about 1895 although its principle was discovered some 25 years earlier. It was not until the late 1920s when power supplies replaced batteries in radio receivers, that aluminum electrolytics were used in any quantities. The first electrolytics contained liquid electrolytes. These wet units disappeared during the late 1930s when the dry gel types took over. Electrolytic capacitors are still not perfect. Low temperatures reduce performance and can even freeze electrolytes, while high temperatures can dry them out and the electrolytes themselves can leak and corrode the equipment. Also, repeated surges over the rated working voltage, excessive ripple currents, and high operating temperature reduce performance and shorten capacitor life. Even with their faults, electrolytic capacitors account for one-third of the total dollars spent on capacitors, probably because they provide high capacitance in small volume at a relatively low cost per microfarad-volt. During the past few years, many new and important developments have occurred. Process controls have improved performance. Better seals have assured longer life, improved etching has given a tenfold increase in volume efficiencies, and leakage characteristics have improved one hundredfold. Basic to the construction of electrolytic capacitors is the electrochemical formation of an oxide film on a metal surface. Intimate contact is made with this oxide film by means of another electrically conductive material. The metal on which the oxide film is formed serves as the anode or positive terminal of the capacitor; the oxide film is the dielectric, and the cathode or negative terminal is either a conducting liquid or a gel. The most commonly used basic materials are aluminum and tantalum. Aluminum Electrolytic Capacitors. Aluminum electrolytic capacitors use aluminum as the base material. The surface is often etched to increase the surface area as much as 100 times that of unetched foil, resulting in higher capacitance in the same volume. The type of etch pattern and the degree to which the surface area is increased involve many carefully controlled variables. If a fine etch pattern is desired to achieve high capacitance per unit area of foil for low voltage devices, the level of current density and time the foil is exposed to the etching solution will be far different from that required for a coarse etch pattern. The foil is then electrochemically treated to form a layer of aluminum oxide on its surface. Time and current density determine the amount of power consumed in the

Chapter 10

process. The oxide film dielectric is thin, usually about 15 Å/V. When formed on a high purity aluminum foil, it has a dielectric constant between 7 and 10 and an equivalent dielectric strength of 25 million volts per inch (25 × 106 V/inch). The thickness of the oxide coating dielectric is determined by the voltage used to form it. The working voltage of the capacitor is somewhat less than this formation voltage. Thin films result in low voltage, high capacitance units; thicker films produce higher voltage, lower capacitance units for a given case size. As a capacitor section is wound, a system of paper spacers is put in place to separate the foils. This prevents the possibility of direct shorts between anode and cathode foils that might result because of rough surfaces or jagged edges on either foil. The spacer material also absorbs the electrolyte with which the capacitor is impregnated, and thus assures uniform and intimate contact with all of the surface eccentricities of the etched anode foil throughout the life of the capacitor. The cathode foil serves only as an electrical connection to the electrolyte which is in fact the true cathode of the electrolytic capacitor. The electrolyte commonly used in aluminum electrolytic capacitors is an ionogen that is dissolved in and reacts with glycol to form a pastelike mass of medium resistivity. This is normally supported in a carrier of high purity craft or hemp paper. In addition to the glycol electrolyte, low resistivity nonaqueous electrolytes are used to obtain a lower ESR and wider operating temperatures. The foil-spacer-foil combination is wound into a cylinder, inserted into a suitable container, impregnated, and sealed. • Electrical Characteristics. The equivalent circuit of an electrolytic capacitor is shown in Fig. 10-18. A and B are the capacitor terminals. The shunt resistance, Rs, in parallel with the effective capacitance, C, accounts for the dc leakage current through the capacitor. Heat is generated in the ESR if there is ripple current and heat is generated in the shunt resistance by the voltage. In an aluminum electrolytic capacitor, the ESR is due mainly to the spacer-electrolyte-oxide system. Generally it varies only slightly except at low temperatures where it increases greatly. L is the self-inductance of the capacitor caused by terminals, electrodes, and geometry. • Impedance. T h e i m p e d a n c e o f a c a p a c i t o r i s frequency dependent, as shown in Fig. 10-19. Here, ESR is the equivalent series resistance, X C is the capacitive reactance, XL is the inductive reactance, and Z is the impedance. The initial downward slope

ESR A

B Rs

Figure 10-18. Simplified equivalent circuit of an electrolytic capacitor.

is a result of the capacitive reactance. The trough (lowest impedance) portion of the curve is almost totally resistive, and the rising upper or higher frequency portion of the curve is due to the capacitor’s self-inductance. If the ESR were plotted separately, it would show a small ESR decrease with frequency to about 5–10 kHz, and then remain relatively constant throughout the remainder of the frequency range.

Effective impedance of capacitor

258

Impedance curve represents sum of ESR and XL or XC Capacitor resonant frequency

Z ESR XC ESR

Figure 10-19. Impedance characteristics of a capacitor.

• Leakage Current. Leakage current in an electrolytic capacitor is the direct current that passes through a capacitor when a correctly polarized dc voltage is applied to its terminals. This current is proportional to temperature and becomes increasingly important when capacitors are used at elevated ambient temperatures. Imperfections in the oxide dielectric film cause high leakage currents. Leakage current decreases slowly after a voltage is applied and usually reaches steady-state conditions after 10 minutes. If a capacitor is connected with its polarity backward, the oxide film is forward biased and offers very little resistance to current flow, resulting in high current, which, if left unchecked, will cause overheating and self destruction of the capacitor. The total heat generated within a capacitor is the sum of the heat created by the I2R losses in the ESR and that created by the ILeakage × Vapplied. • Ac Ripple Current. The ac ripple current rating is one of the most important factors in filter applications, because excessive current produces a greater than permissible temperature rise, shortening capacitor life. The maximum permissible rms ripple

Resistors, Capacitors, and Inductors

temperature will have a life expectancy 64 times that of the same capacitor operating at 85°C (185°F). • Surge Voltage. The surge voltage specification of a capacitor determines its ability to withstand the high transient voltages that occur during the start up period of equipment. Standard tests specify a short on and long off period for an interval of 24 hours or more; the allowable surge voltage levels are usually 10% above the rated voltage of the capacitor. Fig. 10-21 shows how temperature, frequency, time, and applied voltage affect electrolytic capacitors.

Z, ESR, C (normalized)

Frequency DF

Frequency

Figure 10-20. Capacitor charge and discharge on a full-wave rectifier output.

Cap Time

This can be mathematically determined or the ripple current through the capacitor can be measured by inserting a low impedance true rms ammeter in series with the capacitor. It is very important that the impedance of the meter be small compared with that of the capacitor, otherwise, a large measurement error will result. • Standard Life Tests. Standard life tests at rated voltage and maximum rated temperatures are usually the criteria for determining the quality of an electrolytic capacitor. These two conditions rarely occur simultaneously in practice. Capacitor life expectancy is doubled for each 10°C (18°F) decrease in operating temperature, so a capacitor operating at room

ESR C

Temperature

Failure rate

Frequency

Ripple current capability

ESR

25°C Temperature

Frequency

= Increased or higher or later

Cap

DF Time

Failure rate Leakage current

current for any capacitor is limited by the temperature within the capacitor and the rate of heat dissipation from the capacitor. Lower ESR and longer cans or enclosures increase the ripple current rating. • Reverse Voltage. Aluminum electrolytic capacitors can withstand a reverse voltage of up to 1.5 V without noticeable effect from its operating characteristics. Higher reverse voltages, when applied over extended periods, will lead to some loss of capacitance. Excess reverse voltages applied for short periods will cause some change in capacitance but may not lead to capacitor failure during the reverse voltage application or during subsequent operation in the normal polarity direction. A major use of large value capacitors is for filtering in dc power supplies. After a capacitor is fully charged, when the rectifier conduction decreases, the capacitor discharges into the load until the next half cycle, Fig. 10-20. Then on the next cycle the capacitor recharges again to the peak voltage. The 'e shown in the illustration is equal to the total peak-to-peak ripple voltage. This is a complex wave which contains many harmonics of the fundamental ripple frequency and is the ripple that causes the noticeable heating of the capacitor.

259

Temperature

Voltage

% Rated voltage

Figure 10-21. Variations in aluminum electrolytic characteristics caused by temperature, frequency, time, and applied voltage. Courtesy of Sprague Electric Company.

• Tantalum Capacitors. Tantalum electrolytics have become the preferred type where high reliability and long service life are paramount considerations. Most metals form crystalline oxides that are nonprotecting, such as rust on iron or black oxide on

260

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copper. A few metals form dense, stable, tightly adhering, electrically insulating oxides. These are the so-called valve metals and include titanium, zirconium, niobium, tantalum, hafnium, and aluminum. Only a few of these permit the accurate control of oxide thickness by electrochemical means. Of these, the most valuable for the electronics industry are aluminum and tantalum. The dielectric used in all tantalum electrolytic capacitors is tantalum pentoxide. Although wet foil capacitors use a porous paper separator between their foil plates, its function is merely to hold the electrolyte solution and to keep the foils from touching. The tantalum pentoxide compound possesses high dielectric strength and a high dielectric constant. As capacitors are being manufactured, a film of tantalum pentoxide is applied to their electrodes by an electrolytic process. The film is applied in various thicknesses and at various voltages. Although transparent at first, it takes on different colors as light refracts through it. This coloring occurs on the tantalum electrodes of all three types of tantalum capacitors. Rating for rating, tantalum capacitors tend to have as much as three times better capacitance/volume efficiency than aluminum electrolytic capacitors, because tantalum pentoxide has a dielectric constant of 26, some three times greater than that of aluminum oxide. This, in addition to the fact that extremely thin films can be deposited during manufacturing, makes the tantalum capacitor extremely efficient with respect to the number of microfarads available per unit volume. The capacitance of any capacitor is determined by the surface area of the two conducting plates, the distance between the plates, and the dielectric constant of the insulating material between the plates. The distance between the plates in tantalum electrolytic capacitors is very small since it is only the thickness of the tantalum pentoxide film. The dielectric constant of the tantalum pentoxide is high, therefore, the capacitance of a tantalum capacitor is high. Tantalum capacitors contain either liquid or solid electrolytes. The liquid electrolyte in wet-slug and foil capacitors, usually sulfuric acid, forms the cathode or negative plate. In solid-electrolyte capacitors a dry material, manganese dioxide, forms the cathode plate. The anode lead wire from the tantalum pellet consists of two pieces. A tantalum lead is embedded in, or welded to, the pellet, which is welded, in turn, to a nickel lead. In hermetically sealed types, the nickel lead is terminated to a tubular eyelet. An

external lead of nickel or solder-coated nickel is soldered or welded to the eyelet. In encapsulated or plastic-encased designs, the nickel lead, which is welded to the basic tantalum lead, extends through the external epoxy resin coating or the epoxy end fill in the plastic outer shell. Foil Tantalum Capacitors. Foil tantalum capacitors are made by rolling two strips of thin foil, separated by a paper saturated with electrolyte, into a convolute roll. The tantalum foil, which is to be the anode, is chemically etched to increase its effective surface area, providing more capacitance in a given volume. This is followed by anodizing in a chemical solution under direct voltage. This produces the dielectric tantalum pentoxide film on the foil surface. Foil tantalum capacitors can be manufactured in dc working voltage values up to 300 V. However, of the three types of tantalum electrolytic capacitors, the foil design has the lowest capacitance per unit volume. It is also the least often encountered since it is best suited for the higher voltages primarily found in older designs of equipment and requires more manufacturing operations than do the two other types. Consequently, it is more expensive and is used only where neither a solid electrolyte nor a wet-slug tantalum capacitor can be employed. Foil tantalum capacitors are generally designed for operation over the temperature range of 55°C to +125°C (67°F to +257°F) and are found primarily in industrial and military electronics equipment. Wet-Electrolyte Sintered Anode Tantalum Capacitors. Wet-electrolyte sintered anode tantalum capacitors often called wet-slug tantalum capacitors, use a pellet of sintered tantalum powder to which a lead has been attached. This anode has an enormous surface area for its size because of its construction. Tantalum powder of suitable fineness, sometimes mixed with binding agents, is machine-pressed into pellets. The second step is a sintering operation in which binders, impurities, and contaminants are vaporized and the tantalum particles are sintered into a porous mass with a very large internal surface area. A tantalum lead wire is attached by welding the wire to the pellet. (In some cases, the lead is embedded during pressing of the pellet before sintering.) A film of tantalum pentoxide is electrochemically formed on the surface areas of the fused tantalum particles. The oxide is then grown to a thickness determined by the applied voltage. Finally the pellet is inserted into a tantalum or silver container that contains an electrolyte solution. Most liquid electrolytes are gelled to prevent the free movement of the solution inside the container and to keep the

Resistors, Capacitors, and Inductors

261

electrolyte in intimate contact with the capacitor cathode. A suitable end seal arrangement prevents the loss of the electrolyte. Wet-slug tantalum capacitors are manufactured in a working voltage range up to 150 Vdc.

They also have good low temperature performance characteristics and freedom from corrosive electrolytes.

Solid-Electrolyte Sintered Anode Tantalum Capacitors. Solid-electrolyte sintered anode tantalum capacitors differ from the wet versions in their electrolyte. Here, the electrolyte is manganese dioxide, which is formed on the tantalum pentoxide dielectric layer by impregnating the pellet with a solution of manganous nitrate. The pellets are then heated in an oven and the manganous nitrate is converted to manganese dioxide. The pellet is next coated with graphite followed by a layer of metallic silver, which provides a solderable surface between the pellet and its can. The pellets, with lead wire and header attached, are inserted into the can where the pellet is held in place by solder. The can cover is also soldered into place. Another variation of the solid-electrolyte tantalum capacitor encases the element in plastic resins, such as epoxy materials. It offers excellent reliability and high stability for consumer and commercial electronics with the added feature of low cost. Still other designs of solid tantalum capacitors, as they are commonly known, use plastic film or sleeving as the encasing material and others use metal shells which are back filled with an epoxy resin. And, of course, there are small tubular and rectangular molded plastic encasements as well.

Suppression capacitors are used to reduce interference that comes in or out through the power line. They are effective because they are frequency dependent in that they become a short circuit at radio frequencies, without affecting low frequencies. Suppression capacitors are identified as X capacitors and Y capacitors. Fig. 10-22 shows two examples of radio interference suppression. Fig.10-22A is for protection class I which would include drills and hair dryers. Fig.10-22B is for protection class II where no protective conductor is connected to the metal case G.

Tantalum Capacitors. In choosing between the three basic types of tantalum capacitors, the circuit designer customarily uses foil tantalum capacitors only where high voltage constructions are required or where there is substantial reverse voltage applied to a capacitor during circuit operation. Wet-electrolyte sintered anode capacitors, or wet-slug tantalum capacitors, are used where the lowest dc leakage is required. The conventional silver can design will not tolerate any reverse voltages. However, in military or aerospace applications, tantalum cases are used instead of silver cases where utmost reliability is desired. The tantalum-cased wet-slug units will withstand reverse voltages up to 3 V, will operate under higher ripple currents, and can be used at temperatures up to 200°C (392°F). Solid-electrolyte designs are the least expensive for a given rating and are used in many applications where their very small size for a given unit of capacitance is important. They will typically withstand up to 15% of the rated dc working voltage in a reverse direction.

10.2.4.6 Suppression Capacitors

G Cy L Cx

Line N

Cy PE

A. Protective class I G Cy L Cx

Line N

B. Protective class II

Figure 10-22. Radio frequency suppression with X and Y capacitors. Courtesy of Vishay Roederstein.

X Capacitors. X capacitors are used across the mains to reduce symmetrical interference where a failure in the capacitor—i.e., the capacitor shorts out—will not cause injury, shock or death. Y Capacitors. Y capacitors are used between a live conductor and a cabinet or case to reduce asymmetrical

262

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interference. Y capacitors have high electrical and mechanical specifications so they are much less likely to fail. XY Capacitors. When used together they are called XY capacitors. 10.2.4.7 Supercapacitors Supercapacitors, Ultracapacitors, more technically known as electrochemical double-layer capacitors, are one more step beyond the electrolytic capacitors. The charge-separation distance in ultracapacitors has been reduced to literally the dimensions of the ions within the electrolyte. In supercapacitors, the charges are not separated by millimeters or micrometers (microns) but by a few nanometers or from electrostatic capacitors to electrolytic capacitors to ultracapacitors. The charge-separation distance has in each instance dropped by three orders of magnitude, from 10–3 m to 10–6 m to 10–9 m. • How a Supercapacitor Works. An supercapacitor or ultracapacitor, also known as a double-layer capacitor, polarizes an electrolytic solution to store energy electrostatically. Though it is an electrochemical device, no chemical reactions are involved in its energy storage mechanism. This mechanism is highly reversible and allows the ultracapacitor to be charged and discharged hundreds of thousands of times. An ultracapacitor can be viewed as two nonreactive porous plates, or collectors, suspended within an electrolyte, with a voltage potential applied across the collectors. In an individual ultracapacitor cell, the applied potential on the positive electrode attracts the negative ions in the electrolyte, while the potential on the negative electrode attracts the positive ions. A dielectric separator between the two electrodes prevents the charge from moving between the two electrodes. Once the ultracapacitor is charged and energy stored, a load can use this energy. The amount of energy stored is very large compared to a standard capacitor because of the enormous surface area created by the porous carbon electrodes and the small charge separation of 10 angstroms created by the dielectric separator. However, it stores a much smaller amount of energy than does a battery. Since the rates of charge and discharge are determined solely by its physical properties, the ultracapacitor can release energy much faster (with more power) than a battery that relies on slow chemical reactions. Many applications can benefit from ultracapacitors, whether they require short power pulses or

low-power support of critical memory systems. Using an ultracapacitor in conjunction with a battery combines the power performance of the former with the greater energy storage capability of the latter. It can extend the life of a battery, save on replacement and maintenance costs, and enable a battery to be downsized. At the same time, it can increase available energy by providing high peak power whenever necessary. The combination of ultracapacitors and batteries requires additional dc/dc power electronics, which increases the cost of the circuit. Supercapacitors merged with batteries (hybrid battery) will become the new superbattery. Just about everything that is now powered by batteries will be improved by this much better energy supply. They can be made in most any size, from postage stamp to hybrid car battery pack. Their light weight and low cost make them attractive for most portable electronics and phones, as well as for aircraft and automobiles. • Advantages of a Supercapacitor 1. Virtually unlimited life cycle—cycles millions of times—10 to 12 year life. 2. Low internal impedance. 3. Can be charged in seconds. 4. Cannot be overcharged. 5. Capable of very high rates of charge and discharge. 6. High cycle efficiency (95% or more). • Disadvantages of a Supercapacitor: 1. Supercapacitors and ultra capacitors are relatively expensive in terms of cost per watt. 2. Linear discharge voltage prevents use of the full energy spectrum. 3. Low energy density—typically holds one-fifth to one-tenth the energy of an electrochemical battery. 4. Cells have low voltages; therefore, serial connections are needed to obtain higher voltages, which require voltage balancing if more than three capacitors are connected in series. 5. High self-discharge—the self-discharge rate is considerably higher than that of an electrochemical battery. 6. Requires sophisticated electronic control and switching equipment. A supercapacitor by itself cannot totally replace the battery. But, by merging a supercapacitor and a battery together—like a hybrid battery, it will be possible for

Resistors, Capacitors, and Inductors supercapacitors to replace the battery as we know it today. Presently supercapacitors need batteries to store the energy and are basically used as a buffer between the battery and the device. Supercapacitors can be charged and discharged hundreds of thousands of times where a battery cannot do that. • Calculating Backup Time. To calculate the desired backup time the supercapacitor will provide if the power goes off, the starting and ending voltage on the capacitor, the current draw from the capacitor, and the capacitor size must be known. Assuming that the load draws a constant current while running from V BACKUP, then the worst-case backup time in hours would use the equation: C V BACKUPSTART – V BACKUPMIN ------------------------------------------------------------------------------------I BACKUPMAX Backup time = ------------------------------------------------------------------------------------3600 (10-24) where, C is the capacitor value in farads, V BACKUPSTART is the initial voltage in volts. The voltage applied to VCC, less the voltage drop from the diodes, if any, used in the charging circuit, VBACKUPMIN is the ending voltage in volts, I BACKUPMAX is the maximum V BACKUP current in amperes. For example, to determine how long the backup time will be under the following conditions: • • • •

0.2 F capacitor VBACKUPSTART is 3.3 V VBACKUPMIN is 1.3 V IBACKUPMAX is 1000 nA, then:

0.2 3.3 – 1.3 --------------------------------–6 10 Backup time = --------------------------------300 = 111.1 h

263

Mil spec (if required—larger band) 1st digit 2nd digit Multiplier Tolerance (narrower)

Color Black Brown Red Orange Yellow Green Blue Violet Gray White Gold Silver No band

Inductance digits 1st 2nd 0 1 2 3 4 5 6 7 8 9 – – –

0 1 2 3 4 5 6 7 8 9 – – –

Multiplier

Tolerance

1 10 100 1000 10,000

– –

±5% ±10% ±20%

Figure 10-23. Color code for small inductors (in H).

10.3.1 Types of Inductors Inductors are constructed in a variety of ways, depending on their use. 10.3.1.1 Air Core Inductors Air core inductors are either ceramic core or phenolic core. 10.3.1.2 Axial Inductor An axial inductor is constructed on a core with concentric leads on opposite ends, Fig.10-24A. The core material may be phenolic, ferrite, or powdered iron. 10.3.1.3 Bobbin Core Inductor Bobbin core inductors have the shape of a bobbin and may come with or without leads. They may be either axial or radial, Fig. 10-24B.

10.3 Inductors Inductance is used for the storage of electrical energy in a magnetic field, called magnetic energy. Magnetic energy is stored as long as current keeps flowing through the inductor. The current of a sine wave lags the voltage by 90° in a perfect inductor. Figure 10-23 shows the color code for small inductors.

10.3.1.4 Ceramic Core Ceramic core inductors are often used in high frequency applications where low inductance, low core losses, and high Q values are required. Ceramic has no magnetic properties so there is no increase in permeability due to the core material.

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Chapter 10

A. Axial leaded inductor.

such as manganese and zinc (MnZn) or nickel and zinc (NiZn). The general composition is xxFe2O4 where xx is one of the other elements. 10.3.1.7 Laminated Cores

Axial leaded

Laminated cores are made by stacking insulated laminations on top of each other. Some laminations have the grains oriented to minimize core losses, giving higher permeability. Laminated cores are more common in transformers. Radial leaded B. Bobbins.

Leadless

10.3.1.8 Molded Inductor A molded inductor has its case formed via a molding process, creating a smooth, well-defined body with sharp edges. 10.3.1.9 MPP Core

C. Radial inductors.

Non-leaded Leaded D. Slug cores.

MPP, or moly perm alloy powder, is a magnetic material with a inherent distributed air gap, allowing it to store higher levels of magnetic flux compared to other materials. This allows more dc to flow through the inductor before the core saturates. The core consists of 80% nickel, 2–3% molybdenum, and the remaining percentage iron. 10.3.1.10 Multilayer Inductor A multilayer inductor consists of layers of coil between layers of core material. The coil is usually bare metal and is sometimes referred to as nonwirewound.

E. Toroidal core. Figure 10-24. Various inductor core types.

Ceramic has a low thermal coefficient of expansion allowing high inductance stability over a high operating temperature range.

10.3.1.11 Phenolic Core

Epoxy-coated inductors usually have a smooth surface and edges. The coating provides insulation.

Phenolic cores are often called air cores and are often used in high frequency applications where low inductance values, low core losses, and high Q values are required. Phenolic has no magnetic properties so there is no increase in permeability due to the core material. Phenolic cores provide high strength, high flammability ratings, and high temperature characteristics.

10.3.1.6 Ferrite Core

10.3.1.12 Powdered Iron Core

Ferrite cores can be easily magnetized. The core consists of a mixture of oxide of iron and other elements

Powdered iron is a magnetic material with an inherent distributed air gap that allows the core to have high

10.3.1.5 Epoxy-Coated Inductor

Resistors, Capacitors, and Inductors levels of magnetic flux. This allows a high level of dc to flow through the core before saturation. Powdered iron cores are close to 100% iron whose particles are insulated and mixed with a binder such as epoxy or phenolic. They are pressed into a final shape and cured by baking.

10.3.1.13 Radial Inductor A radial inductor is constructed on a core with leads on the same side, Fig. 10-24C. This allows for easy mounting on circuit boards, etc.

10.3.1.14 Shielded Inductor A shielded inductor has its core designed to contain the majority of the magnetic field. Some are self shielding such as toroids, e-cores, and pot cores. Bobbin and slug cores require a magnetic sleeve for shielding.

10.3.1.15 Slug Core Slug cores have the shape of a cylindrical rod and come with or without leads, Fig.10-24D. They have higher flux density characteristics than other core shapes as most of the magnetic energy is stored in the air around the core. 10.3.1.16 Tape Wound Core Tape wound cores are made by rolling insulated and precisely controlled thickness strips of alloy iron into a toroidal shape. The finished cores have an outside coating for protection. Tape wound cores are capable of storing high amounts of energy and contain a high permeability. 10.3.1.17 Toroidal Inductor Toroidals are constructed by placing the winding on a donut-shaped core, Fig. 10-24E. Toroidal cores may be ferrite, powdered iron, tape wound, or alloy and high flux. Toroidals are self shielding andhave efficient energy transfer, high coupling between windings, and early saturation.

265

10.3.2 Impedance Characteristics Impedance. The impedance or inductive reactance (X L ) of an inductor to an ac signal is found with the equation X L = 2SfL

(10-25)

where, f is the frequency in hertz, L is the inductance in henrys. The inductance of a coil is only slightly affected by the type of wire used for its construction. The Q of the coil will be governed by the ohmic resistance of the wire. Coils wound with silver or gold wire have the highest Q for a given design. To increase the inductance, inductors can be connected in series. The total inductance will always be greater than the largest inductor LT = L1 + L2 } + Ln

(10-26)

To reduce the total inductance, place the inductors in parallel. The total inductance will always be less than the value of the lowest inductor 1 L T = --------------------------------------1 } 1 1 -------- + + ----Ln L1 L2

(10-27)

To determine the impedance of circuits with resistance, capacitance, and inductance, see Section 10.4. Mutual Inductance. Mutual inductance is the property that exists between two conductors that are carrying current when the magnetic lines of force from one conductor link with the magnetic lines of force of the other. The mutual inductance of two coils with fields interacting can be determined by LA – LB (10-28) M = ----------------4 where, M is the mutual inductance of LA and LB in henrys, LA is the total inductance of coils L1 and L2 with fields aiding in henrys, LB is the total inductance of coils L1 and L2 with fields opposing in henrys. The coupled inductance can be determined by the following equations. In parallel with fields aiding

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Chapter 10

1 L T = ----------------------------------------M 1 ----------------- + ----------------L1 + M L2 + M

(10-29)

In parallel with fields opposing 1 L T = --------------------------------------M 1 ---------------- – ---------------L1 – M L2 – M

(10-30)

In series with fields aiding L T = L 1 + L 2 + 2M

(10-31)

In series with fields opposing L T = L 1 + L 2 – 2M

(10-32)

where, LT is the total inductance in henrys, L1 and L2 are the inductances of the individual coils in henrys, M is the mutual inductance in henrys. When two coils are inductively coupled to give transformer action, the coupling coefficient is determined by M K = --------------------L1 u L2

(10-33)

where, K is the coupling coefficient, M is the mutual inductance in henrys, L1 and L2 are the inductances of the two coils in henrys. An inductor in a circuit has a reactance of j2SfL : . Mutual inductance in a circuit also has a reactance equal to j2SfM :. The operator j denotes reactance. The energy stored in an inductor can be determined by 2

LI W = -------2 where, W is the energy in joules (watt-seconds), L is the inductance in henrys, I is the current in amperes.

(10-34)

Coil Inductance. The following is the relationship of the turns in a coil to its inductance: • The inductance is proportional to the square of the turns.

• The inductance increases as the permeability of the core material is increased. • The inductance increases as the cross-sectional area of the core material is increased. • The inductance increases as the length of the winding is increased. • A shorted turn decreases the inductance. In an audio transformer, the frequency characteristic will be affected, and the insertion loss increased. • Inserting an iron core in a coil increases the inductance; hence, its inductive reactance is increased. • Introducing an air gap in an iron core coil reduces the inductance. The maximum voltage induced in a conductor moving in a magnetic field is proportional to the number of magnetic lines of force cut by the conductor moving in the field. A conductor moving parallel to the lines of force cuts no lines of force so no current is generated in the conductor. A conductor moving at right angles to the lines of force will cut the maximum number of lines per inch per second; therefore, the voltage will be at the maximum. A conductor moving at any angle to the lines of force cuts a number of lines of force proportional to the sine of the angles. –8

V = ELv sin T u 10 (10-35) where, V is the voltage produced, E is the flux density, L is the length of the conductor in centimeters, v is the velocity in centimeters per second of the conductor moving at an angle T. The direction of the induced electromotive force (emf ) is in the direction in which the axis of a right-hand screw, when turned with the velocity vector, moves through the smallest angle toward the flux density vector. This is called the right-hand rule. The magnetomotive force produced by a coil is derived by V ampere turns = T § --- · ©R ¹ = TI where, T is the number of turns, V is the voltage in volts, R is the resistance of the wire in ohms,

(10-36)

Resistors, Capacitors, and Inductors I is the current in amperes. The inductance of single-layer, spiral, and multilayer coils can be calculated by using either Wheeler’s or Nagaoka’s equations. The accuracy of the calculation will vary between 1% and 5%. The inductance of a single-layer coil, Fig. 10-25A, may be found using Wheeler’s equation 2

The Q of the coil can be measured as follows. Using the circuit of Fig. 10-26, Q of a coil may be easily measured for frequencies up to 1 MHz. Since the voltage across an inductance at resonance equals Q × V, where V is the voltage developed by the oscillator, it is necessary only to measure the output voltage from the oscillator and the voltage across the inductance.

B N L = ----------------------9B + 10A

(10-37)

For the multilayer coil, Fig. 10-25B, the calculations are

Osc

Voltmeter C

0.8B N L = -----------------------------------6B + 9A + 10C

(10-38)

For the spiral coil, Fig. 10-25C, the calculations are: 2

267

B N L = ----------------------8B + 11C where, B is the radius of the winding, N is the number of turns in the coil, A is the length of the winding, C is the thickness of the winding, L is in PH. A

A B

A. Single layer

(10-39)

B. Multilayer

The voltage from the oscillator is introduced across a low value of resistance R, about 1% of the anticipated radiofrequency resistance of the LC combination, to assure that the measurement will not be in error by more than 1%. For average measurements, resistor R will be on the order of 0.10 : . If the oscillator cannot be operated into an impedance of 0.10 : , a matching transformer may be employed. It is desirable to make C as large as convenient to minimize the ratio of the impedance looking from the voltmeter to the impedance of the test circuit. The voltage across R is made small, on the order of 0.10 V. The LC circuit is then adjusted to resonate and the resultant voltage measured. The value of Q may then be equated voltage across C- . --------------------------------------------------------------Q = Resonant Voltage across R

(10-41)

C. Spiral

The Q of a coil may be approximated by the equation

Figure 10-25. Single- and multilayer inductors.

Q. Q is the ratio of the inductive reactance to the internal resistance of the coil. The principal factors that affect Q are frequency, inductance, dc resistance, inductive reactance, and the type of winding. Other factors are the core losses, the distributed capacity, and the permeability of the core material. The Q for a coil where R and L are in series is Q = 2SfL -----------R where, f is the frequency in hertz, L is the inductance in henrys, R is the resistance in ohms.

Figure 10-26. Circuit for measuring the Q of a coil.

(10-40)

Q = 2SfL -----------R (10-42) XL = -----R where, f is the frequency in hertz, L is the inductance in henrys, R is the dc resistance in ohms as measured by an ohmmeter, XL is the inductive reactance of the coil. Time Constant. When a dc voltage is applied to an RL circuit, a certain amount of time is required to change the voltage. In a circuit containing inductance and resis-

268

Chapter 10

tance, the time constant is defined as the time it takes for the current to reach 62.3% of its maximum value. The time constant can be determined with the following equation:

600 7 ±25% Z

600

(10-43) Z, R, X,—7

L T = --R where, T is the time in seconds, L is the inductance in henrys, R is the resistance in ohms.

800

400

200 X

See Section 10.2.1 for a further discussion of time constants. The effect of an inductor is the same as for a capacitor and resistor. Also, curve A in Fig. 10-14 shows the current through an inductor on buildup and curve B shows the current decay when the voltage is removed. Right-Hand Rule. The right-hand rule is a method devised for determining the direction of a magnetic field around a conductor carrying a direct current. The conductor is grasped in the right hand with the thumb extended along the conductor. The thumb points in the direction of the current. If the fingers are partly closed, the fingertips will point in the direction of the magnetic field. Maxwell’s rule states, “If the direction of travel of a right-handed corkscrew represents the direction of the current in a straight conductor, the direction of rotation of the corkscrew will represent the direction of the magnetic lines of force.” 10.3.3 Ferrite Beads The original ferrite beads were small round ferrites with a hole through the middle where a wire passed through. Today they come as the original style plus as multiple apertures and surface mount configurations. The ferrite bead can be considered a frequencydependent resistor whose equivalent circuit is a resistor in series with an inductor. As the frequency increases, the inductive reactance increases and then decreases, and the complex impedance of the ferrite material increases the overall impedance of the bead, Fig. 10-27. At frequencies below 10 MHz, the impedance is less than 10 : . As the frequency increases, the impedance increases to about 100 : and becomes mostly resistive at 100 MHz. Once the impedance is resistive, resonance does not occur as it would using an LC network. Ferrite beads do

0 1

10 100 Frequency—MHz

1000

Figure 10-27. Impedance of ferrite beads. Courtesy of Vishay Dale.

not attenuate low frequencies or dc so are useful for reducing EMI/EMC in audio circuits. 10.3.4 Skin Effect Skin effect is the tendency of ac to flow near the surface of a conductor rather than flowing through the conductor’s entire cross sectional area. This increases the resistance of the conductor because the magnetic field caused by the current creates eddy currents near the center of the conductor. The eddy currents oppose the normal flow of current near the center, forcing the main current flow out toward the surface as the frequency of the ac current increases. To reduce this problem, a wire made up of separately insulated strands woven and/or bunched together is used. Commonly called Litz wire, the current is equally divided between all of the individual strands which equalizes the flux linkage and reactance of the individual strands, reducing the ac losses compared to solid wire. 10.3.5 Shielded Inductor Some inductor designs are self-shielding. Examples are toroid, pot core, and E-core inductors. Slug cores and bobbins may require shielding, depending on the application. It is impossible to completely shield an inductor.

10.4 Impedance The total impedance created by resistors, capacitors, and inductors in circuits can be determined with the following equations.

Resistors, Capacitors, and Inductors

269

RX C Z = ------------------------2 2 R + XC

(10-55)

Parallel circuits RX Z = ---------------------2 2 R +X

(10-44)

Capacitance and inductance in parallel when XL is larger than XC

Series circuits Z =

R +X

(10-45)

Resistance and inductance in series Z =

R + XL

(10-46)

X T = atan -----LR

(10-47)

Z =

R + XC

(10-48)

X T = atan ------C R

(10-49)

Inductance and capacitance in series when XL is larger than XC Z = XL – XC

(10-51)

Resistance, inductance, and capacitance in series 2

XC u XL Z = -----------------XC – XL

(10-57)

RX L X C Z = ------------------------------------------------------------2 2 2 2 XL XC + R XL – XC

(10-58)

R XL – XC T = atan --------------------------XL XC

(10-59)

Inductance and series resistance in parallel with resistance 2

Z = XC – XL

R + XL – XC

Capacitance and inductance in parallel when X C is larger than XL

(10-50)

Inductance and capacitance in series when XC is larger than XL

Z =

(10-56)

Inductance, capacitance, and resistance in parallel

Resistance and capacitance in series 2

XL u XC Z = -----------------XL – XC

XL – XC T = atan -----------------R

(10-52) (10-53)

R1 + XL Z = R 2 ---------------------------------------2 2 R1 + R2 + XL

(10-60)

R2 XL T = atan ----------------------------------------2 2 R1 + XL + R1 R2

(10-61)

Inductance and series resistance in parallel with capacitance 2

R + XL Z = X C -------------------------------------2 2 R + XL – XC

(10-62)

Resistance and inductance in parallel 2

RX L Z = -----------------------2 2 R + XL Capacitance and resistance in parallel

(10-54)

XL XC – XL – R T = atan -----------------------------------------RX C

(10-63)

Capacitance and series resistance in parallel with inductance and series resistance

270

Chapter 10

Z =

R1 + XL R2 + XC --------------------------------------------------------2 2 R1 + R2 + XL – XC 2

(10-64)

1 = -----------------2SCX C

XL R2 + XC – XC R1 + XL Z = atan ---------------------------------------------------------------------------2 2 2 2 R1 R2 + XC + R2 R1 + XL

1 f = -----------------2S LC

(10-65)

where, Z is the impedance in ohms, R is the resistance in ohms, L is the inductance in henrys, XL is the inductive reactance in ohms, XC is the capacitive reactance in ohms. T is the phase angle in degrees by which the current leads the voltage in a capacitive circuit or lags the voltage in an inductive circuit. 0° indicates an in-phase condition.

10.5 Resonant Frequency When an inductor and capacitor are connected in series or parallel, they form a resonant circuit. The resonant frequency can be determined from the equation

(10-66)

XL = --------2SL where, L is the inductance in henrys, C is the capacitance in farads, XL and XC are the impedance in ohms. The resonant frequency can also be determined through the use of a reactance chart developed by the Bell Telephone Laboratories, Fig. 10-28. This chart can be used for solving problems of inductance, capacitance, frequency, and impedance. If two of the values are known, the third and fourth values may be found with its use. As an example, what is the value of capacitance and inductance required to resonate at a frequency of 1000 Hz in a circuit having an impedance of 500 :? Entering the chart on the 1000 Hz vertical line and following it to the 500 : line (impedance is shown along the left-hand margin), the value of inductance is indicated by the diagonal line running upward as 0.08 H (80 mH), and the capacitance indicated by the diagonal line running downward at the right-hand margin is 0.3 μF.

271

Impedance

Inductance or Capacitance

Resistors, Capacitors, and Inductors

Frequency

Figure 10-28. Reactance chart. Courtesy AT&T Bell Laboratories.

272

Chapter 10

References Inductor and Magnetic Product Terminology, Document No. 34053, March 2002, Vishay Dale. ILB, ILBB Ferrite Beads, Document No. 34091, May 1999, Vishay Dale. Ohmite Manual of Engineering Information, Bulletin 1100, Ohmite Mfg. Co. Ohmite Resistor Selection Design Data, Ohmite Mfg. Co. Radio Interference Suppression Capacitors, Document No. 26529, September 2002, Vishay Roederstein.

Chapter

Audio Transformer Basics by Bill Whitlock 11.1 Audio Transformer Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Basic Principles and Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1.1 Magnetic Fields and Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1.2 Windings and Turns Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1.3 Excitation Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Realities of Practical Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2.1 Core Materials and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2.2 Winding Resistances and Auto-Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2.3 Leakage Inductance and Winding Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2.4 Winding Capacitances and Faraday Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2.5 Magnetic Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 General Application Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.1 Maximum Signal Level, Distortion, and Source Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.3 Insertion Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.4 Sources with Zero Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.5 Bi-Directional Reflection of Impedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.6 Transformer Noise Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3.7 Basic Classification by Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Audio Transformers for Specific Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Equipment-Level Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.1 Microphone Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.2 Line Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.3 Moving-Coil Phono Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.4 Line Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.5 Inter-Stage and Power Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1.6 Microphone Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 System-Level Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.1 Microphone Isolation or Splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.2 Microphone Impedance Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.3 Line to Microphone Input or Direct Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.4 Line Isolation or Hum Eliminators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.5 Loudspeaker Distribution or Constant Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.6 Telephone Isolation or Repeat Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.7 Telephone Directional Coupling or Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2.8 Moving-Coil Phono Step-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Measurements and Data Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 Testing and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1.1 Transmission Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

273

275 275 275 276 276 277 278 280 281 282 283 283 283 285 286 287 287 288 289 290 290 290 291 291 292 293 294 295 295 295 296 296 298 300 300 301 302 302 302

11.3.1.2 Balance Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1.3 Resistances, Capacitances, and Other Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Data Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2.1 Data to Impress or to Inform? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2.2 Comprehensive Data Sheet Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Installation and Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 A Few Installation Tips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 De-Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

274

302 303 303 303 303 306 306 306 307

Audio Transformers

275

11.1 Audio Transformer Basics Since the birth of audio electronics, the audio transformer has played an important role. When compared to modern miniaturized electronics, a transformer seems large, heavy, and expensive but it continues to be the most effective solution in many audio applications. The usefulness of a transformer lies in the fact that electrical energy can be transferred from one circuit to another without direct connection (e.g., isolation from ground loops), and in the process the energy can be readily changed from one voltage level to another (e.g., impedance matching). Although a transformer is not a complex device, considerable explanation is required to properly understand how it operates. This chapter is intended to help the audio system engineer properly select and apply transformers. In the interest of simplicity, only basic concepts of their design and manufacture will be discussed.

Figure 11-1. Magnetic field surrounding conductor.

11.1.1 Basic Principles and Terminology 11.1.1.1 Magnetic Fields and Induction As shown in Fig. 11-1, a magnetic field is created around any conductor (wire) in which current flows. The strength of the field is directly proportional to current. These invisible magnetic lines of force, collectively called flux, are set up at right angles to the wire and have a direction, or magnetic polarity, that depends on the direction of current flow. Note that although the flux around the upper and lower wires have different directions, the lines inside the loop aid because they point in the same direction. If an alternating current flows in the loop, the instantaneous intensity and polarity of the flux will vary at the same frequency and in direct proportion to Fig. 11-2, as expanding, contracting, and reversing in polarity with each cycle of the ac current. The law of induction states that a voltage will be induced in a conductor exposed to changing flux and that the induced voltage will be proportional to the rate of the flux change. This voltage has an instantaneous polarity which opposes the original current flow in the wire, creating an apparent resistance called inductive reactance. Inductive reactance is calculated according to the formula X L = 2SfL where, XL is inductive reactance in ohms, f is the frequency in hertz, L is inductance in Henrys.

Figure 11-2. ac magnetic field.

An inductor generally consists of many turns or loops of wire called a coil, as shown in Fig. 11-3, which links and concentrates magnetic flux lines, increasing the flux density. The inductance of any given coil is determined by factors such as the number of turns, the physical dimensions and nature of the winding, and the properties of materials in the path of the magnetic flux.

(11-1) Figure 11-3. Coil concentrates flux.

According to the law of induction, a voltage will be induced in any conductor (wire) that cuts flux lines.

276

Chapter 11

Therefore, if we place two coils near each other as shown in Fig. 11-4, an ac current in one coil will induce an ac voltage in the second coil. This is the essential principle of energy transfer in a transformer. Because they require a changing magnetic field to operate, transformers will not work at dc. In an ideal transformer, the magnetic coupling between the two coils is total and complete, i.e., all the flux lines generated by one coil cut across all the turns of the other. The coupling coefficient is said to be unity or 1.00.

equal 20 W. To do this, a current of 2 A must be drawn by the primary, making input power equal 20 W. Since the primary is now drawing 2 A with 10 V applied, its impedance appears to be 5 ȍ. In other words, the 20 ȍ load impedance on the secondary has been reflected to the primary as 5 ȍ. In this example, a transformer with a 1:2 turns ratio exhibited an impedance ratio of 1:4. Transformers always reflect impedances from one winding to another by the square of their turns ratio or, expressed as an equation Np 2 Zp ----- = § ------· © Ns¹ Zs

(11-2)

where, Zp is primary impedance, Zs is secondary impedance, N p/Ns is turns ratio, which is the same as the voltage ratio.

Figure 11-4. Inductive coupling.

11.1.1.2 Windings and Turns Ratio The coil or winding that is driven by an electrical source is called the primary and the other is called the secondary. The ratio of the number of turns on the primary to the number of turns on the secondary is called the turns ratio. Since essentially the same voltage is induced in each turn of each winding, the primary to secondary voltage ratio is the same as the turns ratio. For example, with 100 turns on the primary and 50 turns on the secondary, the turns ratio is 2:1. Therefore, if 20 V were applied to the primary, 10 V would appear at the secondary. Since it reduces voltage, this transformer would be called a step-down transformer. Conversely, a transformer with a turns ratio of 1:2 would be called a step-up transformer since its secondary voltage would be twice that of the primary. Since a transformer cannot create power, the power output from the secondary of an ideal transformer can only equal (and in a real transformer can only be less than) the power input to the primary. Consider an ideal 1:2 step-up transformer. When 10 V is applied to its primary, 20 V appears at its secondary. Since no current is drawn by the primary (this is an ideal transformer—see “11.1.1.3, Excitation Current,” its impedance appears to be infinite or an open circuit. However, when a 20 ȍ load is connected to the secondary, a current of 1 A flows making output power

When a transformer converts voltage, it also converts impedance—and vice versa. The direction in which coils are wound—i.e., clockwise or counterclockwise—and/or the connections to the start or finish of each winding determines the instantaneous polarity of the ac voltages. All windings that are wound in the same direction will have the same polarity between start and finish ends. Therefore, relative to the primary, polarity can be inverted by either (1) winding the primary and secondary in opposite directions, or (2) reversing the start and finish connections to either winding. In schematic symbols for transformers, dots are generally used to indicate which ends of windings have the same polarity. Observing polarity is essential when making series or parallel connections to transformers with multiple windings. Taps are connections made at any intermediate point in a winding. For example, if 50 turns are wound, an electrical connection brought out, and another 50 turns completes the winding, the 100 turn winding is said to be centertapped. 11.1.1.3 Excitation Current While an ideal transformer has infinite primary inductance, a real transformer does not. Therefore, as shown in Fig. 11-5, when there is no load on the secondary and an ac voltage is applied to the primary, an excitation current will flow in the primary, creating magnetic excitation flux around the winding. In theory, the current is due only to the inductive reactance of the primary winding. In accordance with Ohm’s Law and the equation for inductive reactance,

Audio Transformers Ep I E = -------------2SfL p

(11-3)

where, IE is excitation current in amperes, EP is primary voltage in volts, f is frequency in hertz, LP is primary inductance in henrys.

277

constant. Note that the slope of the Ip and flux waveforms stays constant as frequency is changed. Since, according to the law of induction, the voltage induced in the secondary is proportional to this slope or rate of change, output voltage also remains uniform, or flat versus frequency.

Ep IE

Figure 11-5. Excitation current.

Obviously, if primary inductance were infinite, excitation current would be zero. As shown in Fig. 11-6, when a load is connected, current will flow in the secondary winding. Because secondary current flows in the opposite direction, it creates magnetic flux which opposes the excitation flux. This causes the impedance of the primary winding to drop, resulting in additional current being drawn from the driving source. Equilibrium is reached when the additional flux is just sufficient to completely cancel that created by the secondary. The result, which may surprise some, is that flux density in a transformer is not increased by load current. This also illustrates how load current on the secondary is reflected to the primary.

Ip and flux

Es f

Figure 11-7. Excitation current and flux vary inversely with frequency. RL

Figure 11-6. Cancellation of flux generated by load current.

Fig. 11-7 illustrates the relationships between voltage, excitation current, and flux in a transformer as frequency is changed. The horizontal scale is time. The primary voltage Ep is held constant as the frequency is changed (tripled and then tripled again). For example, the left waveform could represent one cycle at 100 Hz, the middle 300 Hz, and the right 900 Hz. Because of the primary inductance, excitation current Ip will decrease linearly with frequency—i.e., halving for every doubling in frequency or decreasing at 6 dB per octave. The magnitude of the magnetic flux will likewise decrease exactly the same way. Note that the inductance causes a 90q phase lag between voltage and current as well. Since the slew rate of a constant amplitude sine wave increases linearly with frequency—i.e., doubling for every doubling in frequency or increasing at 6 dB per octave—the resultant flux rate of change remains

11.1.2 Realities of Practical Transformers Thus far, we have not considered the unavoidable parasitic elements which exist in any practical transformer. Even the design of a relatively simple 60 Hz power transformer must take parasitics into account. The design of an audio transformer operating over a 20 Hz to 20 kHz frequency range is much more difficult because these parasitics often interact in complex ways. For example, materials and techniques that improve low-frequency performance are often detrimental to high-frequency performance and vice versa. Good transformer designs must consider both the surrounding electronic circuitry and the performance ramifications of internal design tradeoffs. A schematic representation of the major low frequency parasitic elements in a generalized transformer is shown in Fig. 11-8. The IDEAL TRANSFORMER represents a perfect transformer having a turns ratio of 1:N and no parasitic elements of any kind.

Chapter 11

The actual transformer is connected at the PRI terminals to the driving voltage source, through its source impedance RG, and at the SEC terminals to the load RL. RP

RG PRI

IDEAL RC LP

SEC

XFMR

Figure 11-8. Transformer low-frequency parasitic elements.

One of the main goals in the design of any transformer is to reduce the excitation current in the primary winding to negligible levels so as not to become a significant load on the driving source. For a given source voltage and frequency, primary excitation current can be reduced only by increasing inductance LP . In the context of normal electronic circuit impedances, very large values of inductance are required for satisfactory operation at the lowest audio frequencies. Of course, inductance can be raised by using a very large number of coil turns but, for reasons discussed later, there are practical limits due to other considerations. Another way to increase inductance by a factor of 10,000 or more is to wind the coil around a highly magnetic material, generally referred to as the core. 11.1.2.1 Core Materials and Construction Magnetic circuits are quite similar to electric circuits. As shown in Fig. 11-11, magnetic flux always takes a closed path from one magnetic pole to the other and, like an electric current, always favors the paths of highest conductivity or least resistance. The equivalent of applied voltage in magnetic circuits is magnetizing force, symbolized H. It is directly proportional to ampere-turns (coil current I times its number of turns N) and inversely proportional to the flux path length Ɛ in the magnetic circuit. The equivalent of electric current flow is flux density, symbolized B. It represents the number of magnetic flux lines per square unit of area. A graphic plot of the relationship between field intensity and flux density is shown in Fig. 11-9 and is referred to as the “B-H loop” or “hysteresis loop” for a given material. In the United States, the most commonly used units for magnetizing force and flux density are the Oersted and Gauss, respectively, which are CGS (centimeter, gram, second) units. In Europe, the SI (Système Internationale) units amperes per meter and tesla, respectively, are more common. The slope of the B-H loop indicates how an incremental increase in applied magnetizing force changes the resulting flux density. This slope is

effectively a measure of conductivity in the magnetic circuit and is called permeability, symbolized ȝ. Any material inside a coil, which can also serve as a form to support it, is called a core. By definition, the permeability of a vacuum, or air, is 1.00 and common nonmagnetic materials such as aluminum, brass, copper, paper, glass, and plastic also have a permeability of 1 for practical purposes. The permeability of some common ferromagnetic materials is about 300 for ordinary steel, about 5000 for 4% silicon transformer steel, and up to about 100,000 for some nickel-iron-molybdenum alloys. Because such materials concentrate magnetic flux, they greatly increase the inductance of a coil. Audio transformers must utilize both high-permeability cores and the largest practical number of coil turns to create high primary inductance. Coil inductance increases as the square of the number of turns and in direct proportion to the permeability of the core and can be approximated using the equation 2

3.2N PAL = --------------------(11-4) 8 10 l where, L is the inductance in henrys, N is the number of coil turns, μ is the permeability of core, A is the cross-section area of core in square inches, l is the mean flux path length in inches. Saturation

Flux density "—gauss

278

0 Hysteresis

Saturation 0 Magnetizing force H—oersteds

Figure 11-9. B-H loop for magnetic core material.

The permeability of magnetic materials varies with flux density. As shown in Fig. 11-9, when magnetic field intensity becomes high, the material can saturate, essentially losing its ability to conduct any additional

Audio Transformers flux. As a material saturates, its permeability decreases until, at complete saturation, its permeability becomes that of air or 1. In audio transformer applications, magnetic saturation causes low-frequency harmonic distortion to increase steadily for low-frequency signals as they increase in level beyond a threshold. In general, materials with a higher permeability tend to saturate at a lower flux density. In general, permeability also varies inversely with frequency. Magnetic hysteresis can be thought of as a magnetic memory effect. When a magnetizing force saturates material that has high-hysteresis, it remains strongly magnetized even after the force is removed. High-hysteresis materials have wide or square B-H loops and are used to make magnetic memory devices and permanent magnets. However, if we magnetically saturate zero-hysteresis material, it will have no residual magnetism (flux density) when the magnetizing force is removed. But virtually all high-permeability core materials have some hysteresis, retaining a small memory of their previous magnetic state. Hysteresis can be greatly reduced by using certain metal alloys that have been annealed or heat-treated using special processes. In audio transformers, the nonlinearity due to magnetic hysteresis causes increased harmonic distortion for low-frequency signals at relatively low signal levels. Resistor RC in Fig. 11-8 is a nonlinear resistance that, in the equivalent circuit model, represents the combined effects of magnetic saturation, magnetic hysteresis, and eddy-current losses. The magnetic operating point, or zero signal point, for most transformers is the center of the B-H loop shown in Fig. 11-9, where the net magnetizing force is zero. Small ac signals cause a small portion of the loop to be traversed in the direction of the arrows. Large ac signals traverse portions farther from the operating point and may approach the saturation end points. For this normal operating point at the center, signal distortions (discussed in detail later) caused by the curvature of the loop are symmetrical—i.e., they affect the positive and negative signal excursions equally. Symmetrical distortions produce odd-order harmonics such as third and fifth. If dc current flows in a winding, the operating point will shift to a point on the loop away from the center. This causes the distortion of a superimposed ac signal to become nonsymmetrical. Nonsymmetrical distortions produce even-order harmonics such as second and fourth. When a small dc current flows in a winding, under say 1% of the saturation value, the effect is to add even-order harmonics to the normal odd-order content of the hysteresis distortion, which affects mostly low level signals. The same effects occur

279

when the core becomes weakly magnetized, as could happen via the brief accidental application of dc to a winding, for example. However, the narrow B-H loop indicates that only a weak residual field would remain even if a magnetizing force strong enough to saturate the core were applied and then removed. When a larger dc current flows in a winding, the symmetry of saturation distortion is also affected in a similar way. For example, enough dc current might flow in a winding to move the operating point to 50% of the core saturation value. Only half as much ac signal could then be handled before the core would saturate and, when it did, it would occur only for one direction of the signal swing. This would produce strong second-harmonic distortion. To avoid such saturation effects, air gaps are sometimes intentionally built into the magnetic circuit. This can be done, for example, by placing a thin paper spacer between the center leg of the E and I cores of Fig. 11-10. The magnetic permeability of such a gap is so low—even though it may be only a few thousandths of an inch—compared to the core material, that it effectively controls the flux density in the entire magnetic circuit. Although it drastically reduces the inductance of the coil, gapping is done to prevent flux density from reaching levels that would otherwise saturate the core, especially when substantial dc is present in a winding.

Figure 11-10. Core laminations are stacked and interleaved around bobbin that holds windings.

Because high-permeability materials are usually electrical conductors as well, small voltages are also induced in the cross-section of the core material itself, giving rise

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to eddy currents. Eddy currents are greatly reduced when the core consists of a stack of thin sheets called laminations, as shown in Fig. 11-10. Because the laminations are effectively insulated from each other, eddy currents generally become insignificant. The E and I shaped laminations shown form the widely used shell or double-window, core construction. Its parallel magnetic paths are illustrated in Fig. 11-11. When cores are made of laminations, care must be taken that they are flat and straight to avoid tiny air gaps between them that could significantly reduce inductance.

Figure 11-11. Magnetic circuits in shell core.

A toroidal core is made by rolling a long thin strip of core material into a coiled ring shape that looks something like a donut. It is insulated with a conformal coating or tape and windings are wound around the core through the center hole using special machines. With a toroidal core, there are no unintended air gaps that can degrade magnetic properties. Audio transformers don’t often use toroidal cores because, especially in high bandwidth designs where multiple sections or Faraday shields are necessary, physical construction becomes very complex. Other core configurations include the ring core, sometimes called semitoroidal. It is similar to core of Fig. 11-11 but without the center section and windings are placed on the sides. Sometimes a solid—not laminations—metal version of a ring core is cut into two pieces having polished mating faces. These two C-cores are then held together with clamps after the windings are installed.

11.1.2.2 Winding Resistances and Auto-Transformers If zero-resistance wire existed, some truly amazing transformers could be built. In a 60 Hz power transformer, for example, we could wind a primary with tiny wire on a tiny core to create enough inductance to make excitation current reasonable. Then we could wind a secondary with equally tiny wire. Because the wire has

no resistance and the flux density in the core doesn’t change with load current, this postage-stamp-sized transformer could handle unlimited kilowatts of power—and it wouldn’t even get warm! But, at least until practical superconducting wire is available, real wire has resistance. As primary and secondary currents flow in the winding resistances, the resulting voltage drops cause signal loss in audio transformers and significant heating in power transformers. This resistance can be reduced by using larger—lower gauge—wire or fewer turns, but the required number of turns and the tolerable power loss (or resulting heat) all conspire to force transformers to become physically larger and heavier as their rated power increases. Sometimes silver wire is suggested to replace copper, but since its resistance is only about 6% less, its effect is minimal and certainly not cost-effective. However, there is an alternative configuration of transformer windings, called an auto-transformer, which can reduce the size and cost in certain applications. Because an auto-transformer electrically connects primary and secondary windings, it can’t be used where electrical isolation is required! In addition, the size and cost advantage is maximum when the required turns ratio is very close to 1:1 and diminishes at higher ratios, becoming minimal in practical designs at about 3:1 or 1:3. For example, in a hypothetical transformer to convert 100 V to 140 V, the primary could have 100 turns and the secondary 140 turns of wire. This transformer, with its 1:1.4 turns ratio, is represented in the upper diagram of Fig. 11-12. If 1 A of secondary (load) current IS flows, transformer output power is 140 W and 1.4 A of primary current IP will flow since input and output power must be equal in the ideal case. In a practical transformer, the wire size for each winding would be chosen to limit voltage losses and/or heating. An auto-transformer essentially puts the windings in series so that the secondary voltage adds to (boosting) or subtracts from (bucking) the primary input voltage. A step-up auto-transformer is shown in the middle diagram of Fig. 11-12. Note that the dots indicate ends of the windings with the same instantaneous polarity. A 40 V secondary (the upper winding) series connected, as shown with the 100 V primary, would result in an output of 140 V. Now, if 1 A of secondary load current I S flows, transformer output power is only 40 W and only 0.4 A of primary current IP will flow. Although the total power delivered to the load is still 140 W, 100 W have come directly from the driving source and only 40 W have been transformed and added by the auto-transformer. In the auto-transformer, 100 turns of smaller wire can be used for the primary and only 40

Audio Transformers

EP IS

281

result, each winding may have a dc resistance as high as several thousand ohms. Transformer primary and secondary winding resistances are represented by R P and RS, respectively, in Fig. 11-8. 11.1.2.3 Leakage Inductance and Winding Techniques

RL IP

In an ideal transformer, since all flux generated by the primary is linked to the secondary, a short circuit on the secondary would be reflected to the primary as a short circuit. However, in real transformers, the unlinked flux causes a residual or leakage inductance that can be measured at either winding. Therefore, the secondary would appear to have residual inductance if the primary were shorted and vice-versa. The leakage inductance is shown as LL in the model of Fig. 11-13. Note that leakage inductance is reflected from one winding to another as the square of turns ratio, just as other impedances are. CW RG

RP PRI

R CP C

IDEAL 1

XFMR

RS CS

SEC

RL CL

IP RL

Figure 11-12. Auto-transformers employ a buck/boost principle.

turns of heavier wire is needed for the secondary. Compare this to the total of 240 turns of heavier wire required in the transformer. A step-down auto-transformer is shown in the bottom diagram of Fig. 11-12. Operation is similar except that the secondary is connected so that its instantaneous polarity subtracts from or bucks the input voltage. For example, we could step down U.S. 120 Vac power to Japanese 100 Vac power by configuring a 100 V to 20 V step-down transformer as an auto-transformer. Thus, a 100 W load can be driven using only a 20 W rated transformer. The windings of low level audio transformers may consist of hundreds or even many thousands of turns of wire, sometimes as small as #46 gauge, whose 0.0015 inch diameter is comparable to a human hair. As a

Figure 11-13. Transformer high frequency parasitic elements.

The degree of flux coupling between primary and secondary windings depends on the physical spacing between them and how they are placed with respect to each other. The lowest leakage inductance is achieved by winding the coils on a common axis and as close as possible to each other. The ultimate form of this technique is called multi-filar winding where multiple wires are wound simultaneously as if they were a single strand. For example, if two windings—i.e. primary and secondary—are wound as one, the transformer is said to be bi-filar wound. Note in the cross-section view of Fig. 11-14 how the primary and secondary windings are side-by-side throughout the entire winding. Another technique to reduce leakage inductance is to use layering, a technique in which portions or sections of the primary and/or secondary are wound in sequence over each other to interleave them. For example, Fig. 11-15 shows the cross-section of a three-layer transformer where half the primary is wound, then the secondary, followed by the other half of the primary. This results in considerably less leakage inductance than just a secondary over primary two-layer design. Leakage

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inductance decreases rapidly as the number of layers is increased.

= Primary

= Secondary

Figure 11-14. Layered windings.

tances. These capacitances within the windings are represented by CP and CS in the circuit model of Fig. 11-13. Additional capacitances will exist between the primary and secondary windings and are represented by capacitors CW in the model. Sometimes layers of insulating tape are added to increase the spacing, therefore reducing capacitance, between primary and secondary windings. In the bi-filar windings of Fig. 11-14, since the wires of primary and secondary windings are side by side throughout, the inter-winding capacitances CW can be quite high. In some applications, interwinding capacitances are very undesirable. They are completely eliminated by the use of a Faraday shield between the windings. Sometimes called an electrostatic shield, it generally takes the form of a thin sheet of copper foil placed between the windings. Obviously, transformers that utilize multiple layers to reduce leakage inductance will require Faraday shields between all adjacent layers. In Fig. 11-15 the dark lines between the winding layers are the Faraday shields. Normally, all the shields surrounding a winding are tied together and treated as a single electrical connection. When connected to circuit ground, as shown in Fig. 11-16, a Faraday shield intercepts the capacitive current that would otherwise flow between transformer windings. CC1 C1

= Primary

= Secondary

RG1

Figure 11-15. Bi-filar windings.

11.1.2.4 Winding Capacitances and Faraday Shields To allow the maximum number of turns in a given space, the insulation on the wire used to wind transformers is very thin. Called magnet wire, it is most commonly insulated by a thin film of polyurethane enamel. A transformer winding is made, in general, by spinning the bobbin shown in Fig. 11-10 on a machine similar to a lathe and guiding the wire to form a layer one wire thick across the length of the bobbin. The wire is guided to traverse back and forth across the bobbin to form a coil of many layers as shown in Fig. 11-15, where the bobbin cross-section is the solid line on three sides of the winding. This simple side-to-side, back-and-forth winding results in considerable layer-to-layer capacitance within a winding or winding section. More complex techniques such as universal winding are sometimes used to substantially reduce winding capaci-

RP Pri

RG2

C3 LLS RS

Ideal 1

Xfmr C2

Sec

RL CL

C4 CC2

Faraday Shield

Figure 11-16. High frequency equivalent circuit of a transformer with Faraday shield and driven by a balanced source.

Faraday shields are nearly always used in transformers designed to eliminate ground noise. In these applications, the transformer is intended to respond only to the voltage difference or signal across its primary and have no response to the noise that exists equally (or common-mode) at the terminals of its primary. A Faraday shield is used to prevent capacitive coupling, via CW in Fig. 11-13, of this noise to the secondary. For any winding connected to a balanced line, the matching of capacitances to ground is critical to the rejection of

Audio Transformers common-mode noise, or CMRR, as discussed in Chapter 37. In Fig. 11-16, if the primary is driven by a balanced line, C 1 and C 2 must be very accurately matched to achieve high CMRR. In most applications, such as microphone or line input transformers, the secondary is operated unbalanced—i.e., one side is grounded. This relaxes the matching requirements for capacitances C3 and C4. Although capacitances CC1 and CC2 are generally quite small—a few pF—they have the effect of diminishing CMRR at high audio frequencies and limiting rejection of RF interference. 11.1.2.5 Magnetic Shielding A magnetic shield has a completely different purpose. Devices such as power transformers, electric motors, and television or computer monitor cathode-ray tubes generate powerful ac magnetic fields. If such a field takes a path through the core of an audio transformer, it can induce an undesired voltage in its windings—most often heard as hum. If the offending source and the victim transformer have fixed locations, orientation of one or both can sometimes nullify the pickup. In Fig. 11-11 note that an external field that flows vertically through the core will cause a flux gradient across the length of the coil, inducing a voltage in it, but a field that flows horizontally through the core will not. Such magnetic pickup is usually worse in input transformers (discussed later) because they generally have more turns. It should also be noted that higher permeability core materials are more immune to external fields. Therefore, an unshielded output transformer with a high nickel core will be more immune than one with a steel core. Another way to prevent such pickup is to surround the core with a closed—no air gap—magnetic path. This magnetic shield most often takes the form of a can or box with tight-fitting lid and is made of high permeability material. While the permeability of ordinary steel, such as that in electrical conduit, is only about 300, special-purpose nickel alloys can have permeability as high as 100,000. Commercial products include Mumetal®, Permalloy®, HyMu® and Co-Netic®.1,2 Since the shield completely surrounds the transformer, the offending external field will now flow through it instead of the transformer core. Generally speaking, care must be taken not to mechanically stress these metals because doing so will significantly decrease their permeability. For this reason, most magnetic shield materials must be re-annealed after they are fabricated. The effectiveness of magnetic shielding is generally rated in dB. The transformer is placed in an external magnetic field of known strength, generally at 60 Hz.

283

Its output without and with the shield is then compared. For example, a housing of 1 / 8 inch thick cast iron reduces pickup by about 12 dB, while a 0.030 inch thick Mumetal can reduces it by about 30 dB. Where low-level transformers operate near strong magnetic fields, several progressively smaller shield cans can be nested around the transformer. Two or three Mumetal cans can provide 60 dB and 90 dB of shielding, respectively. In very strong fields, because high permeability materials might saturate, an iron or steel outer can is sometimes used. Toroidal power transformers can have a weaker radiated magnetic field than other types. Using them can be an advantage if audio transformers must be located nearby. However, a toroidal transformer must be otherwise well designed to produce a low external field. For example, every winding must completely cover the full periphery of the core. The attachment points of the transformer lead wires are frequently a problem in this regard. To gain size and cost advantages, most commercial power transformers of any kind are designed to operate on the verge of magnetic saturation of the core. When saturation occurs in any transformer, magnetic field radiation dramatically increases. Power transformers designed to operate at low flux density will prevent this. A standard commercial power transformer, when operated at reduced primary voltage, will have a very low external field—comparable to that of a standard toroidal design. 11.1.3 General Application Considerations For any given application, a number of parameters must be considered when selecting or designing an appropriate audio transformer. We will discuss how the performance of a transformer can be profoundly affected by its interaction with surrounding circuitry. 11.1.3.1 Maximum Signal Level, Distortion, and Source Impedance Because these parameters are inextricably interdependent, they must be discussed as a group. Although transformer operating level is often specified in terms of power such as dBm or watts, what directly affects distortion is the equivalent driving voltage. Distortion is caused by excitation current in the primary winding which is proportional to primary voltage, not power. Referring to Fig. 11-8, recall that nonlinear resistance RC represents the distortion-producing mechanisms of the core material. Consider that, if both RG, the driving source impedance, and RP , the internal winding resis-

284

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tance, were zero, the voltage source—by definition zero impedance—would effectively short out RC, resulting in zero distortion! But in a real transformer design there is a fixed relationship between signal level, distortion, and source impedance. Since distortion is also a function of magnetic flux density, which increases as frequency decreases, a maximum operating level specification must also specify a frequency. The specified maximum operating level, maximum allowable distortion at a specified low frequency, and maximum allowable source impedance will usually dictate the type of core material that must be used and its physical size. And, of course, cost plays a role, too. The most commonly used audio transformer core materials are M6 steel (a steel alloy containing 6% silicon) and 49% nic ke l or 84% n ick el (alloys containing 49% or 84% nickel plus iron and molybdenum). Nickel alloys are substantially more expensive than steel. Fig. 11-17 shows how the choice of core material affects low-frequency distortion as signal level changes. The increased distortion at low levels is due to magnetic hysteresis and at high levels is due to magnetic saturation. Fig. 11-18 shows how distortion decreases rapidly with increasing frequency. Because of differences in their hysteresis distortion, the falloff is most rapid for the 84% nickel and least rapid for the steel. Fig. 11-19 shows how distortion is strongly affected by the impedance of the driving source. The plots begin at 40 ȍ because that is the resistance of the primary winding. Therefore, maximum operating levels predicated on higher frequencies, higher distortion, and lower source impedance will always be higher than those predicated on lower frequencies, lower distortion, and lower source impedance. As background, it should be said that THD, or total harmonic distortion, is a remarkably inadequate way to describe the perceived awfulness of distortion. Distortion consisting of low-order harmonics, 2nd or 3rd for example, is dramatically less audible than that consisting of high order harmonics, 7th or 13th for example. Consider that, at very low frequencies, even the finest loudspeakers routinely exhibit harmonic distortion in the range of several percent at normal listening levels. Simple distortion tests whose results correlate well with the human auditory experience simply don’t exist. Clearly, such perceptions are far too complex to quantify with a single figure. One type of distortion that is particularly audible is intermodulation or IM distortion. Test signals generally combine a large low-frequency signal with a smaller high-frequency signal and measure how much the amplitude of the high frequency is modulated by the

1.0%

M6 Steel 0.1% 49% Nickel

THD 0.01%

84% Nickel 0.001%

20 10 0 Signal level—dBu

+10

+20 +30

Figure 11-17. Measured THD at 20 Hz and 40 : source versus signal level for three types of core materials. 1.0%

0.1% THD

M6 STEEL 0.01% 49% NICKEL 84% NICKEL 0.001% 20 Hz

200 Hz 2 kHz Frequency—Hz

20 kHz

Figure 11-18. Measured THD at 0 dBu and 40 : source versus frequency for the cores of Figure 11-17.

10%

1.0% THD 0.1%

M6 Steel 49% Nickel 84% Nickel

0.001%

0.001% 10

100 1k Source impedance—ohms

10 k

Figure 11-19. Measured THD at 0 dBu and 20 Hz versus source impedance for the cores of Figs. 11-17 and 11-18.

lower frequency. Such intermodulation creates tones at new, nonharmonic frequencies. The classic SMPTE (Society of Motion Picture and Television Engineers)

Audio Transformers

11.1.3.2 Frequency Response The simplified equivalent circuit of Fig. 11-20 shows the high-pass RL filter formed by the circuit resistances and transformer primary inductance LP . The effective source impedance is the parallel equivalent of RG + RP and RS + RL. When the inductive reactance of LP equals the effective source impedance, low-frequency response will fall to 3 dB below its mid-band value. For example, consider a transformer having an LP of 10 henrys and winding resistances RP and RS of 50 ȍ each. The generator impedance RG is 600 ȍ and the load RL is 10 kȍ. The effective source impedance is then 600 ȍ + 50 ȍ in parallel with 10 kȍ + 50 ȍ, which computes to about 610 ȍ. A 10 henry inductor will have 610 ȍ of reactance at about 10 Hz, making response 3 dB down at that frequency. If the generator impedance R G were made 50 ȍ instead, response would be í3 dB at 1.6 Hz.

Lower source impedance will always extend low-frequency bandwidth. Since the filter is single pole, response falls at 6 dB per octave. As discussed earlier, the permeability of most core material steadily increases as frequency is lowered and typically reaches its maximum somewhere under 1 Hz. This results in an actual roll-off rate less than 6 dB per octave and a corresponding improvement in phase distortion—deviation from linear phase. Although a transformer cannot have response to 0 Hz or dc, it can have much less phase distortion than a coupling capacitor chosen for the same cutoff frequency. Or, as a salesperson might say, “It’s not a defect, it’s a feature.” RG

RP Pri

Sec

Loss

Increasing R RG + RP II RS + RL r6 dB/Octave Frequency

Figure 11-20. Simplified low frequency transformer equivalent circuit.

The simplified equivalent schematic of Fig. 11-21 shows the parasitic elements that limit and control high-frequency response. CW RG

RP Pri

Loss

IM distortion test mixes 60 Hz and 7 kHz signals in a 4:1 amplitude ratio. For virtually all electronic amplifier circuits, there is an approximate relationship between harmonic distortion and SMPTE IM distortion. For example, if an amplifier measured 0.1% THD at 60 Hz at a given operating level, its SMPTE IM distortion would measure about three or four times that, or 0.3% to 0.4% at an equivalent operating level. This correlation is due to the fact that electronic non-linearities generally distort audio signals without regard to frequency. Actually, because of negative feedback and limited gain bandwidth, most electronic distortions become worse as frequency increases. Distortion in audio transformers is different in a way that makes it sound unusually benign. It is caused by the smooth symmetrical curvature of the magnetic transfer characteristic or B-H loop of the core material shown in Fig. 11-9. The nonlinearity is related to flux density that, for a constant voltage input, is inversely proportional to frequency. The resulting harmonic distortion products are nearly pure third harmonic. In Fig. 11-18, note that distortion for 84% nickel cores roughly quarters for every doubling of frequency, dropping to less than 0.001% above about 50 Hz. Unlike that in amplifiers, the distortion mechanism in a transformer is frequency selective. This makes its IM distortion much less than might be expected. For example, the Jensen JT-10KB-D line input transformer has a THD of about 0.03% for a +26 dBu input at 60 Hz. But, at an equivalent level, its SMPTE IM distortion is only about 0.01%—about a tenth of what it would be for an amplifier having the same THD.

285

RS RC

RL CS

Sec CL

Increasing RD 12 dB/Oct Frequency

Figure 11-21. Simplified high-frequency transformer equivalent circuit.

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Chapter 11

Except in bi-filar wound types discussed below, leakage inductance L L and load capacitance are the major limiting factors. This is especially true in Faraday shields because of the increase in leakage inductance. Note that a low-pass filter is formed by series leakage inductance LL with shunt winding capacitance CS plus external load capacitance CL. Since this filter has two reactive elements, it is a two-pole filter subject to response variations caused by damping. Resistive elements in a filter provide damping, dissipating energy when the inductive and capacitive elements resonate. As shown in the figure, if damping resistance R D is too high, response will rise before it falls and if damping resistance is too low, response falls too early. Optimum damping results in the widest bandwidth with no response peak. It should be noted that placing capacitive loads CL on transformers with high leakage inductance not only lowers their bandwidth but also changes the resistance required for optimum damping. For most transformers, RL controls damping. In the time domain, u n d e r- d a m p i n g m a n i f e s t s i t s e l f a s r i n g i n g o n square-waves as shown in Fig. 11-22. When loaded by its specified load resistance, the same transformer responds as shown in Fig. 11-23. In some transformers, source impedance also provides significant damping.

Figure 11-22. Undamped response.

In bi-filar wound transformers, leakage inductance L L is very low but interwinding capacitance C W and winding capacitances CP and CS are quite high. Leakage inductance must be kept very small in applications such as line drivers because large cable capacitances C L would otherwise be disastrous to high-frequency response. Such transformers are generally referred to as output transformers. Also note that a low-pass filter is formed by series RG and shunt CP plus CS. Therefore, driving sources may limit high-frequency response if their source impedance RG is too high. In normal 1:1

Figure 11-23. Proper damping.

bi-filar output transformer designs, CW actually works to capacitively couple very high frequencies between windings. Depending on the application, this can be either a defect or a feature. 11.1.3.3 Insertion Loss The power output from a transformer will always be slightly less than power input to it. As current flows in its windings, their dc resistance causes additional voltage drops and power loss as heat. Broadly defined, insertion loss or gain is that caused by inserting a device into the signal path. But, because even an ideal lossless transformer can increase or decrease signal level by virtue of its turns ratio, the term insertion loss is usually defined as the difference in output signal level between the real transformer and an ideal one with the same turns ratio. The circuit models, Thevenin equivalent circuits, and equations for both ideal and real transformers are shown in Fig. 11-24. For example, consider an ideal 1:1 turns ratio transformer and RG = RL = 600 ȍ. Since Ns/Np is 1, the equivalent circuit becomes simply Ei in series with RG or 600 ȍ. When RL is connected, a simple voltage divider is formed, making EO = 0.5 Ei or a 6.02 dB loss. For a real transformer having R P = R S = 50 ȍ, the equivalent circuit becomes Ei in series with RG + RP + RS or 700 ȍ. Now, the output EO = 0.462 Ei or a 6.72 dB loss. Therefore, the insertion loss of the transformer is 0.70 dB. Calculations are similar for transformers with turns ratios other than 1:1, except that voltage is multiplied by the turns ratio and reflected impedances are multiplied by the turns ratio squared as shown in the equations. For example, consider a 2:1 turns ratio transformer, R G = 600 ȍ, and R L = 150 ȍ. The ideal transformer

Audio Transformers

287

IDEAL

IDEAL RP

XFMR

NS Np

NS × Ideal EO = Ei × Np

XFMR

N 2 RG × S Np

Ei ×

RS NS

Ei ×

Insertion loss (dB) = 20 log

RP ×

NS 2 Np RS

NS Np

Real EO = Ei ×

N 2 RG × S + RL Np

NS Np

× RG + RP

RL NS 2 + RS + RL × Np

Real EO Ideal EO

Figure 11-24. Insertion loss compares the outputs of real and ideal transformers.

output appears as 0.5 Ei in series with RG /4 or 150 ȍ. When R L is connected, a simple voltage divider is formed making EO = 0.25 Ei or a 12.04 dB loss. For a real transformer having RP = 50 ȍ and RS = 25 ȍ, the equivalent circuit becomes 0.5 E i in series with ( R G + R P ) / 4 + R S o r 1 8 7 . 5 ȍ . N o w, t h e o u t p u t EO = 0.222 Ei or a 13.07 dB loss. Therefore, the insertion loss of this transformer is 1.03 dB. 11.1.3.4 Sources with Zero Impedance One effect of using negative feedback around a high gain amplifier is to reduce its output impedance. Output impedance is reduced by the feedback factor, which is open-loop gain in dB minus closed-loop gain in dB. A typical op-amp with an open-loop gain of 80 dB, set for closed-loop gain of 20 dB, the feedback factor is 80 dB í 20 dB = 60 dB or 1000, will have its open-loop output impedance of 50 ȍ reduced by the feedback factor (1000) to about 0.05 ȍ. Within the limits of linear operation—i.e., no current limiting or voltage clipping—the feedback around the amplifier effectively forces the output to remain constant regardless of loading. For all practical purposes the op-amp output can be considered a true voltage source. As seen in Fig. 11-19, the distortion performance of any transformer is significantly improved when the driving source impedance is less than the dc resistance of the primary. However, little is gained for source impedances below about 10% of the winding dc resistance. For example, consider a typical line output trans-

former with a primary dc resistance of 40 ȍ. A driving source impedance well under 4 ȍ will result in lowest distortion. The line drivers shown in Fig. 11-28 and Fig. 11-29 use a paralleled inductor and resistor to isolate or decouple the amplifier from the destabilizing effects of load (cable) capacitance at very high frequencies. Because the isolator’s impedance is well under an ohm at all audio frequencies, it is much preferred to the relatively large series, or build-out, resistor often used for the purpose. It is even possible for an amplifier to generate negative output resistance to cancel the winding resistance of the output transformer. Audio Precision uses such a patented circuit in their System 1 audio generator to reduce transformer-related distortion to extremely low levels.

11.1.3.5 Bi-Directional Reflection of Impedances The impedances associated with audio transformers may seem confusing. Much of the confusion probably stems from the fact that transformers can simultaneously reflect two different impedances—one in each direction. One is the impedance of the driving source, as seen from the secondary, and the other is the impedance of the load, as seen from the primary. Transformers simply reflect impedances, modified by the square of their turns ratio, from one winding to another. However, because of their internal parasitic elements discussed previously, transformers tend to produce optimum results when used within a specified range of external impedances.

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There is essentially no intrinsic impedance associated with the transformer itself. With no load on its secondary, the primary of a transformer is just an inductor and its impedance will vary linearly with frequency. For example, a 5 H primary winding would have an input impedance of about 3 kȍ at 100 Hz, 30 kȍ at 1 kHz, and 300 kȍ at 10 kHz. In a proper transformer design, this self-impedance, as well as those of other internal parasitics, should have negligible effects on normal circuit operation. The following applications will illustrate the point. A 1:1 output transformer application is shown in Fig. 11-25. It has a winding inductance of about 25 H and negligible leakage inductance. The open circuit impedance, at 1 kHz, of either winding is about 150 kȍ. Since the dc resistance is about 40 ȍ per winding, if the primary is short circuited, the secondary impedance will drop to 80 ȍ. If we place the transformer between a zero-impedance amplifier (more on that later) and a load, the amplifier will see the load through the transformer and the load will see the amplifier through the transformer. In our example, the amplifier would look like 80 ȍ to the output line/load and the 600 ȍ line/load would look like 680 ȍ to the amplifier. If the load were 20 kȍ, it would look like slightly less than 20 kȍ because the open circuit transformer impedance, 150 kȍ at 1 kHz, is effectively in parallel with it. For most applications, these effects are trivial.

16:1 impedance ratio, the secondary open circuit impedance is about 125 kȍ. The dc resistances are about 2.5 kȍ for the primary and 92 ȍ for the secondary. Since this is an input transformer, it must be used with the specified secondary load resistance of 2.43 kȍ for proper damping (flat frequency response). This load on the secondary will be transformed by the turns ratio to look like about 42 kȍ at the primary. To minimize the noise contribution of the amplifier stage, we need to know what the transformer secondary looks like, impedancewise, to the amplifier. If we assume that the primary is driven from the line in our previous output transformer example with its 80 ȍ source impedance, we can calculate that the secondary will look like about 225 ȍ to the amplifier input. Actually, any source impedance less than 1 kȍ would have little effect on the impedance seen at the secondary. Yel Red 2 M7 Org Whi

Brn

Org

Blk

225 7

Yel Red 80 7 Line 42 k7 Org

Brn

2,430 7

Blk

Org Line receiver application.

150 k7

80 7

150 k7

Red Yel Short circuit

Red Yel Open circuit Brn

Org

18 k7

680 7

125 k7

"Open" circuit.

Whi Brn

Brn

80 7 Red

Yel

Brn

Org 80 7

Line

20 k7

Line

600 7

Red Yel Line driver applications

Figure 11-25. Impedance reflection in a 1:1 transformer.

A 4:1 input transformer example is shown in Fig. 11-26. It has a primary inductance of about 300 H and negligible winding capacitance. The open circuit impedance, at 1 kHz, of the primary is about 2 Mȍ. Because this transformer has a 4:1 turns ratio and, therefore a

Figure 11-26. Impedance reflection in a 4:1 transformer.

Transformers are not intelligent—they can’t magically couple signals in one direction only. Magnetic coupling is truly bi-directional. For example, Fig. 11-27 shows a three-winding 1:1:1 transformer connected to drive two 600 ȍ loads. The driver sees the loads in parallel or, neglecting winding resistances, 300 ȍ. Likewise, a short on either output will be reflected to the driver as a short. Of course, turns ratios and winding resistances must be taken into account to calculate actual driver loading. For the same reason, stereo L and R outputs that drive two windings on the same transformer are effectively driving each other, possibly causing distortion or damage. 11.1.3.6 Transformer Noise Figure Although the step-up turns ratio of a transformer may provide noise-free voltage gain, some 20 dB for a 1:10 turns ratio, it’s important to understand that improve-

Audio Transformers

289

noise figure of a transformer is calculated as shown in Fig. 11-28.

1:1:1 600 7 300 7 600 7

11.1.3.7 Basic Classification by Application

Figure 11-27. Multiple loads are effectively paralleled.

ments in signal-to-noise ratio are not solely due to this gain. Because most amplifying devices generate current noise as well as voltage noise at their inputs, their noise performance will suffer when turns ratio is not the optimum for that particular amplifier (see 21.1.2.3 Microphone Preamp Noise). Noise figure measures, in dB, how much the output signal-to-noise ratio of a system is degraded by a given system component. All resistances, including the winding resistances of transformers, generate thermal noise. Therefore, the noise figure of a transformer indicates the increase in thermal noise or hiss when it replaces an ideal noiseless transformer having the same turns ratio—i.e., voltage gain. The

Turns ratio = 1:10 JT - 115k E Mic R1 E

150 7

Red

Yel

Brn Org Whi

Eout R2 150 7 150 k 7

IDEAL Zout

150 k × (15 k + 1970 + 2465) 150 k + 15 k + 1970 + 2465 1150 k + 15 k

17.205 k7

= 13.636 k7

50 k × 15 k

Eout

NF = 20Log

17,206 (REAL)

= 1.01 dB

13,636 (IDEAL)

R2 150 k7

Redrawn circuit with all impedances reflected to secondary Primary side impedances get multiplied by the square of the turns ratio. R1 = 150 7 × 102 = 15 k7 RP = 19.7 7× 102 7 = 1970 7 RS = Secondary DCR = 2465 7 R2 = 150 k7 (load)

There are two components to the calculation.

REAL Zout

Real Transformer RP RS 1970 7 2465 7 (0) (0) Ideal Transformer

The transformer noise figure is calculated by comparing a real transformer with its winding resistances to an ideal transformer with no winding resistances. First, transform all impedances to the secondary as shown to the left.

1. The additional noise due to the increased output impedance.

Blk

RS = 2465 7 RP = 19.7 7 Example transformer circuit

R1 15 k 7

Many aspects of transformer performance, such as level handling, distortion, and bandwidth, depend critically on the impedance of the driving source and, in most cases, the resistance and capacitance of the load. These impedances play such an important role that they essentially classify audio transformers into two basic types. Most simply stated, output transformers are used when load impedances are low, as in line drivers, while input transformers are used when load impedances are high, as in line receivers. The load for a line driver is not just the high-impedance equipment input it drives—it also includes the cable capacitance, whose impedance can become quite low at 20 kHz. The conflicting technical requirements for output and input types make their

2. The decrease in signal level at the output due to the increased series losses. IDEAL Eout

150 k

= 0.909

150 k + 15 k 150 k REALout

= 0.885

150 k + 15 k + 1970 + 2465 0.909 (IDEAL) = 0.232 dB

NF = 20Log 0.885 (REAL)

3. Total NF = 1.01 dB + 0.232 dB = 1.23 dB

Figure 11-28. Finding the noise figure of a transformer.

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Chapter 11

design and physical construction very different. Of course, some audio transformer applications need features of both input and output transformers and are not so easily classified. Output transformers must have very low leakage inductance in order to maintain high-frequency bandwidth with capacitive loads. Because of this, they rarely use Faraday shields and are most often multi-filar wound. For low insertion loss, they use relatively few turns of large wire to decrease winding resistances. Since they use fewer turns and operate at relatively high signal levels, output transformers seldom use magnetic shielding. On the other hand, input transformers directly drive the usually high-resistance, low-capacitance input of amplifier circuitry. Many input transformers operate at relatively low signal levels, frequently have a Faraday shield, and are usually enclosed in at least one magnetic shield.

11.2 Audio Transformers for Specific Applications Broadly speaking, audio transformers are used because they have two very useful properties. First, they can benefit circuit performance by transforming circuit impedances, to optimize amplifier noise performance, for example. Second, because there is no direct electrical connection between its primary and secondary windings, a transformer provides electrical or galvanic isolation between two circuits. As discussed in Chapter 37, isolation in signal circuits is a powerful technique to prevent or cure noise problems caused by normal ground voltage differences in audio systems. To be truly useful, a transformer should take full advantage of one or both of these properties but not compromise audio performance in terms of bandwidth, distortion, or noise.

2× b6.8 k7 p J1 Mic input

+48 V

11.2.1.1 Microphone Input A microphone input transformer is driven by the nominal 150 ȍ, or 200 ȍ in Europe, source impedance of professional microphones. One of its most important functions is to transform this impedance to a generally higher one more suited to optimum noise performance. As discussed in Chapter 21, this optimum impedance may range from 500 ȍ to over 15 kȍ, depending on the amplifier. For this reason, microphone input transformers are made with turns ratios ranging from 1:2 to 1:10 or higher. The circuit of Fig. 11-29 uses a 1:5 turns ratio transformer, causing the microphone to appear as a 3.7 kȍ source to the IC amplifier, which optimizes its noise. The input impedance of the transformer is about 1.5 kȍ. It is important that this impedance remain reasonably flat with frequency to avoid altering the microphone response at frequency extremes, see Fig. 21-6. In all balanced signal connections, common-mode noise can exist due to ground voltage differences or magnetic or electrostatic fields acting on the interconnecting cable. It is called common mode noise because it appears equally on the two signal lines, at least in theory. Perhaps the most important function of a balanced input is to reject (not respond to) this common-mode noise. A figure comparing the ratio of its differential or normal signal response to its commonmode response is called common mode rejection ratio or CMRR. An input transformer must have two attributes to achieve high CMRR. First, the capacitances of its two inputs to ground must be very well matched and as low as possible. Second, it must have minimal capacitance between its primary and secondary windings. This is usually accomplished by precision winding of

T1 JT 13K7 A Org

Brn R1 39.2 k7 Yel

2 3

11.2.1 Equipment-Level Applications

Red Blk

Whi

3 R2 9,760 7 C1 220 pF

A1 NE5534A 6

2 5

Output C3 22 pF

R4 1,960 7 R3 100 7 C2 390 pF Figure 11-29. Microphone preamplifier with 40 dB overall gain.

Audio Transformers the primary to evenly distribute capacitances and the incorporation of a Faraday shield between primary and secondary. Because the common-mode input impedances of a transformer consist only of capacitances of about 50 pF, transformer CMRR is maintained in real-world systems where the source impedances of devices driving the balanced line and the capacitances of the cable itself are not matched with great precision.3 Because tolerable common-mode voltage is limited only by winding insulation, transformers are well suited for phantom power applications. The standard arrangement using precision resistors is shown in Fig. 11-29. Resistors of lesser precision may degrade CMRR. Feeding phantom power through a center tap on the primary requires that both the number of turns and the dc resistance on either side of the tap be precisely matched to avoid small dc offset voltages across the primary. In most practical transformer designs, normal tolerances on winding radius and wire resistance make this a less precise method than the resistor pair. Virtually all microphone input transformers will require loading on the secondary to control high-frequency response. For the circuit in the figure, network R1, R2, and C1 shape the high-frequency response to a Bessel roll-off curve. Because they operate at very low signal levels, most microphone input transformers also include magnetic shielding.

291

11-30, a 4:1 step-down transformer is used which has an input impedance of about 40 kȍ. High CMRR is achieved in line input transformers using the same techniques as those for microphones. Again, because its common-mode input impedances consist of small capacitances, a good input transformer will exhibit high CMRR even when signal sources are real-world equipment with less-than-perfect output impedance balance. The dirty little secret of most electronically balanced input stages, especially simple differential amplifiers, is that they are very susceptible to tiny impedance imbalances in driving sources. However, they usually have impressive CMRR figures when the driving source is a laboratory generator. The pitfalls of measurement techniques will be discussed in section 11.3.1. As with any transformer having a Faraday shield, line input transformers have significant leakage inductance and their secondary load effectively controls their high-frequency response characteristics. The load resistance or network recommended by the manufacturer should be used to achieve specified bandwidth and transient response. Input transformers are intended to immediately precede an amplifier stage with minimal input capacitance. Additional capacitive loading of the secondary should be avoided because of its adverse effect on frequency and phase response. For example, capacitive loads in excess of about 100 pF—about 3 ft of standard shielded cable—can degrade performance of a standard 1:1 input transformer.

11.2.1.2 Line Input A line input transformer is driven by a balanced line and, most often, drives a ground-referenced (unbalanced) amplifier stage. As discussed in Chapter 37, modern voltage-matched interconnections require that line inputs have impedances of 10 kȍ or more, traditionally called bridging inputs. In the circuit of Fig.

11.2.1.3 Moving-Coil Phono Input Moving-coil phonograph pickups are very low-impedance, very low-output devices. Some of them have source impedances as low as 3 ȍ, making it nearly impossible to achieve optimum noise performance in an amplifier. The transformer shown in Fig. 11-31 has a

T1 JT 10KB D Yel J1 Mic input 10 nF

Brn

2 1

Org

Wht

Red R1 2,430 7

A1 AD797 6

2 R3 750 7

Blk

C1 1nF 1 k7

Gnd lift

R2 221 7

R4 150 7

Figure 11-30. Low-noise unity-gain balanced line input stage.

Output

292

Chapter 11

T1 JT-346-AX

J1 M/C input

Red Brn Yel Org Blu

2 1

10 nF

Grn whi blk 1 k7

Gry VIO

Wht Blk

R1 6.8 k7

R2 4.12 k7 C1 680 pF

Output

Gnd lift

Figure 11-31. Preamp for 25 :moving-coil pickups.

three-section primary that can be series-connected as a 1:4 step-up for 25 ȍ to 40 ȍ devices and parallel-connected as a 1:12 step-up for 3 ȍ to 5 ȍ devices. In either case, the amplifier sees a 600 ȍ source impedance that optimizes low-noise operation. The transformer is packaged in double magnetic shield cans and has a Faraday shield. The loading network R1 , R2 , and C1 tailor the high-frequency response to a Bessel curve.

11.2.1.4 Line Output A line-level output transformer is driven by an amplifier and typically loaded by several thousand pF of cable capacitance plus the 20 kȍ input impedance of a balanced bridging line receiver. At high frequencies, most driver output current is actually used driving the cable capacitance. Sometimes, terminated 150 ȍ or 600 ȍ lines must be driven, requiring even more driver output current. Therefore, a line output transformer must have a low output impedance that stays low at high frequencies. This requires both low resistance windings and very low leakage inductance, since they are effectively in series between amplifier and load. To maintain impedance balance of the output line, both driving impedances and inter-winding capacitances must be well matched at each end of the windings. A typical bi-filar-wound design has winding resistances of 40 ȍ each, leakage inductance of a few micro-henries, and a total inter-winding capacitance of about 20 nF matched to within 2% across the windings. The high-performance circuit of Fig. 11-32 uses op-amp A1 and current booster A2 in a feedback loop setting overall gain at 12 dB. A3 provides the high gain for a dc servo feedback loop used to keep dc offset at the output of A2 under 100 ȝV. This prevents any significant dc flow in the primary of transformer T 1 . X 1 provides capacitive load isolation for the amplifier and

X 2 serves as a tracking impedance to maintain high-frequency impedance balance of the output. High-conductance diodes D 1 and D2 clamp inductive kick to protect A2 in case an unloaded output is driven into hard clipping. The circuit of Fig. 11-33 is well suited to the lower signal levels generally used in consumer systems. Because its output floats, it can drive either balanced or unbalanced outputs, but not at the same time. Floating the unbalanced output avoids ground loop problems that are inherent to unbalanced interconnections. In both previous circuits, because the primary drive of T1 is single-ended, the voltages at the secondary will not be symmetrical, especially at high frequencies. THIS IS NOT A PROBLEM. Contrary to widespread myth and as explained in Chapter 37, signal symmetry has absolutely nothing to do with noise rejection in a balanced interface! Signal symmetry in this, or any other floating output, will depend on the magnitude and matching of cable and load impedances to ground. If there is a requirement for signal symmetry, the transformer should be driven by dual, polarity-inverted drivers. The circuit of Fig. 11-34 uses a cathode follower circuit which replaces the usual resistor load in the cathode with an active current sink. The circuit operates at quiescent plate currents of about 10 mA and presents a driving source impedance of about 60 ȍ to the transformer, which is less than 10% of its primary dc resistance. C 2 is used to prevent dc flow in the primary. Since the transformer has a 4:1 turns ratio, or 16:1 impedance ratio, a 600 ȍ output load is reflected back to the driver circuit as about 10 kȍ. Since the signal swings on the primary are four times as large as those on the secondary, high-frequency capacitive coupling is prevented by a Faraday shield. The secondary windings may be parallel connected to drive a 150 ȍ load. Because of the Faraday shield, output winding capacitances are low and the output signal

Audio Transformers

R1 1 k7

A1 LME49710 +

+18 V

A2 LME49600

RS < 1007

293

D1 4 D2

18 V

2 k7 R3 499 7

X1 T1 JT 11 EM Org Brn

C2 100 nF

R6 30 k7 R2 4.64 k7

R5 2.2 M7

Line output

3 A3 + OP97

C1 330 pF

Red

Yel

2 1

X1 and X–2 are JT-OLI-3 or equivalent

Figure 11-32. Typical line output application circuit. +18 V

T1 JT–11–HPMC 2 1

J1 Unbalanced output

2 R2 2 k7

R1 499 7

C1 470 pF

3 3

2 1

P1 Balanced output

18 V

Figure 11-33. Universal isolated output application.

symmetry will be determined largely by the balance of line and load impedances.

11.2.1.5 Inter-Stage and Power Output Inter-stage coupling transformers are seldom seen in contemporary equipment but were once quite popular in vacuum-tube amplifier designs. They typically use turns ratios in the 1:1 to 1:3 range and, as shown in Fig. 11-35, may use a center-tapped secondary producing phase-inverted signals to drive a push-pull output stage. Because both plate and grid circuits are relatively high

impedance, windings are sometimes section-wound to reduce capacitances. Resistive loading of the secondary is usually necessary both to provide damping and to present a uniform load impedance to the driving stage. Although uncommon, inter-stage transformers for solid-state circuitry are most often bi-filar wound units similar to line output designs. The classic push-pull power output stage, with many variations over the years, has been used in hi-fi gear, PA systems, and guitar amplifiers. The turns ratio of the output transformer is generally chosen for a reflected load at the tubes of several thousand ohms plate-to-plate. A typical 30:1 turns ratio may require

294

Chapter 11

+250 V R2 680 7 6 In +120 V bias

V1 12BH7

7 8

C1 220 nF

C2 22 MF

V1 12BH7

2 R1 1M7

T1 JT 10K61 1M Org Grn Yel Brn Blu

R3 330 7

2 3 1

P1 Line output

Red

Blk

Figure 11-34. Double cathode-follower line driver.

Negative feedback (if used)

+250 V

16 7

Amplifier front-end

Bias

+250 V

+350 V

7 Loudspeaker 7 out Com

+250 V

Figure 11-35. Push-pull vacuum-tube power amplifier.

many interleaved sections to achieve bandwidth extending well beyond 20 kHz. If the quiescent plate currents and the number of turns in each half of the primary winding are matched, magnetic flux in the core will cancel at dc. Since any current-balancing in vacuum-tubes is temporary at best, these transformers nearly always use steel cores to better tolerate this unbalanced dc in their windings. The relatively high driving impedance of the tube plates results in considerable transformer related distortion. To reduce distortion, feedback around the transformer is often employed. To achieve stability (freedom from oscillation), very wide bandwidth (actually low phase shift) is required of the transformer when a feedback loop is closed around it. As a result, some of these output transformer designs are very sophisticated. Some legendary wisdom suggests as a rough guide that a good-fidelity output transformer should have a core weight and volume of at least 0.34 pounds and 1.4 cubic inches respectively per watt of rated power.4

A single-ended power amplifier is created by removing the lower tube and the lower half of the transformer primary from the circuit of Fig. 11-35. Now plate current will create a strong dc field in the core. As discussed in section 11.1.2.1, the core will likely require an air gap to avoid magnetic saturation. The air gap reduces inductance, limiting low-frequency response, and increases even-order distortion products. Such a single-ended pentode power amplifier was ubiquitous in classic AM 5-tube table radios of the fifties and sixties.

11.2.1.6 Microphone Output There are two basic types of output transformers used in microphones, step-up and step-down. In a ribbon microphone, the ribbon element may have an impedance of well under 1 ȍ, requiring a step-up transformer with a turns ratio of 1:12 or more to raise its output level and make its nominal output impedance around 150 ȍ. Typ-

Audio Transformers ical dynamic elements have impedances from 10 ȍ to 30 ȍ, which require step-up turns ratios from 1:2 to 1:4. These step-up designs are similar to line output transformers in that they have no Faraday or magnetic shields, but are smaller because they operate at lower signal levels. A condenser microphone has integral circuitry to buffer and/or amplify the signal from its extremely high-impedance transducer. Since this low-power circuitry operates from the phantom supply, it may be unable to directly drive the 1.5 kȍ input impedance of a typical microphone preamp. The output transformer shown in Fig. 11-36, which has an 8:1 step-down ratio, will increase the impedance seen by Q 1 to about 100 kȍ. Because of its high turns ratio, a Faraday shield is used to prevent capacitive coupling of the primary signal to the output. + R1

+ Mic front end

C1 3 2 P1 Mic output 1

can feed a duplicate of the microphone signal to another pre-amp. Of course, a simple Y cable could do this but there are potential problems. There are often large and noisy voltages between the grounds of two pre-amplifiers. The isolation provided by the transformer prevents the noise from coupling to the balanced signal line. To reduce capacitive noise coupling, Faraday shields are included in better designs and double Faraday shields in the best. As discussed in Section 11.1.3.5, the input impedances of all the pre-amps, as well as all the cable capacitances, will be seen in parallel by the microphone. This places a practical upper limit on how many ways the signal can be split. Transformers are commercially available in 2, 3, and 4-winding versions. A 3-way splitter box schematic is shown in Fig. 11-37. Since the microphone is directly connected only to the direct output, it is the only one that can pass phantom power to the microphone. To each preamp, each isolated output looks like a normal floating (ungrounded) microphone. The ground lift switches are normally left open to prevent possible high ground current flow in the cable shields.

11.2.2.2 Microphone Impedance Conversion

JT 6K81 2M

Figure 11-36. Condenser microphone output transformer.

11.2.2 System-Level Applications 11.2.2.1 Microphone Isolation or Splitter The primary of a transformer with a 1:1 turns ratio can bridge the output of a 150 ȍ to 200 ȍ microphone feeding one pre-amp and the secondary of the transformer

Some legacy dynamic microphones are high-impedance, about 50 kȍ, and have two-conductor cable and connector (unbalanced). When such a microphone must be connected to a standard balanced low-impedance microphone pre-amp, a transformer with a turns ratio of about 15:1 is necessary. Similar transformers can be used to adapt a low-impedance microphone to the unbalanced high-impedance input of a legacy pre-amplifier. Commercial products are available which enclose such a transformer in the XLR adapter barrel.

T1 JT-MB-D J1 Microphone input

2 3 1

Org

Gry

P1 Direct output

Brn Red Vio Grn Blu

Yel 1 2 3

295

3 2 1

P2 Isolated output 1

3 2 1

Blk

P3 Isolated output 2

Whi Ground lift

1 k7

10 nF ×2

Figure 11-37. A 3-way microphone splitter box.

1 k7

Ground lift

296

Chapter 11

11.2.2.3 Line to Microphone Input or Direct Box Because its high-impedance, unbalanced input accepts line-level signals and its output drives the low-level, low-impedance balanced microphone input of a mixing console, the device shown in Fig. 11-38 is called a direct box. It is most often driven by an electric guitar, synthesizer, or other stage instrument. Because it uses a transformer, it provides ground isolation as well. In this typical circuit, since the transformer has a 12:1 turns ratio, the impedance ratio is 144:1. When the microphone input has a typical 1.5 kȍ input impedance, the input impedance of the direct box is about 200 kȍ. The transformer shown has a separate Faraday shield for each winding to minimize capacitively coupled ground noise.

T1 JT DB E

R1 6.8 K7 Yel

Line level input

Red Brn

Org Whi Blk Gnd lift

Mic level output 3 2 P 1 1

Gry 1 k7

100

110

120

130

140 20

11.2.2.4 Line Isolation or Hum Eliminators There are a remarkable number of black boxes on the market intended to solve ground loop problems. This includes quite a number of transformer-based boxes. With rare exception, those boxes contain output transformers. Tests were performed to compare noise rejection of the original interface to one with an added output transformer and to one with an added input transformer. The tests accurately simulated typical real-world equipment, see the definitions at the end of this section. Fig. 11-39 shows results of CMRR tests on a balanced interface using the IEC 60268-3 test procedure discussed in Section 11.3.1.2. This test recognizes that the impedances of real-world balanced outputs are not matched with the precision of laboratory equipment. While the output transformer reduces 60 Hz hum by over 20 dB, it has little effect on buzz artifacts over about 1 kHz. The input transformer increases rejection to over 120 dB at 60 Hz and to almost 90 dB at 3 kHz, where the human ear is most sensitive to faint sounds. Fig. 11-40 shows results of ground noise rejection tests on an unbalanced interface. By definition, there is

None Output Input

200 2k Frequency–Hz

20 k

Figure 11-39. Balanced output to balanced input.

0 dB of inherent rejection in an unbalanced interface, see Chapter 37.While the output transformer reduces 60 Hz hum by about 70 dB, it reduces buzz artifacts around 3 kHz by only 35 dB. The input transformer increases rejection to over 100 dB at 60 Hz and to over 65 dB at 3 kHz.

10 nF

Figure 11-38. A transformer-isolated direct box.

Rejection dB Versus Frequency–Hz

100

110

120

130

140 20

Rejection dB versus Frequency–Hz None

Output

Input

200 2k Frequency–Hz

20 k

Figure 11-40. Unbalanced output to unbalanced input.

Fig. 11-41 shows results of CMRR tests when an unbalanced output drives a balanced input. A two-wire connection of this interface will result in zero rejection, see Chapter 37. Assuming a three-wire connection, the í30 dB plot shows how CMRR of typical electronically-balanced input stages is degraded by the 600 ȍ source imbalance. Again, the output transformer improves 60 Hz hum by over 20 dB, it has little effect on buzz artifacts over about 1 kHz. The input transformer increases rejection to almost 100 dB at 60 Hz and to about 65 dB at 3 kHz.

Audio Transformers 0

100

110

120

130

140 20

None Output Input

200 2k Frequency–Hz

20k

Figure 11-41. Unbalanced output to balanced input.

Fig. 11-42 shows results of ground noise rejection tests when a balanced output drives an unbalanced input. Because our balanced output does not float, the direct connection becomes an unbalanced interface having, by definition, 0 dB of rejection. While the output transformer reduces 60 Hz hum by about 50 dB, it reduces buzz artifacts around 3 kHz by less than 20 dB. The input transformer increases rejection to almost 100 dB at 60 Hz and to about 65 dB at 3 kHz. In this application it is usually desirable to attenuate the signal by about 12 dB—from +4 dBu or 1.228 V to í10 dBV or 0.316 V—as well as provide ground isolation. This can be conveniently done by using a 4:1 step-down input transformer such as the one in Fig. 11-29, which will produce rejection comparable to that shown here.

100

110

120

130

140 20

Rejection–dB vs Frequency–Hz None Output

Input

200 2k Frequency–Hz

20 k

Figure 11-42. Balanced output to unbalanced input.

One might fairly ask “Why not use a 1:4 step-up transformer when an unbalanced output drives a

297

balanced input to get 12 dB of signal gain?” Because of the circuit impedances involved, the answer is because it doesn’t work very well. Recall that a 1:4 turns ratio has an impedance ratio of 1:16. This means that the input impedance of the pro balanced input we drive will be reflected back to the consumer output at one-sixteenth that. Since the source impedance—usually unspecified, but not the same as load impedance—of a consumer outputs is commonly 1 kȍ or more, the reflected loading losses are high. A 1:4 step-up transformer would have its own insertion losses, which we will rather optimistically assume at 1 dB. The table below shows actual gain using this transformer with some typical equipment output and input impedances (Z is impedance). Table 11-1. Gain Derived from a 1:4 Step-up Transformer in Typical Circuits Consumer Output Z

Pro Balanced Input Z 10 k:

20 k:

40 k:

(625 :)

(1.25 k:)

(2.5 k:)

200 :

8.6 dB

9.7 dB

10.3 dB

500 :

5.9 dB

8.1 dB

9.4 dB

1 k:

2.7 dB

5.9 dB

8.1 dB

Not only will gain usually be much less than 12 dB, the load reflected to the consumer output, shown in parentheses, is excessive and will likely cause high distortion, loss of headroom, and poor low-frequency response. Often the only specification of a consumer output is 10 kȍ minimum load. It is futile to increase the turns ratio of the transformer in an attempt to overcome the gain problem—it only makes the reflected loading problems worse. In most situations, a 1:1 transformer can be used because the pro equipment can easily provide the required gain. Of course, a 1:1 input transformer will provide far superior noise immunity from ground loops as well. The point here is that the noise rejection provided by an input transformer with a Faraday-shield is far superior to that provided by an output type. But the input transformer must be used at the receiver or destination end of an interface cable. In general, input transformers should drive no more than three feet of typical shielded cable—the capacitance of longer cables will erode their high-frequency bandwidth. Although output type transformers without a Faraday shield are not as good at reducing noise, their advantage is that they can be placed anywhere along an interface cable, at the driver end, at a patch-bay, or at the destination end, and work equally well (or poorly, compared to an input trans-

298

Chapter 11

former). In all the test cases discussed in this section, results of using both an output and an input transformer produced results identical to those using only an input transformer. For example, an unbalanced output does not need to be balanced by a transformer before transmission through a cable (this is a corollary of the balance versus symmetry myth), it needs only an input transformer at the receiver. There is rarely a need to ever use both types on the same line. Definitions (in context of comparison tests only): Balanced Output. ”A normal, non-floating source having a differential output impedance of 600 ȍ and common-mode output impedances of 300 ȍ, matched to within ± 0.1%. Balanced Input. A typical electronically-balanced stage—an instrumentation circuit using 3 op-amps— having a differential input impedance of 40 kȍ and common-mode input impedances of 20 kȍ, trimmed for a CMRR over 90 dB when directly driven by the above Balanced Output. Unbalanced Output. A ground-refere nced output having an output impedance of 600 ȍ. This is representative of typical consumer equipment. Unbalanced Input. A ground-referenced input having an input impedance of 50 kȍ. This is representative of typical consumer equipment. No Transformer. A direct wired connection. Output Transformer. A J e n s e n J T- 11 - E M C F — a popular 1:1 line output transformer. Input Transformer. A Jensen JT-11P-1—the most popular 1:1 line input transformer. 11.2.2.5 Loudspeaker Distribution or Constant Voltage When a number of low-impedance loudspeakers are located far from a power amplifier, there are no good methods to interconnect them in a way that properly loads the amplifier. The problem is compounded by the fact that power losses due to the resistance of the inter-connecting wiring can be substantial. The wire gauge required is largely determined by the current it must carry and its length. Borrowing a technique from power utility companies, boosting the distribution voltage reduces the current for a given amount of power and allows smaller wire to be used in the distribution system. Step-down matching transformers, most often having taps to select power level and/or loudspeaker

impedance, are used at each location. This scheme not only reduces the cost of wiring but allows system designers the freedom to choose how power is allocated among the speakers. These so-called constant-voltage loudspeaker distribution systems are widely used in public address, paging, and background music systems. Although the most popular is 70 V, others include 25 V, 100 V, and 140 V. Because the higher voltage systems offer the lowest distribution losses for a given wire size, they are more common in very large systems. It should also be noted that only the 25 V system is considered low-voltage by most regulatory agencies and the wiring in higher voltage systems may need to conform to power wiring practices. It is important to understand that these nominal voltages exist on the distribution line only when the driving amplifier is operating at full rated power. Many specialty power amplifiers have outputs rated to drive these lines directly but ordinary power amplifiers rated to drive speakers can also drive such lines, according to Table 11-2. Table 11-2. Amplifier Power Required at Various Impedances Versus Output Voltage Amplifier Rated Output, Watts

Output Voltage

at 8 :

at 4 :

at 2 :

1250

2500

5000

625

1250

2500

70.7

312

625

1250

156

312

625

35.3

156

312

100

For example, an amplifier rated to deliver 1,250 W of continuous average power into an 8 ȍ load will drive a 70 V distribution line directly as long as the sum of the power delivered to all the loudspeakers doesn’t exceed 1,250 W. Although widely used, the term rms watts is technically ambiguous.5 In many cases, the benefits of constant-voltage distribution are desired, but the total power required is much less. In that case a step-up transformer can be used to increase the output voltage of an amplifier with less output. This is often called matching it to the line because such a transformer is actually transforming the equivalent line impedance down to the rated load impedance for the amplifier. Most of these step-up transformers will have a low turns ratio. For example, a 1:1.4 turns ratio would increase the 50 V output to 70 V for an amplifier rated at 300 W into 8 ȍ. In such low-ratio applications, the auto-transformer discussed in Section 11.1.2.2 has cost and size advantages. Fig. 11-43 is a schematic of an auto-trans-

Audio Transformers former with taps for turns ratios of 1:1.4 or 1:2 which could be used to drive a 70 V line from amplifiers rated for either 300 or 150 W respectively at 8 ȍ. Several power amplifier manufacturers offer such transformers as options or accessories.

299

100 V 10 W 5W 2.5 W Speaker 1.25 W

70 V Line

Com 70 V

Com

Figure 11-44. Transformer with secondary taps for power selection. 300 W Line

150 W Amp

Line

Com

Figure 11-43. Step-up auto-transformer

87 47

2W 4W 8W

Speaker

Com

A line to voice-coil transformer is usually necessary to step-down the line voltage and produce the desired loudspeaker power, Table 11-3. These step-down transformers can be designed several ways. Fig. 11-44 shows a design where the line voltage is selected at the primary side and the power level is selected at the secondary while Fig. 11-45 shows a design where power level is selected on the primary side and loudspeaker impedance is selected at the secondary. As may be seen from the repeating patterns in the table above, there are many combinations of line voltage, loudspeaker impedance, and power level that result in the same required turns ratio in the matching transformer. Since the constant-voltage line has a very low source impedance, and the transformer is loaded by a

Figure 11-45. Transformer with primary taps for power selection.

low-impedance loudspeaker, transformer highfrequency response is usually not a design issue. As in any transformer, low-frequency response is determined by primary inductance and total source impedance, which is dominated by the primary winding resistance since the driving source impedance is very low. Winding resistances of both primary and secondary contribute to insertion loss. In efforts to reduce size and cost, the fewest turns of the smallest wire possible are often used, which raises insertion loss and degrades low-frequency response. Generally, an insertion loss of 1 dB or less is considered good and 2 dB is marginally acceptable for these applications.

Table 11-3. Transformer Step-Down Turns Ratio Required to Produce the Desired Loudspeaker Power Speaker Power in Watts 16 :

Loudspeaker

Volts

Transformer Step-Down Turns Ratio Required 100 V

70 V

35 V

25 V

128

22.63

4.42

3.12

1.56

1.10

16.00

6.25

4.42

2.21

1.56

11.31

8.84

6.25

3.12

2.21

8.00

12.50

8.84

4.42

3.12

5.66

17.70

12.50

6.25

4.42

4.00

25.00

17.70

8.84

6.25

0.5

2.83

35.30

25.00

12.50

8.84

0.25

0.5

2.00

50.00

35.30

17.70

12.50

0.125

0.25

0.5

1.41

71.00

50.00

25.00

17.70

300

Chapter 11

It is very important to understand that, while the low-level frequency response of a transformer may be rated as í1 dB at 40 Hz, its rated power does NOT apply at that frequency. Rated power, or maximum signal level is discussed in Section 11.1.3.1. In general, level handling is increased by more primary turns and more core material and it takes more of both to handle more power at lower frequencies. This ultimately results in physically larger, heavier, and more expensive transformers. When any transformer is driven at its rated level at a lower frequency than its design will support, magnetic core saturation is the result. The sudden drop in permeability of the core effectively reduces primary inductance to zero. The transformer primary now appears to have only the dc resistance of its winding, which may be only a fraction of an ohms. In the best scenario, some ugly-sounding distortion will occur and the line amplifier will simply current limit. In the worst scenario, the amplifier will not survive the inductive energy fed back as the transformer comes out of saturation. This can be especially dangerous if large numbers of transformers saturate simultaneously. In 1953, the power ratings of loudspeaker matching transformers were based on 2% distortion at 100 Hz.6 Traditionally, the normal application of these transformers has been speech systems and this power rating standard assumes very little energy will exist under 100 Hz. The same reference recommends that transformers used in systems with emphasized bass should have ratings higher than this 100 Hz nominal power rating and those used to handle organ music should have ratings of at least four times nominal. Since the power ratings for these transformers is rarely qualified by an honest specification stating the applicable frequency, it seems prudent to assume that the historical 100 Hz power rating applies to most commercial transformers. If a background music system, for example, requires good bass response, it is wise to use over-rated transformers. Reducing the voltage on the primary side of the transformer will extends its low-frequency power handling. Its possible, using the table above, to use different taps to achieve the same ratio while driving less than nominal voltage into the transformer primary. For example, a 70 V line could be connected to the 100 V input of the transformer in Fig. 11-33 and, for example, the 10 W secondary tap used to actually deliver 5 W. In any constant-voltage system, saturation problems can be reduced by appropriate high-pass filtering. Simply attenuate low-frequency signals before they can reach the transformers. In voice-only systems, problems that arise from breath pops, dropped microphones, or signal switching transients can be effectively

eliminated by a 100 Hz high-pass filter ahead of the power amplifier. In music systems, attenuating frequencies too low for the speakers to reproduce can be similarly helpful. 11.2.2.6 Telephone Isolation or Repeat Coil In telephone systems it was sometimes necessary to isolate a circuit which was grounded at both ends. This metallic circuit problem was corrected with a repeat coil to improve longitudinal balance. Translating from telephone lingo, this balanced line had poor common-mode noise rejection which was corrected with a 1:1 audio isolation transformer. The Western Electric 111C repeat coil was widely used by radio networks and others for high-quality audio transmission over 600 ȍ phone lines. It has split primary and secondary windings and a Faraday shield. Its frequency response was 30 Hz to 15 kHz and it had less than 0.5 dB insertion loss. Split windings allow them to be parallel connected for 150 ȍ use. Fig. 11-46 shows a modern version of this transformer as a general purpose isolator for low-impedance circuits, such as in a recording studio patch-bay. Optional components can be useful in some applications. For example, network R1 and C1 will flatten the input impedance over frequency, R2 will trim the input impedance to exactly 600 ȍ, and R 3 can be used to properly load the transformer when the external load is high-impedance or bridging. 11.2.2.7 Telephone Directional Coupling or Hybrid Telephone hybrid circuits use bridge-nulling principles to separate signals which may be transmitted and received simultaneously or full-duplex on a 2-wire line. This nulling depends critically on well-controlled impedances in all branches of the circuits. This nulling is what suppresses the transmit signal (your own voice) in the receiver of your phone while allowing you to hear the receive signal (the other party). A two-transformer hybrid network is shown in Fig. 11-47. The arrows and dashed lines show the current flow for a signal from the transmitter TX. Remember that the dots on the transformers show points having the same instantaneous polarity. The transformer turns ratios are assumed to be 1:1:1. When balancing network ZN has an impedance that matches the line impedance ZL at all significant frequencies, the currents in the ZL loop (upper) and ZN loop (lower) will be equal. Since they flow in opposite directions in the RX transformer (right), there is cancellation and the TX signal does not appear at RX. A signal originating from the line rather

Audio Transformers

301

T1 JT–11SSP–6M Gry Red R2 3.9 k7 J1 Line input

R1 619 7

Brn

C1 1300 pF

Yel

Vio Blu

Org

Grn

R3 619 7 3 2 1

1 Blk

10 nF

1 k7

Whi

P1 Line output

Gnd lift

Figure 11-46. Repeat coil ground isolation for 600 : lines.

than TX is not suppressed and is heard in RX. A common problem with hybrids of any kind is adjusting network ZN to match the telephone line, which may vary considerably in impedance even over relatively short time spans.

1.4 : 2CT 600 7 2-Wire line

600 7 600 7 600 7

Figure 11-48. Single-transformer hybrid.

2-Wire line

Figure 11-47. Two-transformer hybrid.

If the transmitter and receiver are electrically connected, the single transformer method, shown in Fig. 11-48, can be used. Any well-designed transformers with accurate turns ratio can be used in hybrid applications. 11.2.2.8 Moving-Coil Phono Step-Up Outboard boxes are sometimes used to adapt the output of low-output, low-impedance moving-coil phono pickups to pre-amplifier inputs intended for conventional high-impedance moving-magnet pickups. These pre-amplifiers have a standard input impedance of 47 kȍ. Fig. 11-49 shows a 1:37 step-up transformer

used for this purpose. It has a voltage gain of 31 dB and reflects its 47 kȍ pre-amplifier load to the pickup as about 35 ȍ. This keeps loading loss on a 3 ȍ pickup to about 1 dB. The series RC network on the secondary provides proper damping for smooth frequency response. Double magnetic shield cans are used because of the very low signal levels involved and the low-frequency gain inherent in the RIAA playback equalization. In these applications, it is extremely important to keep all leads to the pickup tightly twisted to avoid hum from ambient magnetic fields.

7–7 M/C pickup

T1 JT-34K DX Yel Red

13 k7

Brn

47 k7 Mag phono input

Org 100 pF Whi Whi Blk

Figure 11-49. Step-up transformer for moving coil phono pickup.

302

Chapter 11

11.3 Measurements and Data Sheets

external power amplifier to boost the generator output as well as some hefty power resistors to serve as loads.

11.3.1 Testing and Measurements 11.3.1.2 Balance Characteristics 11.3.1.1 Transmission Characteristics The test circuits below are the basic setups to determine the signal transmission characteristics of output and input type transformers, respectively, shown in the diagrams as DUT for device under test. In each case, the driving source impedance must be specified and is split into two equal parts for transformers specified for use in balanced systems. For example, if a 600 ȍ balanced source is specified, the resistors R s /2 become 300 ȍ each. The generator indicated in both diagrams is understood to have symmetrical voltage outputs. The buffer amplifiers shown are used to provide a zero source impedance, which is not available from most commercial signal sources. The generator could be used in an unbalanced mode by simply connecting the lower end of the DUT primary to ground. The specified load impedance must also be placed on the secondary. For output transformers, the load and meter are often floating as shown in Fig. 11-50. For input transformers, a specified end of the secondary is generally grounded as shown in Fig. 11-51. Rs/2 Gen

Buf

RL V Meter

Figure 11-50. Transmission tests for output types.

Gen

Buf

Rs/2

DUT

Rs/2 V Meter

Rs/2

Buf

Gen

Rs/2

DUT

Buf

Rs/2

Figure 11-52. Common-mode test for output types.

Rs/2

Buf

Tests for common-mode rejection are intended to apply a common-mode voltage through some specified resistances to the transformer under test. Any differential voltage developed then represents undesired conversion of common-mode voltage to differential mode by the transformer. In general terms, CMRR or common-mode rejection ratio, is the ratio of the response of a circuit to a voltage applied normally (differentially) to that of the same voltage applied in common-mode through specified impedances. This conversion is generally the result of mismatched internal capacitances in the balanced winding. For output transformers, the most common test arrangement is shown in Fig. 11-52. Common values are 300 ȍ for RG and values from zero to 300 ȍ for R s /2. Resistor pairs must be very well matched.

DUT RL V Meter

Figure 11-51. Transmission tests for input types.

These test circuits can be used to determine voltage gain or loss, turns ratio when RL is infinite, frequency response, and phase response. If the meter is replaced with a distortion analyzer, distortion and maximum operating level may be characterized. Multi-purpose equipment such as the Audio Precision System 1 or System 2 can make such tests fast and convenient. Testing of high-power transformers usually requires an

Traditionally, CMRR tests of balanced input stages involved applying the common-mode voltage through a pair of very tightly-matched resistors. As a result, such traditional tests were not accurate predictors of real-world noise rejection for the overwhelming majority of electronically-balanced inputs. The IEC recognized this in 1998 and solicited suggestions to revise the test. The problem arises from the fact that the common-mode output impedances of balanced sources in typical commercial equipment are not matched with laboratory precision. Imbalances of 10 ȍ are quite common. This author, through an educational process about balanced interfaces in general, suggested a more realistic test which was eventually adopted by the IEC in their standards document 60268-3 “Testing of Amplifiers” in August, 2000. The “Informative Annex” of this document is a concise summary explaining the nature of a balanced interface. The method of the new test, as shown in Fig. 11-53, is simply to introduce a 10 ȍ imbalance, first in one line and then in the other. The CMRR is then computed based on the highest differential reading observed.

Audio Transformers

10 7p1% Rs/2

DUT

Gen Buf

V Meter 10 7p1% Rs/2

Figure 11-53. IEC Common-mode test for input types.

11.3.1.3 Resistances, Capacitances, and Other Data Other data which can be very helpful to an equipment or system designer includes resistances of each winding and capacitances from winding to winding or winding to Faraday shield or transformer frame. Do not use an ohmmeter to check winding resistances unless you are able to later demagnetize the part. Ordinary ohmmeters, especially on low-ohm ranges, can weakly magnetize the core. If an ohmmeter simply must be used, use the highest range where the current is least. Capacitances are usually measured on impedance bridges and, to minimize the effects of winding inductances, with all windings shorted. Total capacitances can be measured this way, but balance of capacitances across a winding must be measured indirectly. CMRR tests are effectively measuring capacitance imbalances. As shown in Fig. 11-54, sometimes the input impedance of a winding is measured with specified load on other windings. This test includes the effects of primary resistance, secondary resistance, and the parallel loss resistance RC shown in Fig. 11-8 and Fig. 11-13. If specified over a wide frequency range, it also includes the effects of primary inductance and winding capacitances. Breakdown voltages are sometimes listed as measures of insulation integrity. This is normally done with special equipment, sometimes called a hi-pot tester, which applies a non-destructive high voltage while limiting current to a very low value.

11.3.2 Data Sheets 11.3.2.1 Data to Impress or to Inform? Data sheets and specifications exist to allow easy comparison of one product with others. But, in a world where marketing seems to supersede all else, honest data sheets and guaranteed specifications are becoming increasingly rare. As with many other audio products, most so-called data sheets and specifications are designed to impress rather than inform. Specifications

303

offered with unstated measurement conditions are essentially meaningless, so a degree of skepticism is always appropriate before comparisons are made. A few examples: • Hum Eliminator and Line Level Shifter products with no noise rejection or CMRR specs at all! • Line Level Shifter products with no gain spec at all! Section 11.2.2.4 explains why they won’t tell you! • Maximum Power or Maximum Level listed with no frequency and no source impedance specified!

DUT

Figure 11-54. Impedance tests.

Other specifications, while technically true, are likely to mislead those not wise in the ways of transformers. For example, Maximum Level and Distortion are commonly specified at 50 Hz, 40 Hz, or 30 Hz instead of the more rigorous 20 Hz. Be careful, specs at these higher frequencies will always be much more impressive than those at 20 Hz! There is an approximate 6 dB per octave relationship at work here. A transformer specified for level or distortion at 40 Hz, for example, will handle about 6 dB less level at 20 Hz and have at least twice the distortion! Seen in transformer-based hum eliminator advertising copy: “Frequency response 10 Hz to 40 kHz ±1 dB into 10 kȍ load” and “Distortion less than 0.002% at 1 kHz.” What about the source impedance? Response at 10 Hz and distortion are always much better when a transformer is driven from a 0 ȍ source! What happens when a real-world source drives the box? For a full-range audio transformer, measuring distortion at 1 kHz is nearly meaningless. Section 11.1.3.1 explains.

11.3.2.2 Comprehensive Data Sheet Example For reference, the following is offered as a sample of a data sheet that has been called truly useful and brutally honest. Note that minimum or maximum limits are guaranteed for the most critical specifications!

304

Chapter 11

Figure 11-55. Specification sheet for a quality transformer. Courtesy Jensen Transformers, Inc.

Audio Transformers

Figure 11-55 Continued. Specification sheet for a quality transformer.

305

306

Chapter 11

11.4 Installation and Maintenance 11.4.1 A Few Installation Tips • Remember that there are very tiny wires inside an audio transformer. Its wire leads should never be used like a handle to pick it up. The internal bonds are strong, but pulling too hard might result in an open winding. • Be careful with sharp tools. A gouge through the outer wrapper of an output transformer can nick or cut an internal winding. • When mounting transformers that are in shielded cans, use either the supplied screws or ones no longer than recommended. If the screws are too long, they’ll bore right into the windings—big problem! • Be careful about using magnetized tools. If a screwdriver will pick up a paper clip, it shouldn’t be used to install an audio transformer. • Don’t drop a transformer. It can distort the fit of the laminations in output transformers and affect their low-frequency response. Mechanical stress, as in denting of the magnetic shield can of an input transformer will reduce its effectiveness as a shield. For the same reason, don’t over-tighten the clamps on transformers mounted with them. • Twisting helps avoid hum pickup from ambient ac magnetic fields. This is especially true for microphone level lines in splitters, for example. Separately twist the leads from each winding—twisting the leads from all windings together can reduce noise rejection or CMRR. 11.4.2 De-Magnetization Some subtle problems are created when transformer cores and/or their shield cans become magnetized. Generally, cores become magnetized by having dc flow in a winding, even for a fraction of a second. It can leave the core weakly magnetized. Steel cores, because of their wider hysteresis loops, are generally the most prone to such magnetization. The only way to know if the core has some permanent magnetization is to perform distortion measurements. A transformer with an un-magnetized core will exhibit nearly pure third harmonic distortion, with virtually no even order harmonic distortion while magnetized ones will show significant even order distortion, possibly with 2 nd harmonic even exceeding 3rd. A test signal at a level about 30 or 40 dB below rated maximum operating level at 20 or 30 Hz is typically the most revealing because it maximizes the contribution of hysteresis distortion.

Microphone input transformers used with phantom power are exposed to this possibility whenever a microphone is connected or disconnected from a powered input. However, distortion tests before and after exposure to the worst-case 7 mA current pulses have shown that the effects are indeed subtle. Third harmonic distortion, which normally dominates transformer distortions, is unaffected. Second harmonic, which normally is near the measurement threshold, is typically increased by about 20 dB but is still some 15 dB lower than the third harmonic. Is it audible? Some say yes. But even this distortion disappears into the noise floor above a few hundred Hz. In any case, it can be prevented by connecting and disconnecting microphones only when phantom power is off. And such magnetized transformers can be de-magnetized. Demagnetizing of low level transformers can generally be done with any audio generator having a continuously variable output. It may take a booster of some sort to get enough level for output transformers (be sure there’s no dc offset at its output!). The idea is to drive the transformer deeply into saturation, 5% THD or more, and then slowly bring the level down to zero. Saturation will, of course, be easiest at a very low frequency. How much level it takes will depend on the transformer. If you’re lucky, the level required may not be hazardous to the surrounding electronics and the de-magnetizing can be accomplished without disconnecting the transformer. Start with the generator set to 20 Hz and its minimum output level, connect it to the transformer, then slowly—over a period of a few seconds—increase the level into saturation—maintain it for a few seconds—then slowly turn it back down to minimum. For the vast majority of transformers, this process will leave them in a demagnetized state. Shield cans are usually magnetized by having a brief encounter with a strongly magnetized tool. Sometimes, transformers are unknowingly mounted on a magnetized chassis. When the shield can of an input transformer becomes magnetized, the result is microphonic behavior of the transformer. Even though quality input transformers are potted with a semi-rigid epoxy compound to prevent breakage of very fine wires, vibration between core and can activate what is essentially a variable reluctance microphone. In this case, a good strong tape head de-magnetizer can be used to de-magnetize the can. At the end of the Jensen production line, most transformers are routinely demagnetized with a very strong de-magnetizer just prior to shipment. Although I haven’t tried it, I would expect that something like a degausser for 2 inch video tape (remember that!) would also de-magnetize even a large steel-core output transformer.

Audio Transformers

307

References 1. 2. 3. 4. 5. 6.

Magnetic Shield Corporation, Frequently Asked Questions, www.magnetic-shield.com. Sowter, G.A.V., Soft Magnetic Materials for Audio Transformers: History, Production, and Applications, Journal of the Audio Engineering Society, October 1987, www.sowter.co.uk/pdf/GAVS.pdf. Whitlock, Bill, Balanced Lines in Audio: Fact, Fiction, and Transformers, Journal of the Audio Engineering Society, June 1995, pp 454-464. Smith, F. Langford, Radiotron Designer’s Handbook, Wireless Press, Sydney, 4th Edition, 1953, p 208. Woolf, Lawrence, RMS Watt, or Not?, Electronics World, December 1998, pp 1043-1045. Smith, F. Langford, op. cit., p 227.

Notes Co-Netic® is a registered trademark of Magnetic Shield Corp. HyMu® is a registered trademark of Carpenter Technology Corp. Mumetal® is a registered trademark of Telcon Metals, Ltd. Permalloy® is a registered trademark of B & D Industrial & Mining Services, Inc.

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Chapter

Tubes, Discrete Solid State Devices, and Integrated Circuits by Glen Ballou 12.1 Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Tube Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Tube Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.3 Symbols and Base Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.4 Transconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.5 Amplification Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.6 Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.7 Internal Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.8 Plate Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.9 Grid Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.10 Plate Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.11 Power Sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.12 Screen Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.13 Plate Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.14 Changing Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.15 Tube Heater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Discrete Solid-State Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.1 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.2 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.3 Thyristors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.4 Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Integrated Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.1 Monolithic Integrated Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Hybrid Integrated Circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.3 Operational Voltage Amplifiers (Op-Amp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4 Dedicated Analog Integrated Circuits for Audio Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4.1 Voltage-Controlled Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4.2 Peak, Average, and RMS Level Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4.3 Peak and Average Detection with Integrated Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4.4 Rms Level Detection Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4.5 Rms Level Detection ICs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5 Integrated Circuit Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5.1 transformer input microphone preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5.2 Active Microphone Preamplifiers Eliminate Input Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5.3 The Evolution of Active Microphone Preamplifier ICs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.5.4 Integrated Circuit Mic Preamplifier Application Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

309

311 311 311 311 312 312 313 313 314 314 315 315 315 315 316 317 317 317 320 322 325 334 334 335 335 340 342 345 345 345 347 349 349 350 350 351

12.3.6 Balanced Line Interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.1 Balanced Line Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.2 Balanced Line Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.3 Integrated Circuits for Balanced Line Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.4 Balanced Line Input Application Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.5 Balanced Line Receivers with the Common-Mode Performance of a Transformer . . . . . . . . . . . . . . 12.3.6.6 InGenius High Common-Mode Rejection Line Receiver ICs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.6.7 Balanced Line Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.7 Digital Integrated Circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

310

353 354 354 355 356 357 358 359 360 364

Tubes, Discrete Solid State Devices, and Integrated Circuits 12.1 Tubes In 1883, Edison discovered that electrons flowed in an evacuated lamp bulb from a heated filament to a separate electrode (the Edison effect). Fleming, making use of this principle, invented the Fleming valve in 1905, but when DeForest, in 1907, inserted the grid, he opened the door to electronic amplification with the audion. The millions of vacuum tubes are an outgrowth of the principles set forth by these men.1 It was thought that, with the invention of the transistor and integrated circuits, the tube would disappear from audio circuits. This has hardly been the case. Recently tubes have had a revival because some “golden ears” like the smoothness and nature of the tube sound. The 1946 vintage 12AX7 is not dead and is still used today as are miniature tubes in condenser microphones and 6L6s in power amplifiers. It is interesting that many feel that a 50 W tube amplifier sounds better than a 250 W solid-state amplifier. For this reason, like the phonograph, tubes are still discussed in this handbook. 12.1.1

Tube Elements

Vacuum tubes consist of various elements or electrodes, Table 12-1. The symbols for these elements are shown in Fig. 12-1. Table 12-1. Vacuum Tube Elements and Their Designation Filament

The cathode in a directly heated tube that heats and emits electrons. A filament can also be a separate coiled element used to heat the cathode in an indirectly heated tube. Cathode The sleeve surrounding the heater that emits electrons. The surface of the cathode is coated with barium oxide or thoriated tungsten to increase the emission of electrons. Plate The positive element in a tube and the element from which the output signal is usually taken. It is also called an anode. Control grid The spiral wire element placed between the plate and cathode to which the input signal is generally applied. This element controls the flow of electrons or current between the cathode and the plate. Screen grid The element in a tetrode (four element) or pentode (five element) vacuum tube that is situated between the control grid and the plate. The screen grid is maintained at a positive potential to reduce the capacitance existing between the plate and the control grid. It acts as an electrostatic shield and prevents self-oscillation and feedback within the tube. S u p p r e s s o r The gridlike element situated between the plate grid and screen in a tube to prevent secondary electrons emitted by the plate from striking the screen grid. The suppressor is generally connected to the ground or to the cathode circuit.

311

Filament

Cathode

Grid

Plate

Beam forming plates

Eye-tube deflection plate

Photo cathode

Cold cathode

Gas filled

Figure 12-1. Tube elements and their designation.

12.1.2 Tube Types There are many types of tubes, each used for a particular purpose. All tubes require a type of heater to permit the electrons to flow. Table 12-2 defines the various types of tubes. Table 12-2. The Eight Types of Vacuum Tubes Diode

A two-element tube consisting of a plate and a cathode. Diodes are used for rectifying or controlling the polarity of a signal as current can flow in one direction only.

Triode

A three-element tube consisting of a cathode, a control grid, and a plate. This is the simplest type of tube used to amplify a signal.

Tetrode

A four-element tube containing a cathode, a control grid, a screen grid, and a plate. It is frequently referred to as a screen-grid tube.

Pentode

A five-element tube containing a cathode, a control grid, a screen grid, a suppressor grid, and a plate.

Hexode

A six-element tube consisting of a cathode, a control grid, a suppressor grid, a screen grid, an injector grid, and a plate.

Heptode

A seven-element tube consisting of a cathode, a control grid, four other grids, and a plate.

Pentagrid A seven-element tube consisting of a cathode, five grids, and a plate. Beampower tube

A power-output tube having the advantage of both the tetrode and pentode tubes. Beam-power tubes are capable of handling relatively high levels of output power for application in the output stage of an audio amplifier. The power-handling capabilities stem from the concentration of the plate-current electrons into beams of moving electrons. In the conventional tube the electrons flow from the cathode to the plate, but they are not confined to a beam. In a beam-power tube the internal elements consist of a cathode, a control grid, a screen grid, and two beam-forming elements that are tied internally to the cathode element. The cathode is indirectly heated as in the conventional tube.

12.1.3

Symbols and Base Diagrams

Table 12-3 gives the basic symbols used for tube circuits. The basing diagrams for various types of vacuum tubes are shown in Fig. 12-2.

312

Chapter 12

Table 12-3. Tube Nomenclature

12.1.4 Transconductance

C Cg2

Coupling capacitor between stages Screen grid bypass capacitor

Cathode bypass capacitor

Ebb

Supply voltage

Eff

Plate efficiency

Actual voltage at plate

Esg

Actual voltage at screen grid

Output voltage

Esig

Signal voltage at input

Voltage at control grid

Filament or heater voltage

Filament or heater current

Plate current

Cathode current

Transconductance (g m ) is the change in the value of plate current expressed in microamperes (μA) divided by the signal voltage at the control grid of a tube, and is expressed by conductance. Conductance is the opposite of resistance, and the name mho (ohm spelled backward) was adopted for this unit of measurement. Siemens (S) have been adopted as the SI standard for conductance and are currently replacing mhos in measurement. The basic mho or siemen is too large for practical usage; therefore, the terms micromho (μmho) and microsiemens (μS) are used. One micromho is equal to one-millionth of a mho. The transconductance (gm) of a tube in μmhos may be found with the equation

Isg

Screen-grid current

Ipa

Average plate current

Ipac

Average ac plate current

Ika

Average cathode current

Isga

Average screen grid current

Transconductance (mutual conductance)

mu Psg

Amplification factor (μ) Power at screen grid

Power at plate

P-P Rg

Plate-to-plate or push–-pull amplifier Grid resistor

Cathode resistor

Plate-load impedance or resistance

Plate-load resistor

Rsg

Screen-dropping resistor

Decoupling resistor

Internal plate resistance

Voltage gain

'I p g m = -----------'E sig

(12-1)

where, 'Ip is the change of plate current, 'Esig is the change of control-grid signal voltage, Ebb is the plate supply voltage and is held constant. For example, a change of 1 mA of plate current for a change of 1 V at the control grid is equal to a transconductance of 1000 μmho. A tube having a change of 2 mA plate current for a change of 1 V at the control grid would have a transconductance of 2000 μmho. g m = I pac u 1000

(12-2)

where, gm is the transconductance in micromho or microsiemens, Ipac is the ac plate current. 12.1.5 Amplification Factor

Diode

Pentagrid converter

Triode

Tetrode

Eye tube

Gas-filled Photo tube High-voltage rectifier rectifier

Duo-diode Dual-triode triode

Pentode or sheet-beam

Two-section

Beam power

Full-wave rectifier

Figure 12-2. Basing diagrams for popular tubes.

Amplification factor (μ) or voltage gain (Vg) is the ratio of the incremental plate voltage change to the control-electrode voltage change at a fixed plate current and constant voltage on all other electrodes. This normally is the amount the signal at the control grid is increased in amplitude after passing through the tube. Tube voltage gain may be computed using the equation 'E V g = ---------p'E g where, Vg is the voltage gain,

(12-3)

Tubes, Discrete Solid State Devices, and Integrated Circuits 'Ep is the change in signal plate voltage, 'Eg is the change in the signal grid voltage.

connected to the cathode terminal. Generally, the capacitance is measured with the heater or filament cold and with no voltage applied to any of the other elements.

If the amplifier consists of several stages, the amount of amplification is multiplied by each stage. The gain of an amplifier stage varies with the type of tube and the interstage coupling used. The general equation for voltage gain is V gt = V g1 V g2 }V gn

313

Rsg

Isg + Esg

+ Esig

12.1.6 Polarity

The internal capacitance of a vacuum tube is created by the close proximity of the internal elements, Fig. 12-4. Unless otherwise stated by the manufacturer, the internal capacitance of a glass tube is measured using a close-fitting metal tube shield around the glass envelope

B+ A. Polarity reversal of the signal between the elements of a pentode vacuum tube. Ip + Ep

12.1.7 Internal Capacitance

0°

where, Vgt is the total gain of the amplifier, Vg1, Vg2, and Vgn are the voltage gain of the individual stages.

Polarity reversals take place in a tube. The polarity reversal in electrical degrees between the elements of a self-biased pentode for a given signal at the control grid is shown in Fig. 12-3A. The reversals are the same for a triode. Note that, for an instantaneous positive voltage at the control grid, the voltage polarity between the grid and plate is 180° and will remain so for all normal operating conditions. The control grid and cathode are in polarity. The plate and screen-grid elements are in polarity with each other. The cathode is 180° out of polarity with the plate and screen-grid elements. The polarity reversal of the instantaneous voltage and current for each element is shown in Fig. 12-3B. For an instantaneous positive sine wave at the control grid, the voltages at the plate and screen grid are negative, and the currents are positive. The voltage and current are both positive in the cathode resistor and are in polarity with the voltage at the control grid. The reversals are the same in a triode for a given element.

0°

Esig

(12-4)

Triode tubes are classified by their amplification factor. A low-μ tube has an amplification factor less than 10. Medium-μ tubes have an amplification factor from 10–50, with a plate resistance of 5 :–15,000 : . High-μ tubes have an amplification factor of 50–100 with a plate resistance of 50 k:–100 k: .

180°

180° +

Ik + Ek Rsg

B+ B. Polarity reversal of the current and voltage in a pentode vacuum tube.

Figure 12-3. Polarity characteristics of a vacuum tube.

Cg-p

P G

Cp-c

C Cg-c

Figure 12-4. Interelectrode capacitance of a triode.

In measuring the capacitance, all metal parts, except the input and output elements, are connected to the cathode. These metal parts include internal and external shields, base sleeves, and unused pins. In testing a midsection tube, elements not common to the section being measured are connected to ground. Input capacitance is measured from the control grid to all other elements, except the plate, which is connected to ground.

314

Chapter 12

Output capacitance is measured from the plate to all other elements, except the control grid, which is connected to ground. Grid-to-plate capacitance is measured from the control grid to the plate with all other elements connected to ground. 12.1.8 Plate Resistance The plate resistance (rp) of a vacuum tube is a constant and denotes the internal resistance of the tube or the opposition offered to the passage of electrons from the cathode to the plate. Plate resistance may be expressed in two ways: the dc resistance and the ac resistance. Dc resistance is the internal opposition to the current flow when steady values of voltage are applied to the tube elements and may be determined simply by using Ohm’s Law rp

Ep = -----Ip

(12-5) Rg

where, Ep is the dc plate voltage, Ip is the steady value of plate current.

(12-6)

where, ' Ep is the change in voltage at the plate, ' Ip is the change in plate current, E sig is the control grid signal voltage and is held constant. The values of Ep and Ip are taken from the family of curves supplied by the manufacturer for the particular tube under consideration.

Input

Input Bias cell

The ac resistance requires a family of plate-current curves from which the information may be extracted. As a rule, this information is included with the tube characteristics and is used when calculating or selecting components for an amplifier. The equation for calculating ac plate resistance is 'E = ---------p'I p

self-biased by the use of a resistor connected in the cathode circuit. In Fig. 12-5C the circuit is also a form of self-bias; however, the bias voltage is obtained by the use of a grid capacitor and grid-leak resistor connected between the control grid and ground. In Fig. 12-5D the bias voltage is developed by a grid-leak resistor and capacitor in parallel, connected in series with the control grid. The method illustrated in Fig. 12-5E is called combination bias and consists of self-bias and battery bias. The resultant bias voltage is the negative voltage of the battery, and the bias created by the self-bias resistor in the cathode circuit. Another combination bias circuit is shown in Fig. 12-5F. The bias battery is connected in series with the grid-leak resistor. The bias voltage at the control grid is that developed by the battery and the self-bias created by the combination of the grid resistor and capacitor.

A. Fixed-bias battery.

B. Self-bias. Cg

Cg Rg Input

Input

D. Grid-leak bias.

C. Grid-leak bias.

Cg Rg Input Bias cell

Input Ck

Bias cell

12.1.9 Grid Bias Increasing the plate voltage or decreasing the grid-bias voltage decreases the plate resistance. The six methods most commonly used to bias a tube are illustrated in Fig. 12-5. In Fig. 12-5A bias cell (battery) is connected in series with the control grid. In Fig. 12-5B the tube is

E. Combination bias.

F. Combination bias.

Figure 12-5. Various methods of obtaining grid bias.

If the control grid becomes positive with respect to the cathode, it results in a flow of current between the

Tubes, Discrete Solid State Devices, and Integrated Circuits control grid and the cathode through the external circuits. This condition is unavoidable because the wires of the control grid, having a positive charge, attract electrons passing from the cathode to the plate. It is important that the control-grid voltage is kept negative, reducing grid current and distortion. Grid-current flow in a vacuum tube is generally thought of as being caused by driving the control grid into the positive region and causing the flow of grid current. The grid voltage, plate-current characteristics are found through a series of curves supplied by the tube manufacturer, as shown in Fig. 12-6. The curves indicate that for a given plate voltage the plate current and grid bias may be determined. For example, the manufacturer states that for a plate voltage of 250 V and a negative grid bias of –8 V, the plate current will be 9 mA, which is indicated at point A on the 250 V curve. If it is desired to operate this tube with a plate voltage of 150 V and still maintain a plate current of 9 mA, the grid bias will have to be changed to a –3 V.

watts E ff = ---------------- u 100 E pa I pa

315

(12-7)

where, watts is the power output, Epa is the average plate voltage, Ipa is the average plate current. The measurement is made with a load resistance in the plate circuit equal in value to the plate resistance stated by the manufacturer. 12.1.11 Power Sensitivity Power sensitivity is the ratio of the power output to the square of the input voltage, expressed in mhos or siemens and is determined by the equation Po Power sensitivity = --------2 E in

(12-8)

where, Po is the power output of the tube in watts, Esig is the rms signal voltage at the input.

15 200 V

150 V

13 12 11

250 V 100 V

300 V

Plate current (Ip)—mA

10 9

The screen grid series-dropping resistance is calculated by referring to the data sheet of the manufacturer and finding the maximum voltage that may be applied and the maximum power that may be dissipated by the screen grid. These limitations are generally shown graphically as in Fig. 12-7. The value of the resistor may be calculated using the equation E sg u E bb – E sg R sg = -----------------------------------------P sg

7 6

(12-9)

where, Rsg is the minimum value for the screen-grid voltage-dropping resistor in ohms, Esg is the selected value of screen-grid voltage, Ebb is the screen-grid supply voltage, Psg is the screen-grid input in watts corresponding to the selected value of Esg.

5 4 3 2 1 0

18 16 14 12 10 8 6 4 Grid voltage (Eg)—V

12.1.12 Screen Grid

Figure 12-6. Grid voltage, plate-current curves for a triode tube.

12.1.13

Plate Dissipation

12.1.10 Plate Efficiency

Plate dissipation is the maximum power that can be dissipated by the plate element before damage and is found with the equation

The plate efficiency (Eff) is calculated by the equation:

Watts dissipation = E p I p

(12-10)

316

Chapter 12

Grid-No. 2 input expressed as percent of max. grid-No. 2 input rating

180 F 1 = --------250

Maximum operating conditions

100

= 0.72 80

The screen and grid voltage will be proportional to the plate voltage:

60 Area of permissible operation

E g = F 1 u old grid voltage

(12-12)

E sg = F 1 u old screen voltage

(12-13)

In the example,

0 0

60 80 100 20 40 Grid-No. 2 voltage expressed as percent of max. grid-No. 2 supply voltage rating

E g = 0.72 u 12.5 = – 9V

Figure 12-7. Typical graph for determining the maximum power dissipated by the screen grid.

E sg = 0.72 u 250

where, Ep is the voltage at the plate, Ip is the plate current.

F2 is used to calculate the plate and screen currents

12.1.14 Changing Parameters If a tube is to operate at a different plate voltage than published, the new values of bias, screen voltage, and plate resistance can be calculated by the use of conversion factors F 1 , F 2 , F 3 , F 4 , and F 5 . Assume the following conditions are specified for a single beam-power tube: Plate voltage 250.0 V Screen voltage 250.0 V Grid voltage –12.5 V Plate current 45.0 mA Screen current 4.5 mA Plate resistance 52,000.0 : Plate load 5000.0 : Transconductance 4100.0 μS Power output 4.5 W F1 is used to find the new plate voltage Ep new F 1 = -----------Ep

(12-11)

old

For example, the new plate voltage is to be 180 V. The conversion factor F1 for this voltage is obtained by dividing the new plate voltage by the published plate voltage Eq. 12-11:

= 180 V.

F2 = F1 F1

(12-14)

I P = F 2 u old plate current

(12-15)

I s = F 2 u old screen current

(12-16)

In the example, F 2 = 0.72 u 0.848 = 0.61 I P = 0.61 u 45 mA = 27.4 mA I sg = 0.61 u 4.5 mA = 2.74 mA The plate load and plate resistance may be calculated by use of factor F3: F F 3 = -----1F2

(12-17)

r p = F 3 u old internal plate resistance

(12-18)

R L = F 3 u old plateload resistance

(12-19)

In the example,

Tubes, Discrete Solid State Devices, and Integrated Circuits

317

The most satisfactory region of operation will be between 0.7 and 2.0. When the factor falls outside this region, the accuracy of operation is reduced.

0.720 F 3 = ------------0.610 = 1.18 r p = 1.18 u 52,000

12.1.15

= 61,360: R L = 1.18 u 5000 = 5900: F4 is used to find the power output F4 = F1 F2

(12-20)

Power output = F 4 u old power output

(12-21)

In the example: F 4 = 0.72 u 0.610

The data sheets of tube manufacturers generally contain a warning that the heater voltage should be maintained within ±10% of the rated voltage. As a rule, this warning is taken lightly, and little attention is paid to heater voltage variations, which have a pronounced effect on the tube characteristics. Internal noise is the greatest offender. Because of heater-voltage variation, emission life is shortened, electrical leakage between elements is increased, heater-to-cathode leakage is increased, and grid current is caused to flow. Thus, the life of the tube is decreased with an increase of internal noise.

12.2 Discrete Solid-State Devices

= 0.439 Power output = 0.439 u 4.5

12.2.1

= 1.97 W F5 is used to find the transconductance where 1 F 5 = -----F3

Tube Heater

(12-22)

transconductance = F5 u old transconductance (12-23) In the example, 1F 5 = --------1.18 = 0.847 transconductance = 0.847 u 4100 = 3472 μ mho or μ S The foregoing method of converting for voltages other than those originally specified may be used for triodes, tetrodes, pentodes, and beam-power tubes, provided the plate and grid 1 and grid 2 voltages are changed simultaneously by the same factor. This will apply to any class of tube operation, such as class A, AB1, AB2, B, or C. Although this method of conversion is quite satisfactory in most instances, the error will be increased as the conversion factor departs from unity.

Semiconductors

Conduction in solids was first observed by Munck and Henry in 1835 and later in 1874 by Braum. In 1905, Col. Dunwoody invented the crystal detector used in the detection of electromagnetic waves. It consisted of a bar of silicon carbide or carborundum held between two contacts. However, in 1903, Pickard filed a patent application for a crystal detector in which a fine wire was placed in contact with the silicon. This was the first mention of a silicon rectifier and was the forerunner of the present-day silicon rectifier. Later, other minerals such as galena (lead sulfide) were employed as detectors. During World War II, intensive research was conducted to improve crystal detectors used for microwave radar equipment. As a result of this research, the original point-contact transistor was invented at the Bell Telephone Laboratories in 1948. A semiconductor is an electronic device whose main functioning part is made from materials, such as germanium and silicon, whose conductivity ranges between that of a conductor and an insulator. Germanium is a rare metal discovered by Winkler in Saxony, Germany, in 1896. Germanium is a by-product of zinc mining. Germanium crystals are grown from germanium dioxide powder. Germanium in its purest state behaves much like an insulator because it has very few electrical charge carriers. The conductivity of germanium may be increased by the addition of small amounts of an impurity.

318

Chapter 12

Silicon is a nonmetallic element used in the manufacture of diode rectifiers and transistors. Its resistivity is considerably higher than that of germanium. The relative position of pure germanium and silicon is given in Fig. 12-8. The scale indicates the resistance of conductors, semiconductors, and insulators per cubic centimeter. Pure germanium has a resistance of approximately 60 :/cm³. Germanium has a higher conductivity or less resistance to current flow than silicon and is used in low- and medium-power diodes and transistors.

Polystyrene Mica Glass

Insulators

Wood

Pure silicon 100 10 1 0.1 0.01

Pure germanium Transistor germanium Impure germanium

Semiconductors

Material for heating coils Platinum Copper

Conductors

Figure 12-8. Resistance of various materials per cubic centimeter.

The base elements used to make semiconductor devices are not usable as semiconductors in their pure state. They must be subjected to a complex chemical, metallurgical, and photolithographical process wherein the base element is highly refined and then modified with the addition of specific impurities. This precisely controlled process of diffusing impurities into the pure base element is called doping and converts the pure base material into a semiconductor material. The semiconductor mechanism is achieved by the application of a voltage across the device with the proper polarity so as to have the device act either as an extremely low resistance (the forward biased or conducting mode) or as an extremely high resistance (reversed bias or nonconducting mode). Because the device is acting as

both a good conductor of electricity and also, with the proper reversal of voltage, as a good electrical nonconductor or insulator, it is called a semiconductor. Some semiconductor materials are called p or positive type because they are processed to have an excess of positively charged ions. Others are called n or negative type because they are processed to have an excess of negatively charged electrons. When a p-type of material is brought into contact with an n-type of material, a pn junction is formed. With the application of the proper external voltage, a low-resistance path is produced between the n and p material. By reversing the previously applied voltage, an extremely high-resistance called the depletion layer between the p and n types results. A diode is an example because its conduction depends upon the polarity of the externally applied voltage. Combining several of these pn junctions together in a single device produces semiconductors with extremely useful electrical properties. The theory of operation of a semiconductor device is approached from its atomic structure. The outer orbit of a germanium atom contains four electrons. The atomic structure for a pure germanium crystal is shown in Fig. 12-9A. Each atom containing four electrons forms covalent bonds with adjacent atoms, therefore, there are no “free” electrons. Germanium in its pure state is a poor conductor of electricity. If a piece of “pure” germanium (the size used in a transistor) has a voltage applied to it, only a few microamperes of current caused by electrons that have been broken away from their bonds by thermal agitation will flow in the circuit. This current will increase at an exponential rate with an increase of temperature. When an atom with five electrons, such as antimony or arsenic, is introduced into the germanium crystal, the atomic structure is changed to that of Fig. 12-9B. The extra electrons (called free electrons) will move toward the positive terminal of the external voltage source. When an electron flows from the germanium crystal to the positive terminal of the external voltage source, another electron enters the crystal from the negative terminal of the voltage source. Thus, a continuous stream of electrons will flow as long as the external potential is maintained. The atom containing the five electrons is the doping agent or donor. Such germanium crystals are classified as n-type germanium. Using a doping agent of indium, gallium, or aluminum, each of which contains only three electrons in its outer orbit, causes the germanium crystal to take the atomic structure of Fig. 12-9C. In this structure, there is a hole or acceptor. The term hole is used to

Tubes, Discrete Solid State Devices, and Integrated Circuits

external electrical circuits are concerned, there is no difference between electron and hole current flow. However, the method of connection to the two types of transistors differs.

Electron

+4 Germanium nucleus +4

Covalent bond

A. Atomic structure of a pure germanium crystal. In this condition germanium is a poor conductor. Free electron +4

Free electron +

B. Atomic structure of an n-type germanium crystal when a doping agent containing five electrons is induced. +4

Hole

319

When a germanium crystal is doped so that it abruptly changes from an n-type to a p-type, and a positive potential is applied to the p-region, and a negative potential is applied to the n-region, the holes move through the junction to the right and the electrons move to the left, resulting in the voltage-current characteristic shown in Fig. 12-10A. If the potential is reversed, both electrons and holes move away from the junction until the electrical field produced by their displacement counteracts the applied electrical field. Under these conditions, zero current flows in the external circuit. Any minute amount of current that might flow is caused by thermal-generated hole pairs. Fig. 12-10B is a plot of the voltage versus current for the reversed condition. The leakage current is essentially independent of the applied potential up to the point where the junction breaks down.

0.1 +4

I C. Atomic structure of a p-type germanium crystal when a doping agent containing three electrons is induced.

Figure 12-9. Atomic structure of germanium.

denote a mobile particle that has a positive charge and that simulates the properties of an electron having a positive charge. When a germanium crystal containing holes is subjected to an electrical field, electrons jump into the holes, and the holes appear to move toward the negative terminal of the external voltage source. When a hole arrives at the negative terminal, an electron is emitted by the terminal, and the hole is canceled. Simultaneously, an electron from one of the covalent bonds flows into the positive terminal of the voltage source. This new hole moves toward the negative terminal causing a continuous flow of holes in the crystal. Germanium crystals having a deficiency of electrons are classified p-type germanium. Insofar as the

1 V A. Voltage-versus-current characteristic of the junction.

I – MA

Breakdown B. Voltage-versus-current characteristic of the junction transistor with the battery polarities in the reverse condition.

Figure 12-10. Voltage-versus-current characteristics.

320

Chapter 12

12.2.2 Diodes

The diode is a device that exhibits a low resistance to current flow in one direction and a high resistance in the oth er. Id ea lly, wh en re ve rse bi asin g the dio de (connecting the negative of the supply to the diode anode), no current should flow regardless of the value of voltage impressed across the diode. A forward-biased diode presents a very low resistance to current flow. Fig. 12-11 shows the actual diode characteristics. Starting with the diode reverse biased, a small reverse current does flow. The size of this reverse-leakage current has been exaggerated for clarity and typically is in the order of nanoamperes. The forward resistance is not co nsta nt, a nd the re fo re i t d oes n ot yield a straight-line forward-conduction curve. Instead, it begins high and drops rapidly at relatively low applied voltage. Above a 0.5–1 V drop it approaches a steep straight line slope (i.e., low resistance). In the reverse-biased region of Fig. 12-11, when the applied voltage (–V) becomes large enough, the leakage current suddenly begins to increase very rapidly, and the slope of the characteristic curves becomes very steep. Past the knee in the characteristic, even a small increase in reverse voltage causes a large increase in the reverse current. This steep region is called the breakdown or avalanche region of the diode characteristic. The application of high reverse voltage causes the diode to break down and stop behaving like a diode. Peak-reverse-voltage rating, or prv is one of the two most important diode parameters. This is also referred to as the peak-inverse-voltage rating, or piv. This rating indicates how high the reverse voltage can be without approaching the knee and risking breakdown. Additional diode parameters are: Maximum average current Peak repetitive current Surge current

Causes overheating of the device Maximum peak value of current on a repetitive basis Absolute maximum allowed current even if just momentary

The maximum average current is limited by power dissipation in the junction. This power dissipation is represented by the product of forward voltage drop (VF) and the forward current (IF): P = VF IF

(12-24)

Selenium Rectifiers and Diodes. A selenium rectifier cell consists of a nickel-plated aluminum baseplate

Forward voltage drop Avalanche region Breakdown knee

+V Reverse leakage current (exaggerated)

Figure 12-11. Actual diode characteristics.

coated with selenium, over which a low-temperature alloy is sprayed. The aluminum base serves as a negative electrode and the alloy as the positive. Current flows from the base plate to the alloy but encounters high resistance in the opposite direction. The efficiency of conversion depends to some extent on the ratio of the resistance in the conducting direction to that of the blocking direction. Conventional rectifiers generally have ratios from 100:1 to 1000:1. Selenium rectifiers may be operated over temperatures of –55°C to +150°C (–67°F to +302°F). Rectification efficiency is on the order of 90% for three-phase bridge circuits and 70% for single-phase bridge circuits. As a selenium cell ages, the forward and reverse resistance increases for approximately one year and then stabilizes, decreasing the output voltage by approximately 15%. The internal impedance of a selenium rectifier is low and exhibits a nonlinear characteristic with respect to the applied voltage, maintaining a good voltage regulation. They are often used for battery charging. Selenium rectifiers, because of their construction, have considerable internal capacitance which limits their operating range to audio frequencies. Approximate capacitance ranges are 0.10–0.15 μF/in2 of rectifying surface. The minimum voltage required for conduction in the forward direction is termed the threshold voltage and is about 1 V, therefore, selenium rectifiers cannot be used successfully below that voltage. Silicon Rectifiers and Diodes. The high forward-toreverse current characteristic of the silicon diode produces an efficiency of about 99%. When properly used, silicon diodes have long life and are not affected by aging, moisture, or temperature when used with the proper heat sink. As an example, four individual diodes of 400 Vpiv may be connected in series to withstand a piv of 1600 V.

Tubes, Discrete Solid State Devices, and Integrated Circuits In a series arrangement, the most important consideration is that the applied voltage be equally distributed between the several units. The voltage drops across each individual unit must be very nearly identical. If the instantaneous voltage is not equally divided, one of the units may be subjected to a voltage exceeding its rated value, causing it to fail. This causes the other rectifiers to absorb the piv, often creating destruction of all the rectifiers. Uniform voltage distribution can be obtained by the connection of capacitors or resistors in parallel with the individual rectifier unit, Fig. 12-12. Shunt resistors are used for steady-state applications, and shunt capacitors are used in applications where transient voltages are expected. If the circuit is exposed to both dc and ac, both shunt capacitors and resistors should be employed. V+

D1 D2

V+

V– V+

V– Figure 12-13. Rectifiers connected in parallel.

V+

321

C3 C4

V– V– Figure 12-12. Rectifiers connected in series.

When the maximum current of a single diode is exceeded, two or more units may be connected in parallel. To avoid differences in voltage drop across the individual units, a resistor or small inductor is connected in series with each diode, Fig. 12-13. Of the two methods, the inductance is favored because of the lower voltage drop and consumption of power. Zener and Avalanche Diodes. W h e n t h e r e v e r s e voltage is increased beyond the breakdown knee of the diode characteristics as shown in Fig. 12-11, the diode impedance suddenly drops sharply to a very low value. If the current is limited by an external circuit resistance, operating in the “zener region” is normal for certain diodes specifically designed for the purpose. In zener diodes, sometimes simply called zeners, the breakdown characteristic is deliberately made as vertical as possible in the zener region so that the voltage across the diode is essentially constant over a wide reverse-current range,

acting as a voltage regulator. Since its zener region voltage can be made highly repeatable and very stable with respect to time and temperature, the zener diode can also function as a voltage reference. Zener diodes come in a wide variety of voltages, currents, and powers, ranging from 3.2 V to hundreds of volts, from a few milliamperes to 10 A or more, and from about 250 mW to over 50 W. Avalanche diodes are diodes in which the shape of the breakdown knee has been controlled, and the leakage current before breakdown has been reduced so that the diode is especially well suited to two applications: high-voltage stacking and clamping. In other words, they prevent a circuit from exceeding a certain value of voltage by causing breakdown of the diode at or just below that voltage. Small-Signal Diodes. Small-signal diodes or generalpurpose diodes are low-level devices with the same general characteristics as power diodes. They are smaller, dissipate much less power, and are not designed for high-voltage, high-power operation. Typical rating ranges are: IF (forward current) VF (forward voltage drop at IF) piv or prv IR (leakage current at 80% prv)

1–500 mA 0.2–1.1 V 6–1000 V 0.1–1.0 μA

Switching Diodes. Switching diodes are small-signal diodes used primarily in digital-logic and control applications in which the voltages may change very rapidly so that speed, particularly reverse-recovery time, is of

322

Chapter 12

paramount importance. Other parameters of particular importance are low shunt capacitance, low and uniform V F (forward voltage drop), low I R (reverse leakage current), and in control circuits, prv. Noise Diodes. Noise diodes are silicon diodes used in the avalanche mode (reverse biased beyond the breakdown knee) to generate broadband noise signals. All diodes generate some noise; these, however, have special internal geometry and are specially processed so as to generate uniform noise power over very broad bands. They are low-power devices (typically, 0.05–0.25 W) and are available in several different bandwidth classes from as low as 0 kHz–100 kHz to as high as 1000–18,000 MHz. Varactor Diodes. Varactor diodes are made of silicon or gallium arsenide and are used as adjustable capacitors. Certain diodes, when operated in the reverse-biased mode at voltages below the breakdown value, exhibit a shunt capacitance that is inversely proportional to the applied voltage. By varying the applied reverse voltage, the capacitance of the varactor varies. This effect can be used to tune circuits, modulate oscillators, generate harmonics, and mix signals. Varactors are sometimes referred to as voltage-tunable trimmer capacitors.

Shockley breakover diode. Adding a terminal (gate) to the second layer creates a gate-controlled, reverse-blocking thyristor, or silicon-controlled rectifier (SCR), as shown in Fig. 12-15A. +I Positive Resistance

Positive Resistance

+V Vd

No breakdown knee Very low reverse resistance

Figure 12-14. Tunnel-diode characteristics showing negative region (tunnel region).

Anode

Anode p1

Ohmic contacts

- + + - + + -

Gate

Tunnel Diodes. The tunnel diode takes its name from the tunnel effect, a process where a particle can disappear from one side of a barrier and instantaneously reappear on the other side as though it had tunneled through the barrier element. Tunnel diodes are made by heavily doping both the p and n materials with impurities, giving them a completely different voltage-current characteristic from regular diodes. This characteristic makes them uniquely useful in many high-frequency amplifiers as well as pulse generators and radiofrequency oscillators, Fig. 12-14. What makes the tunnel diode work as an active element is the negative-resistance region over the voltage range V d (a small fraction of a volt). In this region, increasing the voltage decreases the current, the opposite of what happens with a normal resistor. Tunnel diodes conduct heavily in the reverse direction; in fact, there is no breakdown knee or leakage region.

Negative Resistance

+ +

+ -

+ + + + + +

- - -

n2 Gate Cathode

Cathode

A. Electrical layout of a thyristor. Anode p1n2p2 a2Ib

a1a2Ib + I0

n1p2n2

Gate Ib

Cathode B. Two-transistor equivalent circuit. Anode SCR Gate

12.2.3 Thyristors Stack four properly doped semiconductor layers in series, pnpn (or npnp), and the result is a four-layer, or

Cathode C. SCR layout.

Figure 12-15. Thyristor schematics.

n1 p2

Tubes, Discrete Solid State Devices, and Integrated Circuits The four-layer diode connects (fires) above a specific threshold voltage. In the SCR, the gate controls this firing threshold voltage, called the forward blocking voltage. To understand how four-layer devices work, separate the material of the layers into two three-layer transistor devices. Fig. 12-15B is an equivalent two-transistor representation in a positive-feedback connection. Assuming a 1 and a 2 are the current gains of the two transistor sections with each gain value less than unity, the total base current Ib into the n1p2n2 transistor is Ib = a1 a2 Ib + Io + Ig

(12-25)

where, a1 and a2 are the transistor current gains, Ib is the total base current, I o is the leakage current into the base of the n 1 p 2 n 2 transistor, Ig is the current into the gate terminal. The circuit turns on and becomes self-latching after a certain turn-on time needed to stabilize the feedback action, when the equality of Eq. 12-18 is achieved. This result becomes easier to understand by solving for Ib, which gives Io + Ig I b = ------------------1 – a1 a2

(12-26)

When the product a1a2 is close to unity, the denominator approaches zero and Ib approaches a large value. For a given leakage current Io, the gate current to fire the device can be extremely small. Moreover, as I b becomes large, Ig can be removed, and the feedback will sustain the on condition since a1 and a2 then approach even closer to unity. As applied anode voltage increases in the breakover diode, where Ig is absent, Io also increases. When the quality of Eq. 12-18 is established, the diode fires. The thyristor fires when the gate current Ig rises to establish equality in the equation with the anode voltage fixed. For a fixed Ig, the anode voltage can be raised until the thyristor fires, with Ig determining the firing voltage, Fig. 12-16. Once fired, a thyristor stays on until the anode current falls below a specified minimum holding current for a certain turnoff time. In addition, the gate loses all control once a thyristor fires. Removal or even reverse biasing of the gate signal will not turn off the device although reverse biasing can help speed turnoff. When the device is used with an ac voltage on the anode, the unit automatically turns off on the negative half of the

323

l Anode Current Anode Volts lg = 0 Ig = 100 MA Thyristor breakover as function of gate current l Forward Quadrant On state Reverse blocking Holding current voltage Breakover (firing) voltage

V Reverse V Quadrant Off state Reverse breakover

l voltage

Figure 12-16. Thyristor breakover as a function of gate current and forward voltage.

voltage cycle. In dc switching circuits, however, complex means must often be used to remove, reduce, or reverse the anode voltage for turnoff. Figure 12-17 shows a bilaterally conductive arrangement that behaves very much like two four-layer diodes (diacs), or two SCRs (triacs), parallel and oppositely conductive. When terminal A is positive and above the breakover voltage, a path through p1n1p2n2 can conduct; when terminal B is positive, path p2n1p1n3 can conduct. When terminal A is positive and a third element, terminal G, is sufficiently positive, the p1 n 1p 2 n2 path will fire at a much lower voltage than when G is zero. This action is almost identical with that of the SCR. When terminal G is made negative and terminal B is made positive, the firing point is lowered in the reverse, or p2n1p1n3, direction. Because of low impedances in the on condition, four-layer devices must be operated with a series resistance in the anode and gate that is large enough to limit the anode-to-cathode or gate current to a safe value. To understand the low-impedance, high-current capability of the thyristor, the device must be examined as a whole rather than by the two-transistor model. In Fig. 12-17B the p1n1p2 transistor has holes injected to fire the unit, and the n 1 p 2 n 2 transistor has electrons injected. Considered separately as two transistors, the space-charge distributions would produce two typical transistor saturation-voltage forward drops, which are quite high when compared with the actual voltage drop of a thyristor. However, when the thyristor shown in Fig. 12-17A is considered, the charges of both polarities exist simulta-

324

Chapter 12

A IA

Ohmic contacts G

n3 n4

p1 n1

G B A (pV)

Off state VA On state

On state Firing point VA+ G

B ( V)

Figure 12-17. Bilateral arrangement to create a triac or ac operating device.

neously in the same n1 and p2 regions. Therefore, at the high injection levels that exist in thyristors, the mobile-carrier concentration of minority carriers far exceeds that from the background-doping density. Accordingly, the space charge is practically neutralized so that the forward drop becomes almost independent of the current density to high current levels. The major resistance to current comes from the ohmic contacts of the unit and load resistance. The price paid for this low-impedance capability in a standard thyristor is a long turnoff time relative to turn-on time necessary to allow the high level of minority current carriers to dissipate. This long turnoff time limits the speed of a thyristor. Fortunately, this long turnoff time does not add significantly to switching power losses the way that a slow turnon time would. Turnoff time is the minimum time between the forward anode current ceasing and the device being able to block reapplied forward voltage without turning on again. Reverse-recovery time is the minimum time after forward conduction ceases that is needed to block reverse-voltage with ac applied to the anode-cathode circuit. A third specification, turnon time, is the time a thyristor takes from the instant of triggering to when conduction is fully on. These timing specifications limit the operating frequency of a thyristor. Two additional important specifications, the derivative of voltage with respect to time (dv/d t) and the derivative of current with respect to time

(di/d t) limit the rates of change of voltage and current application to thyristor terminals. A rapidly varying anode voltage can cause a thyristor to turn on even though the voltage level never exceeds the forward breakdown voltage. Because of capacitance between the layers, a current large enough to cause firing can be generated in the gated layer. Current through a capacitor is directly proportional to the rate of change of the applied voltage; therefore, the dv/d t of the anode voltage is an important thyristor specification. Turnon by the dv/d t can be accomplished with as little as a few volts per microsecond in some units, especially in older designs. Newer designs are often rated in tens to hundreds of volts per microsecond. The other important rate effect is the anode-current di/dt rating. This rating is particularly important in circuits that have low inductance in the anode-cathode path. Adequate inductance would limit the rate of current rise when the device fires. When a thyristor fires, the region near the gate conducts first; then the current spreads to the rest of the semiconductor material of the gate-controlled layer over a period of time. If the current flow through the device increases too rapidly during this period because the input-current d i/d t is too high, the high concentration of current near the gate could damage the device do to localized overheating. Specially designed gate structures can speed up the turnon time of a thyristor, and thus its operational frequency, as well as alleviate this hot-spot problem. Silicon-Controlled Rectifiers. The SCR thyristor can be considered a solid-state latching relay if dc is used as the supply voltage for the load. The gate current turns on the SCR, which is equivalent to closing the contacts in the load circuit. If ac is used as the supply voltage, the SCR load current will reduce to zero as the positive ac wave shape crosses through zero and reverses its polarity to a negative voltage. This will shut off the SCR. If the positive gate voltage is also removed it will not turn on during the next positive half cycle of applied ac voltage unless positive gate voltage is applied. The SCR is suitable for controlling large amounts of rectifier power by means of small gate currents. The ratio of the load current to the control current can be several thousand to one. For example, a 10 A load current might be triggered on by a 5 mA control current. The major time-related specification associated with SCRs is the dv/dt rating. This characteristic reveals how fast a transient spike on the power line can be before it

Tubes, Discrete Solid State Devices, and Integrated Circuits false-triggers the SCR and starts its conducting without gate control current. Apart from this time-related parameter and its gate characteristics, SCR ratings are similar to those for power diodes. SCRs can be used to control dc by using commutating circuits to shut them off. These are not needed on ac since the anode supply voltage reverses every half cycle. SCRs can be used in pairs or sets of pairs to generate ac from dc in inverters. They are also used as protective devices to protect against excessive voltage by acting as a short-circuit switch. These are commonly used in power supply crowbar overvoltage protection circuits. SCRs are also used to provide switched power-amplification, as in solid-state relays. Triacs. The triac in Fig. 12-18 is a three-terminal semiconductor that behaves like two SCRs connected back to front in parallel so that they conduct power in both directions under control of a single gate-control circuit. Triacs are widely used to control ac power by phase shifting or delaying the gate-control signal for some Anode (2)/cathode (1)

325

Current

Voltage

Figure 12-19. Schematic of a diac.

Opto-Coupled Silicon-Controlled Rectifiers. An optocoupled SCR is a combination of a light-emitting diode (LED) and a photo silicon-controlled rectifier (photo-SCR). When sufficient current is forced through the LED, it emits an infrared radiation that triggers the gate of the photo-SCR. A small control current can regulate a large load current, and the device provides insulation and isolation between the control circuit (the LED) and the load circuit (the SCR). Opto-coupled transistors and Darlington transistors that operate on the same principle will be discussed later. 12.2.4 Transistors

Gate Anode (1)/cathode (2)

Figure 12-18. Schematic of a triac.

fraction of the half cycle during which the power diode could be conducting. Light dimmers found in homes and offices and variable-speed drills are good examples of triac applications. Light-Activated Silicon-Controlled Rectifiers. W h e n sufficient light falls on the exposed gate junction, the SCR is turned on just as if the gate-control current were flowing. The gate terminal is also provided for optional use in some circuits. These devices are used in projector controls, positioning controls, photo relays, slave flashes, and security protection systems. Diacs. The diac is shown in Fig. 12-19. It acts as two zener (or avalanche) diodes connected in series, back to back. When the voltage across the diac in either direction gets large enough, one of the zeners breaks down. The action drops the voltage to a lower level, causing a current increase in the associated circuit. This device is

There are many different types of transistors,1 and they are named by the way they are grown, or made. Fig. 12-20A shows the construction of a grown-junction transistor. An alloy-junction transistor is shown in Fig. 12-20B. During the manufacture of the material for a grown junction, the impurity content of the semiconductor is altered to provide npn or pnp regions. The grown material is cut into small sections, and contacts are attached to the regions. In the alloy-junction type, small dots of n- or p-type impurity elements are attached to either side of a thin wafer of p- or n-type semiconductor material to form regions for the emitter and collector junctions. The base connection is made to the original semiconductor material. Drift-field transistors, Fig. 12-20C, employ a modified alloy junction in which the impurity concentration in the wafer is diffused or graded. The drift field speeds up the current flow and extends the frequency response of the alloy-junction transistor. A variation of the drift-field transistor is the microalloy diffused transistor, as shown in Fig. 12-20D. Very narrow base dimensions are achieved by etching techniques, resulting in a shortened current path to the collector. Mesa transistors shown in Fig. 12-20E use the original semiconductor material as the collector, with the

326

Chapter 12

E A. Grown-junction transistor. C

E B. Alloy-junction transistor. C

Diffused base B

E D. Microalloy-diffused transistor.

E C. Drift-field transistor. E

Diffused base

B Epitaxial layer

C C E. Mesa transistor. Diffused emitter

Original wafer F. Epitaxial mesa transistor.

Emitter contact Base

Diffused base

Collector Epitaxial original wafer layer G. Double-diffused epitaxial planar transistor.

Figure 12-20. Construction of various transistors.

base material diffused into the wafer and an emitter dot alloyed into the base region. A flat-topped peak or mesa is etched to reduce the area of the collector at the base junction. Mesa devices have large power-dissipation capabilities and can be operated at very high frequencies. Double-diffused epitaxial mesa transistors are grown by the use of vapor deposition to build up a crystal layer on a crystal wafer and will permit the precise control of the physical and electrical dimensions independently of the nature of the original wafer. This technique is shown in Fig. 12-20F. The planar transistor is a highly sophisticated method of constructing transistors. A limited area source is used for both the base diffusion and emitter diffusion, which provides a very small active area, with a large wire contact area. The advantage of the planar construction is its high dissipation, lower leakage current, and lower collector cut-off current, which increases the stability and reliability. Planar construction is also used with several of the previously discussed base designs. A double-diffused epitaxial planar transistor is shown in Fig. 12-20G.

The field-effect transistor, or FET as it is commonly known, was developed by the Bell Telephone Laboratories in 1946, but it was not put to any practical use until about 1964. The principal difference between a conventional transistor and the FET is the transistor is a current-controlled device, while the FET is voltage controlled, similar to the vacuum tube. Conventional transistors also have a low-input impedance, which may at times complicate the circuit designer’s problems. The FET has a high-input impedance with a low-output impedance, much like a vacuum tube. The basic principles of the FET operation can best be explained by the simple mechanism of a pn junction. The control mechanism is the creation and control of a depletion layer, which is common to all reverse-biased junctions. Atoms in the n region possess excess electrons that are available for conduction, and the atoms in the p region have excess holes that may also allow current to flow. Reversing the voltage applied to the junction and allowing time for stabilization, very little current flows, but a rearrangement of the electrons and holes will occur. The positively charged holes will be drawn toward the negative terminals of the voltage source, and the electrons, which are negative, will be attracted to the positive terminal of the voltage source. This results in a region being formed near the center of the junction having a majority of the carriers removed and therefore called the depletion regions. Referring to Fig. 12-21A, a simple bar composed of n-type semiconductor material has a nonrectifying contacts at each end. The resistance between the two end electrodes is PLR = ------WT where, P is the function of the material sensitivity, L is the length of the bar, W is the width, T is the thickness.

(12-27)

Varying one or more of the variables of the resistance of the semiconductor changes the bar. Assume a p-region in the form of a sheet is formed at the top of the bar shown in Fig. 12-21B. A pn junction is formed by diffusion, alloying, or epitaxial growth creating a reverse voltage between the p and n-material producing two depletion regions. Current in the n-material is caused primarily by means of excess electrons. By reducing the concentration of electrons or majority carriers, the resistivity of the material is increased. Removal of the excess electrons by means of the deple-

Tubes, Discrete Solid State Devices, and Integrated Circuits

Length

P-Type

Gate

Width

Thickness

327

Gate-1

Source

Drain

p-Type n-Type Channel

n-Type

Gate-2 C. Cross-sectional view of the construction for a single- or doublegate field-effect transistor.

B. Bar with gate added and drain voltage applied.

A. Plain semiconductor bar.

Source P Silicon

Field

Source Metallic Film Drain P Silicon

20 V 2 k7

+ G

Drain

22 M7

Input Gate

Gate insulator silicon dioxide D. Internal construction of an insulated-gate transistor (IGT).

D+

Substrate Source

RLD

n Silicon

+ G

D+ S

E. Typical circuit for an IGT transistor. + G

F. n-channel field-effect transistor circuit. D+ S

RLD RG

G. p-channel field-effect transistor circuit.

RLD

H. n-channel double-gate field-effect transistor circuit.

Figure 12-21. Field-effect transistors (FETs).

tion region causes the material to become practically nonconductive. Disregarding the p region and applying a voltage to the ends of the bar cause a current and create a potential gradient along the length of the bar material, with the voltage increasing toward the right, with respect to the negative end or ground. Connecting the p region to ground causes varying amounts of reverse-bias voltage across the pn junction, with the greatest amount developed toward the right end of the p region. A reverse voltage across the bar will produce the same depletion regions. If the resistivity of the p-type material is made much smaller than that of the n-type material, the depletion region will then extend much farther into the n material than into the p material. To simplify the following explanation, the depletion of p material will be ignored. The general shape of the depletion is that of a wedge, increasing the size from left to right. Since the resistivity of the bar material within the depletion area is increased, the effective thickness of the conducting portion of the bar becomes less and less, going from the

end of the p region to the right end. The overall resistance of the semiconductor material is greater because the effective thickness is being reduced. Continuing to increase the voltage across the ends of the bar, a point is reached where the depletion region is extended practically all the way through the bar, reducing the effective thickness to zero. Increasing the voltage beyond this point produces little change in current. The p region controls the action and is termed a gate. The left end of the bar, being the source of majority carriers, is termed the source. The right end, being where the electrons are drained off, is called the drain. A cross-sectional drawing of a typical FET is shown in Fig. 12-21C, and three basic circuits are shown in Fig. 12-21F–H. Insulated-gate transistors (IGT) are also known as field-effect transistors, metal-oxide silicon or semiconductor field-effect transistors (MOSFET), metal-oxide silicon or semiconductor transistors (MOST), and insulated-gate field-effect transistors (IGFET). All these devices are similar and are simply names applied to them by the different manufacturers.

328

Chapter 12

The outstanding characteristics of the IGT are its extremely high input impedance, running to 10 15 :. IGTs have three elements but four connections—the gate, the drain, the source, and an n-type substrate, into which two identical p-type silicon regions have been diffused. The source and drain terminals are taken from these two p regions, which form a capacitance between the n substrate and the silicon-dioxide insulator and the metallic gate terminals. A cross-sectional view of the internal construction appears in Fig. 12-21D, with a basic circuit shown in Fig. 12-21E. Because of the high input impedance, the IGT can easily be damaged by static charges. Strict adherence to the instructions of the manufacturer must be followed since the device can be damaged even before putting it into use. IGTs are used in electrometers, logic circuits, and ultrasensitive electronic instruments. They should not be confused with the conventional FET used in audio equipment.

lE A. Current flow in a pnp transistor.

lE B. Current flow in an npn transistor.

Vo 90 7 +

40 k7

C. Polarity and impedances in a common-base circuit.

100 k7

1 k7

+ D. Polarity and impedances in a common-collector circuit.

40 k7

rc re

Transistor Equivalent Circuits, Current Flow, and Polarity. Transistors may be considered to be a T configuration active network, as shown in Fig. 12-22. re

Vi 700 7

A. Common base.

B. Common emitter. re

rb rc

+ E. Polarity and impedances in a common-emitter circuit.

Figure 12-23. Current, polarity. and impedance relationships.

C. Common collector.

Figure 12-22. Equivalent circuits for transistors.

The current flow, phase, and impedances of the npn and pnp transistors are shown in Fig. 12-23 for the three basic configurations, common emitter, common base and common collector. Note phase reversal only takes place in the common-emitter configuration. The input resistance for the common-collector and common-base configuration increases with an increase of the load resistance RL. For the common emitter, the input resistance decreases as the load resistance is increased; therefore, changes of input or output resistance are reflected from one to the other. Fig. 12-24 shows the signal-voltage polarities of a p-channel field-effect transistor. Note the similarity to tube characteristics.

Voltage, power, and current gains for a typical transistor using a common-emitter configuration are shown in Fig. 12-25. The current gain decreases as the load resistance is increased, and the voltage gain increases as the load resistance is increased. Maximum power gain occurs when the load resistance is approximately 40,000 : , and it may exceed unity. For the common-collector connection, the current gain decreases as the load resistance is increased and the voltage gain increases as the load resistance is increased, but it never exceeds unity. Curves such as these help the designer to select a set of conditions for a specific result. The power gain varies as the ratio of the input to output impedance and may be calculated with the equation

Tubes, Discrete Solid State Devices, and Integrated Circuits

+VDS RD 180o

Input

Outputs

0o RG

VDS

Figure 12-24. Signal-voltage polarities in a p-channel field-effect transistor (FET).

AV = Voltage Amplification AI = Current Amplification

Volt Current Gain Gain 1500 75

r Gain

Powe

1000

500

lta

Power Gain—dB

rre

20 1k

10k

0 100k 200k

Load Resistance (RL)—Ohms

Figure 12-25. Typical voltage, power, and current gains for a conventional transistor using a common-emitter configuration.

Z dB = 10 log ------oZ in

(12-28)

where, Zo is the output impedance in ohms, Zin is the input impedance in ohms. Forward-Current-Transfer Ratio. An important characteristic of a transistor is its forward-current-transfer ratio, or the ratio of the current in the output to the current in the input element. Because of the many different configurations for connecting transistors, the forward transfer ratio is specified for a particular circuit configuration. The forward-current-transfer ratio for the common-base configuration is often referred to as alpha (D) and the common-emitter forward-current-transfer ratio as beta (E). In common-base circuitry, the emitter is the input element, and the collector is the output element. Therefore, Ddc is the ratio of the dc collector

329

current IC to the dc emitter current IE. For the common emitter, the E dc is then the ratio of the dc collector current IC to the base current IB. The ratios are also given in terms of the ratio of signal current, relative to the input and output, or in terms of ratio of change in the output current to the input current, which causes the change. The terms Dand E are also used to denote the frequency cutoff of a transistor and is defined as the frequency at which the value of D for a common-base configuration, or E for a common-emitter circuit, falls to 0.707 times its value at a frequency of 1000 Hz. Gain-bandwidth product is the frequency at which the common-emitter forward-current-transfer ratio E is equal to unity. It indicates the useful frequency range of the device and assists in the determination of the most suitable configuration for a given application. Bias Circuits. Several different methods of applying bias voltage to transistors are shown in Fig. 12-26, with a master circuit for aiding in the selection of the proper circuit shown in Fig. 12-27. Comparing the circuits shown in Fig. 12-26, their equivalents may be found by making the resistors in Fig. 12-27 equal to zero or infinity for analysis and study. As an example, the circuit of Fig. 12-26D may be duplicated in Fig. 12-27 by shorting out resistors R4 and R5 in Fig. 12-27. The circuit Fig. 12-26G employs a split voltage divider for R2. A capacitor connected at the junction of the two resistors shunts any ac feedback current to ground. The stability of circuits A, D, and G in Fig. 12-26 may be poor unless the voltage drop across the load resistor is at least one-third the value of the power supply voltage Vcc. The final determining factors will be gain and stability. Stability may be enhanced by the use of a thermistor to compensate for increases in collector current with increasing temperature. The resistance of the thermistor decreases as the temperature increases, decreasing the bias voltage so the collector voltage tends to remain constant. Diode biasing may also be used for both temperature and voltage variations. The diode is used to establish the bias voltage, which sets the transistor idling current or the current flow in the quiescent state. When a transistor is biased to a nonconducting state, small reverse dc currents flow, consisting of leakage currents that are related to the surface characteristics of the semiconductor material and saturation currents. Saturation current increases with temperature and is related to the impurity concentration in the material. Collector-cutoff current is a dc current caused when the collector-to-base circuit is reverse biased and the

330

Chapter 12

Length

P-Type

Gate

Width

Thickness

Gate-1

Source

Drain

p-Type n-Type Channel

n-Type

Gate-2 C. Cross-sectional view of the construction for a single- or doublegate field-effect transistor.

B. Bar with gate added and drain voltage applied.

A. Plain semiconductor bar.

Source P Silicon

Field

Source Metallic Film Drain P Silicon

20 V 2 k7

+ G

Drain

22 M7

Substrate Source

Input Gate

Gate insulator silicon dioxide D. Internal construction of an insulated-gate transistor (IGT).

D+

RLD

n Silicon

+ G

D+ S

E. Typical circuit for an IGT transistor. + G

F. n-channel field-effect transistor circuit. D+ S

RLD RG

RLD

H. n-channel double-gate field-effect transistor circuit.

G. p-channel field-effect transistor circuit.

Figure 12-26. Basic design circuit for transistor bias circuits.

VCC R1 Out R5 R2 R4

C E

Figure 12-27. Basic bias circuits for transistors

emitter-to-base circuit is open. Emitter-cutoff current flows when the emitter to base is reverse biased and the collector-to-base circuit is open.

Small- and Large-Signal Characteristics. T h e t r a n sistor, like the vacuum tube, is nonlinear and can be classified as a nonlinear active device. Although the transistor is only slightly nonlinear, these nonlinearities become quite pronounced at very low and very high current and voltage levels. If an ac signal is applied to the base of a transistor without a bias voltage, conduction will take place on only one-half cycle of the applied signal voltage, resulting in a highly distorted output signal. To avoid high distortion, a dc-biased voltage is applied to the transistor, and the operating point is shifted to the linear portion of the characteristic curve. This improves the linearity and reduces the distortion to a value suitable for small-signal operation. Even though the transistor is biased to the most linear part of the characteristic curve, it can still add considerable distortion to the signal if driven into the nonlinear portion of the characteristic. Small-signal swings generally run from less than 1 μV to about 10 mV so it is important that the dc-biased voltage be large enough that the applied ac

Tubes, Discrete Solid State Devices, and Integrated Circuits signal is small compared to the dc bias current and voltage. Transistors are normally biased at current values between 0.1 mA and 10 mA. For large-signal operation, the design procedures become quite involved mathematically and require a considerable amount of approximation and the use of nonlinear circuit analysis. It is important to provide an impedance match between cascaded stages because of the wide difference of impedance between the input and output circuits of transistors. If the impedances are not matched, an appreciable loss of power will take place. The maximum power amplification is obtained with a transistor when the source impedance matches the internal input resistance, and the load impedance matches the internal output resistance. The transistor is then said to be image matched. If the source impedance is changed, it affects the internal output resistance of the transistor, requiring a change in the value of the load impedance. When transistor stages are connected in tandem, except for the grounded-emitter connection, the input impedance is considerably lower than the preceding stage output impedance. Therefore, an interstage transformer should be used to supply an impedance match in both directions. When working between a grounded base and a grounded-emitter circuit, a step-down transformer is used. Working into a grounded-collector stage, a step-up transformer is used. Grounded-collector stages can also be used as an impedance-matching device between other transistor stages. When adjusting the supply voltages for a transistor amplifier employing transformers, the battery voltage must be increased to compensate for the dc voltage drop across the transformer windings. The data sheets of the manufacturer should be consulted before selecting a transformer to determine the source and load impedances. Transistor Noise Figure (nf ). In a low-level amplifier, such as a preamplifier, noise is the most important single factor and is stated as the SNR or nf. Most amplifiers employ resistors in the input circuit which contribute a certain amount of measurable noise because of thermal activity. This power is generally about –160 dB, re: 1 W, for a bandwidth of 10,000 Hz. When the input signal is amplified, the noise is also amplified. If the ratio of the signal power to noise power is the same, the amplifier is noiseless and has a noise figure of unity or more. In a practical amplifier some noise is present, and the degree of impairment is the noise figure (nf ) of the amplifier, expressed as the ratio of signal power to noise power at the output:

331

S1 u No nf = ----------------So u N1

(12-29)

where, S1 is the signal power, N1 is the noise power, So is the signal power at the output, No is the noise at the output. nf dB = 10 log nf of the power ratio

(12-30)

For an amplifier with various nf, the SNR would be: nf 1 dB 3 dB 10 dB 20 dB

SNR 1.26 2 10 100

An amplifier with an nf below 6 dB is considered excellent. Low nf can be obtained by the use of an emitter current of less than 1 mA, a collector voltage of less than 2 V, and a signal-source resistance below 2000 : . Internal Capacitance. The paths of internal capacitance in a typical transistor are shown in Fig. 12-28. The width of the pn junction in the transistor varies in accordance with voltage and current, and the internal capacit a n c e a l s o v a r i e s . Va r i a t i o n o f c o l l e c t o r- b a s e capacitance C with collector voltage and emitter current is shown in Figs. 12-28B and C. The increase in the width of the pn junction between the base and collector, as the reverse bias voltage (V C B ) is increased, is reflected in lower capacitance values. This phenomenon is equivalent to increasing the spacing between the plates of a capacitor. An increase in the emitter current, most of which flows through the base-collector junction, increases the collector-base capacitance (CCB). The increased current through the pn junction may be considered as effectively reducing the width of the pn junction. This is equivalent to decreasing the spacing between the plates of a capacitor, therefore increasing the capacitance. The average value of collector-base capacitance (CCB) varies from 2–50 pF, depending on the type transistor and the manufacturing techniques. The collector-emitter capacitance is caused by the pn junction. It normally is five to ten times greater than that of the collector-base capacitance and will vary with the emitter current and collector voltage.

332

Chapter 12

CCB CCE CBE

90 60

IE = 1mA 30 15 6 1

100

Capacitance CCB—pF

Collector volts VCB —V B. Variation of CCB with collector voltage. 90 60

VCB = 6 V 30 15 6 0.1

0.2

0.5

Emitter current IE—mA C. Variation of CCB with emitter current.

Figure 12-28. Internal capacitance of a transistor.

Punch-Through. Punch-through is the widening of the space charge between the collector element and the base of a transistor. As the potential VCB is increased from a low to a high value, the collector-base space charge is widened. This widening effect of the space charge narrows the effective width of the base. If the diode space charge does not avalanche before the space charge spreads to the emitter section, a phenomenon termed punch-through is encountered, as shown in Fig. 12-29.

Breakdown Voltage. Breakdown voltage is that voltage value between two given elements in a transistor at which the crystal structure changes and current begins to increase rapidly. Breakdown voltage may be measured with the third electrode open, shorted, or biased in either the forward or reverse direction. A group of collector characteristics for different values of base bias are shown in Fig. 12-30. The collectorto-emitter breakdow n voltage increases as the base-to-emitter bias is decreased from the normal forward values through zero to reverse. As the resistance in the base-to-emitter circuit decreases, the collector characteristics develop two breakdown points. After the initial breakdown, the collector-to-emitter voltage decreases with an increasing collector current, until another breakdown occurs at the lower voltage.

Ib >>> 0 Rbe = 10 7 Collector Current

Capacitance CCB—pF

A. Capacitance between terminals.

The effect is the base disappears as the collector-base space-charge layer contacts the emitter, creating relatively low resistance between the emitter and the collector. This causes a sharp rise in the current. The transistor action then ceases. Because there is no voltage breakdown in the transistor, it will start functioning again if the voltage is lowered to a value below where punch-through occurs. When a transistor is operated in the punch-through region, its functioning is not normal, and heat is generated internally that can cause permanent damage to the transistor.

Vbe = 0 Ib >> 0

Vbe = 0.5 Rb = 10 7

Ib > 0 Ib = 0

Space charge C

BVCEO BV CES BVCER BVCEX Collector-to-emitter voltage

VEE

VCB B

Figure 12-29. Spreading of the space charge between the emitter and the collector, which creates punch-through.

Figure 12-30. Typical collector characteristic curves showing locations of various breakdown voltages.

Breakdown can be very destructive in power transistors. A breakdown mechanism, termed second breakdown, is an electrical and thermal process in which

Tubes, Discrete Solid State Devices, and Integrated Circuits

Maximum collector current Maximum collector voltage Base current Maximum power dissipation

10 mA –22 V 0 to 300 μA 300 mW

The base current curves are shown in Fig. 12-31A. The amplifier circuit is to be Class A, using a common-emitter circuit, as shown in Fig. 12-31B. By proper choice of the operating point, with respect to the transistor characteristics and supply voltage, low-distortion Class A performance is easily obtained within the transistor power ratings. The first requirement is a set of collector-current, collector-voltage curves for the transistor to be employed. Such curves can generally be obtained from the data sheets of the manufacturer. Assuming that such data is at hand and referring to Fig. 12-31A, a curved line is plotted on the data sheet, representing the maximum power dissipation by the use of the equation P I c = -----c Vc

(12-31)

or P V c = -----c Ic

(12-32)

where, Ic is the collector current, Pc is the maximum power dissipation of the transistor, Vc is the collector voltage. At any point on this line at the intersection of VcIc, the product equals 0.033 W or 33 mW. In determining the points for the dissipation curve, voltages are selected along the horizontal axis and the corresponding current is equated using:

240MA

270MA

210MA 180MA

150MA

8 Lo

90MA

xim

lin

2 0

120 MA

Base current

um 33 m diss W apa tion

60MA 30MA 0MA

4 6 8 10 12 14 16 18 20 Collector-to-Emitter Voltage (VCE) A. Common-emitter-collector family of curves, with load line and maximum dissipation power curve. IC IB

Input

VCE R L RS

Vdc

Output RB RE

B. Amplifier circuit used for load-line calculations. IC1–max

Collector Current

Transistor Load Lines. Transistor load lines are used to design circuits. An example of circuit design uses a transistor with the following characteristics:

300 MA

Collector Current (Ic)–mA

current is concentrated in a very small area. The high current, together with the voltage across the transistor, causes intense heating, melting a hole from the collector to the emitter. This causes a short circuit and internal breakdown of the transistor. The fundamental limitation to the use of transistors is the breakdown voltage (BV cer ). The breakdown voltage is not sharp so it is necessary to specify the value of collector current at which breakdown will occur. This data is obtained from the data sheet of the manufacturer.

333

Constant Dissipation Curve Maximum Operating Point

Original VC1–max Point Collector-To-Emitter Voltage

C. Load line moved to right for maximum power output. Dotted lines are the original load line and operating point.

Figure 12-31. Load-line calculation curves.

PC I C = --------V CE

(12-33)

The current is determined for each of the major collector-voltage points, starting at 16 V and working backward until the upper end of the power curve intersects the 300 μA base current line. After entering the value on the graph for the power dissipation curve, the area to the left of the curve encompasses all points within the maximum dissipation rating of the transistor. The area to the right of the curve is the overload region and is to be avoided. The operating point is next determined. A point that results in less than a 33 mW dissipation is selected somewhere near the center of the power curve. For this example, a 5 mA collector current at 6 V, or a dissipation of 30 mW, will be used. The selected point is indi-

334

Chapter 12

cated on the graph and circled for reference. A line is drawn through the dot to the maximum collector current, 10 mA, and downward to intersect the VCE line at the bottom of the graph, which, for this example, is 12 V. This line is termed the load line. The load resistance RL may be computed with dV CE R L = -----------dI C

(12-34)

where, RL is the load resistance, dVCE is the range of collector-to-emitter voltage, dIC is the range of collector current. In the example, 0 – 12 R L = ------------------0 – 0.01 12 = --------0.01 = 1200: Under these conditions, the entire load line dissipates less than the maximum value of 33 mW, with 90 μA of base current and 5 mA of collector current. The required base current of 90 μA may be obtained by means of one of the biasing arrangements shown in Fig. 12-26. To derive the maximum power output from the transistor, the load line may be moved to the right and the operating point placed in the maximum dissipation curve, as shown in Fig. 12-31C. Under these conditions, an increase in distortion may be expected. As the operating point is now at 6.5 V and 5 mA, the dissipation is 33 mW. Drawing a line through the new operating point and 10 mA (the maximum current), the voltage at the lower end of the load line is 13.0 V; therefore, the load impedance is now 1300 : .

12.3 Integrated Circuits An integrated circuit (IC) is a device consisting of hundreds and even thousands of components in one small enclosure, and came into being when manufacturers learned how to grow and package semiconductors and resistors. The first ICs were small scale and usually too noisy for audio circuits; however, as time passed, the noise was reduced, stability increased, and the operational amplifier (op-amp) IC became an important part of the audio circuit. With the introduction of medium-scale

integration (MSI) and large-scale integration (LSI) circuits, power amplifiers were made on a single chip with only capacitors, gain, and frequency compensation components externally connected. Typical circuit components might use up a space 4 mils × 6 mils (1 mil = 0.001 inch) for a transistor, 3 mils × 4 mils for a diode, and 2 mils × 12 mils for a resistor. These components are packed on the surface of the semiconductor wafer and interconnected by a metal pattern that is evaporated into the top surface. Leads are attached to the wafer that is then sealed and packaged in several configurations, depending on their complexity. ICs can be categorized by their method of fabrication or use. The most common are monolithic or hybrid and linear or digital. Operational amplifiers and most analog circuits are linear while flip-flops and on–off switch circuits are digital. An IC is considered monolithic if it is produced on one single chip and hybrid if it consists of more than one monolithic chip tied together and/or includes discrete components such as transistors, resistors, and capacitors. With only a few external components, ICs can perform math functions, such as trigonometry, squaring, square roots, logarithms and antilogarithms, integration, and differentiation. ICs are well suited to act as voltage comparators, zero-crossing detectors, ac and dc amplifiers, audio and video amplifiers, null detectors, and sine-, square-, or triangular-wave generators, and all at a fraction of the cost of discrete-device circuits. 12.3.1 Monolithic Integrated Circuits All circuit elements, both active and passive, are formed at the same time on a single wafer. The same circuit can be repeated many times on a single wafer and then cut to form individual 50 mil2 ICs. Bipolar transistors are often used in ICs and are fabricated much like the discrete transistor by the planar process. The differences are the contact-to-the-collector region is through the top surface rather than the substrate, requiring electrical isolation between the substrate and the collector. The integrated transistor is isolated from other components by a pn junction that creates capacitance, reducing high-frequency response and increasing leakage current, which in low-power circuits can be significant. Integrated diodes are produced the same way as transistors and can be regarded as transistors whose terminals have been connected to give the desired characteristics.

Tubes, Discrete Solid State Devices, and Integrated Circuits Resistors are made at the same time as transistors. The resistance is characterized in terms of its sheet resistance, which is usually 100–200 :/square material for diffused resistors and 50–150 :/square material for deposited resistors. To increase the value of a resistor, square materials are simply connected in series. It is very difficult to produce resistors with much closer tolerance than 10%; however, it is very easy to produce two adjacent resistors to be almost identical. When making comparator-type circuits, the circuits are balanced and are made to perform on ratios rather than absolute values. Another advantage is uniformity in temperature. As the temperature of one component varies, so does the temperature of the other components, allowing good tracking between components and circuits so ICs are usually more stable than discrete circuits. Capacitors are made as thin-film integrated capacitors or junction capacitors. The thin-film integrated capacitor has a deposited metal layer and an n+ layer isolated with a carrier-free region of silicon dioxide. In junction capacitors, both layers are diffused low-resistance semiconductor materials. Each layer has a dopant of opposite polarity; therefore, the carrier-free region is formed by the charge-depleted area at the pn junction. The MOSFET transistor has many advantages over the bipolar transistor for use in ICs as it occupies only 1 e 25 the area of the bipolar equivalent due to lack of isolation pads. The MOSFET acts like a variable resistor and can be used as a high-value resistor. For instance, a 100 k: resistor might occupy only 1 mil2 as opposed to 250 mil2 for a diffused resistor. The chip must finally be connected to terminals or have some means of connecting to other circuits, and it must also be packaged to protect it from the environment. Early methods included using fine gold wire to connect the chip to contacts. This was later replaced with aluminum wire ultrasonically bonded. Flip-chip and beam-lead methods eliminate the problems of individually bonding wires. Relatively thick metal is deposited on the contact pads before the ICs are separated from the wafer. The deposited metal is then used to contact a matching metal pattern on the substrate. In the flip-chip method, globules of solder deposited on each contact pad ultrasonically bond the chip to the substrate. In the beam-lead method, thin metal tabs lead away from the chip at each contact pad. The bonding of the leads to the substrate reduces heat transfer into the chip and eliminates pressure on the chip.

335

The chip is finally packaged in either hermetically sealed metal headers or is encapsulated in plastic, which is an inexpensive method of producing ICs. 12.3.2

Hybrid Integrated Circuits

Hybrid circuits combine monolithic and thick- and thin-film discrete components for obtaining the best solution to the design. Active components are usually formed as monolithics; however, sometimes discrete transistors are soldered into the hybrid circuit. Passive components such as resistors and capacitors are made with thin- and thick-film techniques. Thin films are 0.001–0.1 mil thick, while thick films are normally 60 mils thick. Resistors can be made with a value from ohms to megohms with a tolerance of 0.05% or better. High-value capacitors are generally discrete, miniature components that are welded or soldered into the circuit, and low-value capacitors can be made as film capacitors and fabricated directly on the substrate. Along with being certain that the components will fit into the hybrid package, the temperature must also be taken into account. The temperature rise T R of the package can be calculated with the following equation: TR = TC – TA = P T TT CA

(12-35)

where, TC is the case temperature, TA is the ambient temperature, PT is the total power dissipation, TCA is the case-to-ambient thermal resistance. The T CA for a package in free air can be approximated at 35°C/W/in2 or a device will have a 35°C rise in temperature above ambient if 1 W is dissipated over an area of 1 in2. 12.3.3

Operational Voltage Amplifiers (Op-Amp)

One of the most useful ICs for audio is the op-amp. Op-amps can be made with discrete components, but they would be very large and normally unstable to temperature and external noise. An op-amp normally has one or more of the following features: • Very high input impedance (>106–1012 :). • Very high open-loop (no feedback) gain.

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Low output impedance (100 MHz). Low input noise. High symmetrical slew rate and/or high input dynamic range. • Low inherent distortion.

• • • •

EO is calculated with the equation EO = AV u E1 – E2

Often one of the inputs is grounded, either through a direct short or a capacitor. Therefore, the gain is either EO = AV E1

By adding external feedback paths, gain, frequency response, and stability can be controlled. Op-amps are normally two-input differential devices; one input inverting the signal and the second input not inverting the signal, and hence called noninverting. Several typical op-amp circuits are shown in Fig. 12-32. Because there are two inputs of opposite polarity, the output voltage is the difference between the inputs where EO + = AV E2

(12-36)

EO – = AV E1

(12-37)

Rf Ein

Rin

(12-39)

or (12-40)

EO = AV E2

To provide both a positive and negative output with respect to ground, a positive and negative power supply is required, as shown in Fig. 12-33. The supply should be regulated and filtered. Often a + and power supply is not available, such as in an automobile, so the op-amp must operate on a single supply, as shown in Fig. 12-34. In this supply, the output dc voltage is set by adjusting R 1 and R 2 so the voltage at the noninverting input is about one-third the power supply voltage.

Rf Rin

Ein

–Rf E Rin in

A. dc amplifier (inverting).

Ein

EO E0 =

(12-38)

EO=

EO Rin + Rf Ein Rin

C. Analog-to-digital converter.

B. dc amplifier (noninverting).

Rf >Vref

C Ein

Ein

EO E0 = Rf C

Ein 3

EO =

¾ Ein dt

Vref F. Monostable multivibrator.

EO EO =

1 RC

E. Integrator.

R1 R1

d E dt in

D. Differentiator.

Ein1 Ein 2

+ Rf

Ein

Rf ( E 1 + Ein 2 + Ein3) R1 in

G. Averaging or summing amplifier.

R1 EO R2 H. Sweep generator.

Figure 12-32. Typical op-amp circuits.

Ein

R2 R1 R4 I. Rectifier.

Tubes, Discrete Solid State Devices, and Integrated Circuits The diodes and zener diodes in Fig. 12-35 are used to protect the op-amp from damage caused by transients, reverse voltage, and overdriving. D6 and D7 clip the inputs before overdriving, D1 and D2 protect against reverse polarity, D4 and D5 regulate the supply, and D3 limits the total voltage across the op-amp.

337

accomplished by one of several methods, Fig. 12-36. Connecting the feedback resistor Rf usually causes an offset and can be found with the equation (12-41)

E Oo = I bias R f Rf

VCC

VCC Rin

Input

Output

Ground

+ +

Rcomp

Rcomp =

VEE

Figure 12-33. Positive- and negative-type power supply.

A. Rf

VCC Input

R1 Input

Rf Rin Rf + Rin

Rin

Output

Output R2

VEE

ECC

Figure 12-34. Simple circuit for operating on a singleended power supply.

EEE

B. R1

VCC Input

Output

D1 D5

Input 1 R1

Output +

VEE

R 3 = R1 R 2 R1 + R2 C.

Input 2 R2

Figure 12-36. Various methods of correcting dc error.

D4 D2

VEE

To obtain minimum offset, make the compensating resistor shown in Fig. 12-36A equal to R f R in R comp = -----------------R f + R in

(12-42)

Figure 12-35. Diode protection circuits for op-amps.

The dc error factors result in an output offset voltage EOo, which exists between the output and ground when it should be zero. The dc offset error is most easily corrected by supplying a voltage differential between the inverting and noninverting inputs, which can be

If this method is not satisfactory, the methods of Figs. 12-36B or C might be required. Many op-amps are internally compensated. Often it is advantageous to compensate a device externally to optimize bandwidth and slew rate, lowering distortion. Internally compensated op-amp ICs come in standard

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Chapter 12

packages—the 8 pin TO-99 metal can, the 8 pin dual-in-line package (MINI DIP), and the 14 pin DIP. Inverting Amplifiers. In the inverting amplifier the + input is grounded and the signal is applied to the minus ( input, Fig. 12-37. The output of the circuit is determined by the input resistor R1 and the feedback resistor Rf. –Rf E O = E in § --------· © R1 ¹

(12-43)

where, Ein is the signal input voltage in volts, Rf is the feedback resistor in ohms, R1 is the input resistor in ohms. The low frequency rolloff is fC

1 = ------------------2SR 1 C 1

Ein

(12-44)

Eo 2 3

Figure 12-37. A simple inverting amplifier.

Noninverting Amplifier. In the noninverting amplifier, Fig. 12-38. the signal is applied to the plus input, while the minus input is part of the feedback loop. The output is (12-45)

The low-frequency rolloff is in two steps. C1

Eo C2

Ein

2 3 +

Figure 12-38. A simple noninverting amplifier.

(12-46)

1 f C = ------------------2 2SR 3 C 2

(12-47)

To keep low-frequency noise gain at a minimum, keep f C ! f C . 1

Power Supply Compensation. The power supply for wideband op-amp circuits should be bypassed with capacitors, Fig. 12-39A, between the plus and minus pin and common. The leads should be as short as possible and as close to the IC as possible. If this is not possible, bypass capacitors should be on each printed circuit board. Input Capacitance Compensation. Stray input capacitance can lead to oscillation in feedback op-amps because it represents a potential phase shift at the frequency of 1 f = ----------------2SR f C s

(12-48)

where, Rf is the feedback resistor, Cs is the stray capacitance.

1 + Rf E O = I in § --------------· © R1 ¹

1 f C = ------------------1 2SR 1 C 1

One way to reduce this problem is to keep the value of Rf low. The most useful way, however, is to add a compensation capacitor, Cf, across Rf as shown in Fig. 12-39B. This makes C f /R f and C s /R in a frequency compensated divider. Output Capacitance Compensation. Output capacitance greater than 100 pF can cause problems, requiring a series resistor Ro being installed between the output of the IC and the load and stray capacitance as shown in Fig. 12-39C. The feedback resistor (R f) is connected after Ro to compensate for the loss in signal caused by Ro. A compensating capacitor (Cf) bypasses Rf to reduce gain at high frequencies. Gain and Bandwidth. A perfect op-amp would have infinite gain and infinite bandwidth. In real life however, the dc open loop voltage gain is around 100,000 or 100 dB and the bandwidth where gain is 0 is 1 MHz, Fig. 12-40. To determine the gain possible in an op-amp, for a particular bandwidth, determine the bandwidth, follow vertically up to the open loop gain response curve and horizontally to the voltage gain. This, of course, is with no feedback at the upper frequency. For example, for a

Tubes, Discrete Solid State Devices, and Integrated Circuits

V+

Input

C1*

105 104

A +

Output C2*

Voltage gain

Input

339

103 102 101

*Low-inductance short-lead capacitors—0.1 μF stacked film preferred. For high-speed op amps, connect C1 and C2 directly at supply pins, with low-inductance ground returns. A. Power-supply bypassing. Cf** (3–0 pF typical) Rin

Input

Output

A +

Cf Cs

100 10 1

100

101

102

106

107

Differential Amplifiers. Two differential amplifier circuits are shown in Fig. 12-41. The ability of the differential amplifier to block identical signals is useful to reduce hum and noise that is picked up on input lines such as in low-level microphone circuits. This rejection is called common-mode rejection and sometimes eliminates the need for an input transformer.

Rf Rin

B. Compensation of stray input capacitance.

V+

Ein

C1*** (3–10 pF typical)

2 3 +

Ein Rf

105

Figure 12-40. Typical open loop gain response.

C1 may be larger. If A is unity-gain compensated.

Input

104

103

Frequency—Hz

Output

R4 V

Ro‡‡

A‡

A. Basic differential amplifier.

V+

CL R1

@ f of A t 10 ‡ A is compensated for unity gain ‡‡ Ro 50–200 7 ***XC1 =

C1 Ein

C. Compensation of stray output capacitance. C2

Figure 12-39. Stability enhancement techniques.

2 3 +

Ein

frequency bandwidth of 0–10 kHz, the maximum gain of the op-amp in Fig. 12-40 is 100. To have lower distortion, it would be better to have feedback at the required upper frequency limit. To increase this gain beyond 100 would require a better op-amp or two op-amps with lower gain connected in series.

B. Single supply differential amplifier.

Figure 12-41. Differential amplifiers.

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Chapter 12

In Fig. 12-41A, capacitors C1 and C2 block dc from the previous circuit and provide a 6 dB/octave rolloff below

–E I in + I in + } I in = --------o1 2 n Rf

1 f C = ------------------1 2SR 1 C 1

(12-49)

The output voltage is found with the equation

1 f C = -----------------------------------2 2S R 3 + R 4 C 2

(12-50)

R2 = E in – E in -----2 1 R 1

(12-51)

To reduce the common mode rejection ratio (CMRR), R2 R4 ------ { -----R1 R3

(12-52)

and fC = fC 1

§ R · § R · § R · E O = R in ¨ --------f -¸ + R in ¨ --------f -¸ + } R in ¨ --------f -¸ 1 R 2 R n R © in1¹ © in 2¹ © inn¹ (12-58)

The output voltage is EO

(12-57)

(12-53)

Summing Inverter Amplifiers. I n t h e s u m m i n g i n verter, Fig. 12-32G, the virtual ground characteristic of the amplifier's summing point is used to produce a scaling adder. In this circuit, Iin is the algebraic sum of the number of inputs. E in I in = ---------1 1 R in

It is interesting that even though the inputs mix at one point, all signals are isolated from each other and one signal does not effect the others and one impedance does not effect the rest. Operational Transconductance Amplifiers. The operational transconductance amplifier (OTA) provides transconductance gain and current output rather than voltage gain and output as in an operational amplifier. The output is the product of the input voltage and amplifier transconductance, and it can be considered an infinite impedance current generator. Varying the bias current on the OTA can completely control the open-loop gain of the device and can also control the total power input. OTAs are useful as multipliers, automatic gain control (agc) amplifiers, sample and hold circuits, multiplexers, and multivibrators to name a few. 12.3.4 Dedicated Analog Integrated Circuits for Audio Applications By Les Tyler and Wayne Kirkwood, THAT Corp.

E in I in = ---------2 2 R in

(12-54)

I in

E in = ---------n R in n

and the total input current is I in = I in + I in + }I in 1

= If

(12-55)

and –E I f = ---------ORf Therefore

(12-56)

The first ICs used in audio applications were general-purpose op-amps like the famous Fairchild μA741. Early op-amps like the classic 741 generally had drawbacks that limited their use in professional audio, from limited slew rate to poor clipping behavior. Early on, IC manufacturers recognized that the relatively high-volume consumer audio market would make good use of dedicated ICs tailored to specific applications such as phono preamplifiers and companders. The National LM381 preamplifier and Signetics NE570 compander addressed the needs of consumer equipment makers producing high-volume products such as phono preamplifiers and cordless telephones. Operational Transconductance Amplifiers, such as the RCA CA3080, were introduced around 1970 to primarily serve the industrial market. It was not long before professional audio equipment manufacturers adapted OTAs for professional audio use as early voltage-

Tubes, Discrete Solid State Devices, and Integrated Circuits controlled amplifiers (VCAs). However, through the 1970s all these integrated circuits were intended more for use in consumer and industrial applications than professional audio. In the mid-1970s, semiconductor manufacturers began to recognize that professional audio had significantly different requirements from the needs of consumer audio or industrial products. The Philips TDA1034 was the first op-amp to combine low noise, 600 : drive capability and high slew rate—all important characteristics to pro audio designers. Shortly after its introduction, Philips transferred production of the TDA1034 to the newly purchased Signetics division which re-branded it the NE5534. At about the same time, Texas Instruments and National Semiconductor developed general-purpose op-amps using a combination of bipolar and FET technology (the TI TLO70- and TLO80- series, and the National LF351-series, sometimes called “BIFET”). These parts offered high slew rates, low distortion, and modest noise (though not the 600 : drive capability of the 5534). While not specifically aimed at pro audio, these characteristics made them attractive to pro audio designers. Along with the NE5534, these op-amps became pro audio industry standards much like the 12AX7 of the vacuum tube era. Op-amps are fundamentally general-purpose devices. The desire to control gain via a voltage, and the application of such technology to tape noise reduction, in particular, created a market forICs that were dedicated to a specific function. This paralleled the way that phono preamplifiers spawned ICs designed for preamplification. In many ways, the VCA drove the development of early pro audio ICs. The design of audio VCAs benefitted from the early work of Barrie Gilbert, inventor of the “Gilbert Cell” multiplier, who in 1968 published “a precise four-quadrant multiplier with subnanosecond response.”1 Gilbert discovered a current mode analog multiplication cell using current mirrors that was linear with respect to both of its inputs. Although its primary appeal at the time was to communications system designers working at RF frequencies, Gilbert laid the groundwork for many audio VCA designs. In 1972, David E. Blackmer received U.S. Patent 3,681,618 for an “RMS Circuit with Bipolar Logarithmic Converter” and in the following year patent 3,714,462 for a “Multiplier Circuit” useful as an audio voltage-controlled amplifier. Unlike Gilbert, Blackmer used the logarithmic properties of bipolar transistors to perform the analog computation necessary for gain control and rms level detection. Blackmer’s development was targeted at professional audio.2,3

341

Blackmer’s timing could not have been better as the number of recording tracks expanded and, due to reduced track width coupled with the effect of summing many tracks together, tape noise increased. The expanded number of recorded tracks also increased mix complexity. Automation became a desirable feature for recording consoles because there just were not enough hands available to operate the faders. Companies such as dbx Inc. and Dolby Laboratories benefited from this trend with tape noise reduction technologies and, in the case of dbx, VCAs for console automation. Blackmer’s discrete transistor-based rms level detectors and VCAs, made by dbx, were soon used in companding multitrack tape noise reduction and console automation systems. The early Blackmer VCAs used discrete NPN and PNP transistors that required careful selection to match each other. Blackmer’s design would benefit greatly from integration into monolithic form. For some time this proved to be very difficult. Nonetheless, Blackmer’s discrete audio VCAs and Gilbert’s transconductance cell laid the groundwork for dedicated audio ICs. VCAs became a major focus of audio IC development. Electronic music, not professional recording, primarily drove the early integration of monolithic VCAs and dedicated audio ICs. In 1976, Ron Dow of Solid State Music (SSM) and Dave Rossum of E-mu Systems developed some of the first monolithic ICs for analog synthesizers. SSM’s first product was the SSM2000 monolithic VCA.4 Solid State Music, later to become Solid State Microtechnology, developed an entire line of audio ICs including microphone preamplifiers, VCAs, voltage-controlled filters, oscillators, and level detectors. Later, Douglas Frey developed a VCA topology known as the operational voltage-controlled element (OVCE) that was first used in the SSM2014.5 Doug Curtis, of Interdesign and later founder of Curtis Electro Music (CEM), also developed a line of monolithic ICs for the synthesizer market that proved to be very popular with manufacturers such as Oberheim, Moog, and ARP. 6 VCAs produced for electronic music relied on NPN transistor gain cells to simplify integration. In the professional audio market, Paul Buff of Valley People, David Baskind and Harvey Rubens of VCA Associates, and others in addition to Blackmer also advanced discrete VCA technology. Baskind and Rubens eventually produced a VCA IC that ultimately became the Aphex/VCA Associates “1537.”7 Blackmer’s VCAs and rms detectors used the precise logarithmic characteristics of bipolar transistors to perform mathematical operations suitable for VCAs and rms detection. The SSM, CEM, and Aphex products

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used variations on the linear multiplier, where a differential pair, or differential quad, is varied to perform VCA functions and analog voltage-controlled filtering. Close transistor matching and control of temperature-related errors are required for low distortion and control feed-through in all VCA topologies. The Gilbert multiplier, the CA3080-series of OTAs, and the VCAs produced by SSM, CEM, and Aphex all relied solely on NPN transistors as the gain cell elements. This greatly simplified the integration of the circuits. Blackmer’s log-antilog VCAs required, by contrast, precisely matched NPN and PNP transistors. This made Blackmer’s VCAs the most difficult to integrate. dbx finally introduced its 2150-series monolithic VCAs in the early 1980s, almost six years after the introduction of the SSM2000.8 Many of the earlier developers of VCAs changed ownership or left the market as analog synthesis faded. Analog Devices currently produces many of the SSM products after numerous ownership changes. THAT Corporation assumed the patent portfolio of dbx Inc. Today Analog Devices, THAT Corporation, and Texas Instruments’ Burr Brown division are the primary manufacturers making analog ICs specifically for the professional audio market. 12.3.4.1 Voltage-Controlled Amplifiers Modern IC VCAs take advantage of the inherent and precise matching of monolithic transistors that, when

combined with on-chip trimming, lowers distortion to very low levels. Two types of IC audio VCAs are commonly used and manufactured today: those based on Douglas Frey’s Operational Voltage Controlled Element (OVCE)9 and those based on David Blackmer’s bipolar log-antilog topology.10 The Analog Devices SSM2018. The Frey OVCE gain cell was first introduced in the SSM2014 manufactured by Solid State Microtechnology (SSM). 11 SSM was acquired by Precision Monolithics, Inc, which was itself acquired by Analog Devices, who currently offers a Frey OVCE gain cell branded the SSM2018T. Frey’s original patents, U.S. 4,471,320 and U.S. 4,560,947, built upon the work of David Baskind and Harvey Rubens (see U.S. Patent 4,155,047) by adding corrective feedback around the gain cell core. 12,13,14 Fig. 12-42 shows a block diagram of the SSM2018T VCA. The OVCE is unique in that it has two outputs: VG and V1-G . As the VG output increases gain with respect to control voltage, the V1-G output attenuates. The result is that the audio signal pans from one output to the other as the control voltage is changed. The following expressions show how this circuit works mathematically: V out1 = V G = 2K u V in and

Figure 12-42. A block diagram of the SSM2018T VCA. Courtesy Analog Devices, Inc.

(12-59)

Tubes, Discrete Solid State Devices, and Integrated Circuits V out2 = V 1 – G

(12-60)

= 2 1 – K u V in

where, K varies between 0 and 1 as the control voltage is changed from full attenuation to full gain. When the control voltage is 0 V, K = 0.5 and both output voltages equal the input voltage. The value K is exponentially proportional to the applied control voltage; in the SSM2018T, the gain control constant in the basic VCA configuration is 30 mV/dB, so the decibel gain is directly proportional to the applied control voltage. This makes the part especially applicable to audio applications. The SSM2018 has many applications as a VCA, but its use as a voltage-controlled panner (VCP) is perhaps one of the most unique, Fig. 12-43.

Vc Vin

18 k7

343

I out = anti log > log I in + 0 @ = I in u > anti log 0 @ = I in u 1 I out = I in Blackmer VCAs exploit the logarithmic properties of a bipolar junction transistor (BJT). In the basic Blackmer circuit, the input signal I in (the Blackmer VCA works in the current, not the voltage domain) is first converted to its log-domain equivalent. A control voltage, E C , is added to the log of the input signal. Finally, the antilog is taken of the sum to provide an output signal I out . This multiplies I in by a control constant, EC. When needed, the input signal voltage is converted to a current via an input resistor, and the output signal current is converted back to a voltage via an op-amp and feedback resistor. Like the Frey OVCE, the Blackmer VCA’s control voltage (EC) is exponentiated in the process. This makes the control law exponential, or linear in dB. Many of the early embodiments of VCAs for electronic music were based on linear multiplication and required exponential converters, either external or internal to the VCA, to obtain this desirable characteristic.15 Fig. 12-44 shows the relationship between gain and EC for a Blackmer VCA.

18 k7

Figure 12-43. SSM2018 as a VCP. Courtesy Analog Devices, Inc.

THAT Corporation’s 2180 and 2181 VCAs. T h e Blackmer VCAs now offered by THAT Corporation (which registered the trademark “Blackmer” for this application) exploit the mathematical property that adding a constant to the logarithm of a number is equivalent, in the linear domain, to multiplying the number by the antilog of the constant. The equation for determining the output is I out = anti log > log I in + E C @ = I in u > anti log E C @

(12-61)

I in is multiplied by the antilog of E C to produce I out . Conveniently, and fortunately for Blackmer, the exponential response of EC is linear in dB. Consider the unity-gain case when EC = 0.

–

– – –

–

– Ec+ —mV

Figure 12-44. THAT 2180 gain versus EC+. Courtesy THAT Corporation.

Audio signals are of both polarities; that is, the sign of Iin in the above equations will be either positive or negative at different times. Mathematically, the log of a negative number is undefined, so the circuit must be designed to handle both polarities. The essence of David Blackmer ’s invention was to handle each phase—positive and negative—of the signal waveform

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Chapter 12

with different “genders” of transistors—NPN and PNP—and to provide a class A-B bias scheme to deal with the crossover region between the two. This made it possible to generate a sort of bipolar log and antilog. A block diagram of a Blackmer VCA is shown in Fig. 12-45.

+ D1

Ec+

IN Q3

IIN

D2 Q2 Voltage Bias Generator

Ec– 8

OUT Q4

SYM

25 D3

Icell

Iadj

V–

Figure 12-45. THAT 2180 equivalent schematic. Courtesy THAT Corporation.

Briefly, the circuit functions as follows. An ac input signal current I IN flows in pin 1, the input pin. An internal operational transconductance amplifier (OTA) maintains pin 1 at virtual ground potential by driving the emitters of Q1 and (through the Voltage Bias Generator) Q3. Q3/D3 and Q1/D1 act to log the input current, producing a voltage (V 3 ) that represents the bipolar logarithm of the input current. (The voltage at the junction of D1 and D2 is the same as V3, but shifted by four forward Vbe drops.) Pin 8, the output, is usually connected to a virtual ground. As a result, Q2/D2 and Q4/D4 take the bipolar antilog of V3, creating an output current flowing to the virtual ground, which is a precise replica of the input current. If pin 2 (E C +) and pin 3 (E C ) are held at ground, the output current will equal the input current. For pin 2 positive or pin 3 negative, the output current will be scaled larger than the input current. For pin 2 negative or pin 3 positive, the output current is scaled smaller than the input. The log portion of the VCA, D1/Q1 and D3/Q3, and the antilog stages, D 2 /Q 2 and D 4 /Q 4 in Fig. 12-45,

require both the NPN and the PNP transistors to be closely matched to maintain low distortion. As well, all the devices (including the bias network) must be at the same temperature. Integration solves the matching and temperature problems, but conventional “junction-isolated” integration is notorious for offering poor-performing PNP devices. Frey and others avoided this problem by basing their designs exclusively on N PN d e v i c e s f o r t h e c r it i c a l m u l t i p l i e r s t a g e . Blackmer’s design required “good” PNPs as well as NPNs. One way to obtain precisely matched PNP transistors that provide discrete transistor performance is to use an IC fabrication technology known as dielectric isolation. THAT Corporation uses dielectric isolation to fabricate integrated PNP transistors that equal or exceed the performance of NPNs. With dielectric isolation, the bottom layers of the devices are available early in the process, so both N- and P-type collectors are possible. Furthermore, each transistor is electrically insulated from the substrate and all other devices by an oxide layer, which enables discrete transistor performance with the matching and temperature characteristics only available in monolithic form. In Fig. 12-45, it can also be seen that the Blackmer VCA has two E C inputs having opposite control response—E C + and E C . This unique characteristic allows both control inputs to be used simultaneously. Individually, gain is exponentially proportional to the voltage at pin 2, and exponentially proportional to the negative of the voltage at pin 3. When both are used simultaneously, gain is exponentially proportional to the difference in voltage between pins 2 and 3. Overall, because of the exponential characteristic, the control voltage sets gain linearly in decibels at 6 mV/dB. Fig. 12-46 shows a typical VCA application based on a THAT2180 IC. The audio input to the VCA is a current; an input resistor converts the input voltage to a current. The VCA output is also a current. An op-amp and its feedback resistor serve to convert the VCA’s current output back to a voltage. As with the basic topologies from Gilbert, Dow, Curtis, and other transconductance cells, the current input/output Blackmer VCA can be used as a variable conductance to tune oscillators, filters, and the like. An example of a VCA being used to control a first-order state-variable filter is shown in Fig. 12-47 with the response plot in Fig. 12-48. When combined with audio level detectors, VCAs can be used to form a wide range of dynamics processors, including compressors, limiters, gates, duckers,

Tubes, Discrete Solid State Devices, and Integrated Circuits

Vcc 2180 Series VCA

7 V+

Ec–

10u

Power Supplies Vcc = +15 V Vee = –15 V

Ec– SYM Ec+ 4 GND 2 V–

20k

1 –IN

22p

5 6 NC

OUT 8

– OP275

OUT

5.1k

Vee

Figure 12-46. Basic THAT 2180 VCA application. Courtesy THAT Corporation.

companding noise reduction systems, and signalcontrolled filters.

12.3.4.2 Peak, Average, and RMS Level Detection It is often desirable to measure audio level for display, dynamics control, noise reduction, instrumentation, etc. Level detectors take different forms: among the most common are those that represent peak level, some form of average level over time, and root-mean-square (more simply known as rms level). Peak signal level is usually interpreted to mean the highest instantaneous level within the audio bandwidth. Measuring peak level involves a detector with very fast charge (attack) response and much slower decay. Peak levels are often used for headroom and overload indication and in audio limiters to prevent even brief overload of transmission or storage media. However, peak measurements do not correlate well with perceived loudness, since the ear responds not only to the amplitude, but also to the duration of a sound. Average-responding level detectors generally average out (or smooth) full or half-wave rectified signals to provide envelope information. While a pure average response (that of an R-C circuit) has equal rise (attack) and fall (decay) times, in audio applications, level detectors often have faster attack than decay. The familiar VU meter is average responding, with a response time and return time of the indicator both equal to 300 ms. The PPM meter, commonly used in Europe for audio program level measurement, combines a specific quick attack response with an equally specific, slow fall time. PPM metering provides a reliable indication of meaningful peak levels.16 Rms level detection is unique in that it provides an ac measurement suitable for the calculation of signal power. Rms measurements of voltage, current, or both indicate effective power. Effective power is the heating

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power of a dc signal equivalent to that offered by an ac signal. True rms measurements are not affected by the signal waveform complexity, while peak and average readings vary greatly depending on the nature of the waveform. For example, a resistor heated by a 12 Vac rms signal produces the same number of watts—and heat—as a resistor connected to 12 Vdc. This is true regardless of whether the ac waveform is a pure sinusoid, a square wave, a triangle wave or music. In instrumentation, rms is often referred to as true rms to distinguish it from average-responding instruments that are calibrated to read rms only for sinusoidal inputs. Importantly, in audio signal-processing applications, rms response is thought to closely approximate the human perception of loudness.17

12.3.4.3 Peak and Average Detection with Integrated Circuits The fast response of a peak detector is often desirable for overload indication or dynamics control when a signal needs to be limited to fit the strict level confines of a transmission or storage medium. A number of opamp-based circuits detect peak levels using full or half-wave rectification. General-purpose op-amps are quite useful for constructing peak detectors and are discussed in Section 12.3.3. The recently discontinued Analog Devices PKD01 was perhaps the only peak detector IC suited for audio applications. Average-responding level detection is performed by rectification followed by a smoothing resistor/capacitor (R-C) filter whose time constants are chosen for the application. If the input is averaged over a sufficiently long period, the signal envelope is detected. Again, general-purpose op-amps serve quite well as rectifiers with R-C networks or integrators serving as averaging filters. Other than meters, most simple electronic audio level detectors use an asymmetrical averaging response that attacks more quickly than it decays. Such circuits usually use diode steering to charge a capacitor quickly through a relatively small-value resistor, but discharge it through a larger resistor. The small resistor yields a fast attack, and the large resistor yields a slower decay. 12.3.4.4 Rms Level Detection Basics Rms detection has many applications in acoustic and industrial instrumentation. As mentioned previously, rms level detectors are thought to respond similarly to

346

Chapter 12

U1 2180A

High Pass 2

Input

U2A – 1 3 + 5532 2

EC+

Rset

V+ 4

GND

3 Vcontrol

V+ OUT

U3 LF351

SYM

IN EC–

Cset

V–

2 3

Low Pass

Rbias V–

Figure 12-47. VCA state-variable filter. Courtesy THAT Corporation.

Figure 12-48. State-variable filter response. Courtesy THAT Corporation.

the human perception of loudness. This makes them particularly useful for audio dynamics control. Rms is mathematically defined as the square root of the mean of the square of a waveform. Electronically, the mean is equal to the average, which can be approximated by an R-C network or an op-amp-based integrator. However, calculating the square and square root of waveforms is more difficult. Designers have come up with a number of clever techniques to avoid the complexity of numerical rms calculation. For example, the heat generated by a resistive element may be used to measure power. Power is directly proportional to the square of the voltage across, or current through, a resistor, so the heat given off is proportional to the square of the applied signal level. To measure large amounts of power having very complex waveforms, such as the RF output of a television transmitter, a resistor dummy load is used to heat water. The

temperature rise is proportional to the transmitter power. Such caloric instruments are naturally slow to respond, and impractical for the measurement of sound. Nonetheless, solid-state versions of this concept have been integrated, as, for example U.S. Patent 4,346,291, invented by Roy Chapel and Macit Gurol.18 This patent, assigned to instrumentation manufacturer Fluke, describes the use of a differential amplifier to match the power dissipated in a resistive element, thus measuring the true rms component of current or voltage applied to the element. While very useful in instrumentation, this technique has not made it into audio products due to the relatively slow time constants of the heating element. To provide faster time constants to measure small rms voltages or currents with complex waveforms such as sound, various analog computational methods have been employed. Computing the square of a signal generally requires extreme dynamic range, which limits the usefulness of direct analog methods in computing rms value. As well, the square and square-root operations require complex analog multipliers, which have traditionally been expensive to fabricate. As with VCAs, the analog computation required for rms level detection is simplified by taking advantage of the logarithmic properties of bipolar junction transistors. The seminal work on computing rms values for audio applications was developed by David E. Blackmer, who received U.S. Patent 3,681,618 for an “RMS Circuit with Bipolar Logarithmic Converter.”17 Blackmer’s circuit, discussed later, took advantage of two important log-domain properties to compute the square and square root. In the log domain, a number is squared by multiplying it by 2; the square root is obtained by dividing it by 2. For example, to square the signal Vin use

Tubes, Discrete Solid State Devices, and Integrated Circuits 2

V in = anti log > log V in u 2 @

(12-62)

To take the square root of V log, log V log V log = antilog -------------------------2

(12-63)

12.3.4.5 Rms Level Detection ICs Because rms level detectors are more complex than either peak- or average-responding circuits, they benefit greatly from integration. Fortunately, a few ICs are suitable for the professional audio applications. Two ICs currently in production are the Analog Devices AD636 and the THAT Corporation THAT2252. Analog Devices AD636. The AD636 has enjoyed wide application in audio and instrumentation. Its predecessor, the AD536, was used in the channel dynamics processor of the SSL 4000 series console in conjunction with a dbx VCA. Thousands of these channels are in daily use worldwide. The AD636 shown in Fig. 12-49 provides both a linear-domain rms output and a dB-scaled logarithmic output. The linear output at pin 8 is ideal for applications where the rms input voltage must be read with a dc meter. Suitably scaled, 1 Vrms input can produce 1 Vdc at the buffer output, pin 6. In audio applications such as signal processors, it is often most useful to express the signal level in dB. The AD636 also provides a dB-scaled current output at pin 5. The linear dB output is particularly useful with exponentially controlled VCAs such as the SSM2018 or THAT 2180 series. Current mirror

+V S 14

Com 10

20 μA FS

R1 25k7 I3

|VIN| +

Buf in Q3

8k7

Q2 Q4 A2

R3 10k7

dB out

IREF Q1

One-quadrant square/divider

R2 10k7 C AV +V S

I4 I1

VIN

C AV IOUT

10 μA FS

Absolute value/ voltage-current converter

R4 20k7

Buffer A4

Buf out 6

Q5 10k7

–V S 3

Figure 12-49. The AD636 block diagram. Courtesy Analog Devices, Inc.

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Averaging required to calculate the mean of the sum of the squares is performed by a capacitor, C A V , connected to pin 4. Fig. 12-50 shows an AD636 used as an audio dB meter for measurement applications. THAT Corporation THAT2252. The 2252 IC uses the technique taught by David Blackmer to provide wide dynamic range, logarithmic linear dB output, and relatively fast time constants. Blackmer’s detector delivers a fast attack with a slow linear dB decay characteristic in the log domain.17 Because it was specifically developed for audio applications, it has become a standard for use in companding noise reduction systems and VCA-based compressor/limiters. A simplified schematic of Blackmer’s rms detector, used in the THAT2252, is shown in Fig. 12-51. The audio input is first converted to a current Iin by an external resistor (not shown in Fig. 12-51). I in is full-wave rectified by a current mirror rectifier formed by OA1 and Q1-Q3, such that IC4 is a full-wave rectified version of Iin. Positive input currents are forced to flow through Q1, and mirrored to Q2 as IC2; negative input currents flow through Q3 as IC3; both IC2 and IC3 thus flow through Q4. (Note that pin 4 is normally connected to ground through an external 20 : resistor.) Performing the absolute value before logarithmic conversion avoids the problem that, mathematically, the log of a negative number is undefined. This eliminates the requirement for bipolar logarithmic conversion and the PNP transistors required for log-domain VCAs. OA2, together with Q4 and Q5, forms a log amplifier. Due to the two diode-connected transistors in the feedback loop of OA2, the voltage at its output is proportional to twice the log of IC4 . This voltage, V log , is therefore proportional to the log of Iin 2 (plus the bias voltage V2). To average V log , pin 6 is usually connected to a capacitor C T and a negative current source R T . see Fig. 12-52. The current source establishes a quiescent dc bias current, IT, through diode-connected Q6. Over time, CT charges to 1 Vbe below Vlog. Q6’s emitter current is proportional to the antilog of its Vbe. The potential at the base (and collector) of Q6 represents the log of Iin2 while the emitter of Q6 is held at ac ground via the capacitor. Thus, the current in Q6 is proportional to the square of the instantaneous change in input current. This dynamic antilogging causes the capacitor voltage to represent the log of the mean of the square of the input current. Another way to characterize the operation of Q6, CT, and RT is that of a “log domain” filter.20

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Chapter 12

Figure 12-50. AD636 as an audio dB meter. Courtesy Analog Devices, Inc.

OA1 IC3

Iin

IC1 Q1

– + + V2 OA1

Q4 Q3 IC + 2 IC4 V – 1 Q2

Vlog V3

– +

Q6 IT

– 7

OA3

Vout

6 V6

Figure 12-51. Block diagram of a THAT2252 IC. Courtesy THAT Corporation.

when the input signal current equals a reference current determined by Ibias and IT. It varies in dc level above and below this value to represent the dB input level at the rate of ~6 mV/dB. Fig. 12-53 shows the tone burst response of a THAT2252, while Fig.12-54 is a plot of THAT2252 output level versus input level. The THAT2252 has linear dB response over an almost 100 dB range. V–

In the THAT2252, the square root portion of the rms calculation is not computed explicitly but is implied by the constant of proportionality for the output. Since, in the log domain, taking the square root is equivalent to dividing by two, the voltage at the output (pin 7) is proportional to the mean of the square at approximately 3 mV/dB and proportional to the square root of the mean of the square at approximately 6 mV/dB. The attack and release times of rms detectors are locked in a relationship to each other and separate controls for each are not possible while still maintaining rms response. Varying the value of C T and R T in the THAT2252, and C AV in the AD636 allow the time constant to be varied to suit the application. More complex approaches, such as a nonlinear capacitor, are possible with additional circuitry.21 Fig. 12-52 shows a typical application for the THAT2252. The input voltage is converted to a current by R in . C in blocks input dc and internal op-amp bias currents. The network around pin 4 sets the waveform symmetry for positive versus negative input currents. Internal bias for the THAT2252 is set by R b and bypassed by a 1 μF capacitor. RT and CT set the timing of the log-domain filter. The output signal (pin 7) is 0 V

Sym 50k

1k 10M

24k

V+ 47k 20

4 1

8 V+

2252

OUT

Out

V– GND CAP

RT 2M2

+ Cin 20M

SYM IBIAS

V+

Rb 560k

Rin 10k

CT 10M

V– Rf 22M

Figure 12-52. Typical application of a THAT2252 IC. Courtesy THAT Corporation.

The Analog Devices AD636 and THAT Corporation THAT2252 provide precise, low-cost rms detection due to their integration into monolithic form. On their own, rms detectors are very useful at monitoring signal level, controlling instrumentation, and other applications. When combined with VCAs for gain control, many different signal processing functions can be realized including noise reduction, compression, and limiting.

Tubes, Discrete Solid State Devices, and Integrated Circuits

Audio input

Detector output

Figure 12-53. THAT2252 tone burst response. Courtesy THAT Corporation

Output–mV

+300

300

0 Input–dBr

+50

Figure 12-54. THAT2252 input versus output. Courtesy THAT Corporation.

12.3.5 Integrated Circuit Preamplifiers The primary applications of preamplifiers for professional audio in the post-tape era are for use with microphones. Before the development of monolithic ICs dedicated to the purpose, vacuum tubes, discrete bipolar or field-effect transistors,22 or general-purpose audio op-amps were used as preamplifiers.23 Dynamic microphones generally produce very small signal levels and have low output impedance. Ribbon microphones are notorious for low output levels. For many audio applications, significant gain (40–60 dB) is required to bring these mic level signals up to pro audio levels. Condenser microphones, powered by phantom power, external power supplies, or batteries, often produce higher signal levels requiring less gain. To avoid adding significant noise to the microphone’s output, professional audio preamplifiers must have very low input noise. Transformer-coupled preamps ease the requirement for very low noise ampli-

349

fication, since they take advantage of the voltage step-up possible within the input transformer. Early transformerless, or active, designs required performance that eluded integration until the early 1980s. Until semiconductor process and design improvements permitted it and the market developed to generate sufficient demand, most microphone preamplifiers were based on discrete transistors or discrete transistors augmented with commercially available op-amps. Virtually all professional microphones use two signal lines to produce a balanced output. This allows a preamplifier to distinguish the desired differential audio signal—which appears as a voltage difference between the two signal lines—from hum and noise pickup—which appears as a “common-mode” signal with the same amplitude and polarity on both signal lines. Common mode rejection quantifies the ability of the preamplifier to reject common mode interference while accepting differential signals. Therefore, one goal of a pro-audio mic preamp is to amplify differential signals in the presence of common-mode hum. As well, the preamp should ideally add no more noise than the thermal noise of the source impedance—well below the self-noise of the microphone and ambient acoustic noise. Phantom power is required for many microphones, especially professional condenser types. This is usually a +48 Vdc power supply applied to both polarities of the differential input through 6.8 k: resistors (one for each input polarity). Dc supply current from the microphone returns through the ground conductor. Phantom power appears in common mode essentially equal on both inputs. The voltage is used to provide power to the circuitry inside the microphone. 12.3.5.1 transformer input microphone preamplifiers Many microphone preamplifiers use transformers at their inputs. Transformers, although costly, provide voltage gain that can ease the requirements for low noise in the subsequent amplifier. The transformer’s voltage gain is determined by the turns ratio of the secondary versus the primary. This ratio also transforms impedance, making it possible to match a low-impedance microphone to a high-impedance amplifier without compromising noise performance. A transformer’s voltage gain is related to its impedance ratio by the following equation: Z Gain = 20 log -----s Zp

(12-64)

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Chapter 12

where, Gain is the voltage gain in dB of the transformer, Zp is the primary transformer impedance in ohms, Zs is the secondary transformer impedance in ohms. A properly designed transformer with a 150 : primary and 15 k: secondary produces 20 dB of free voltage gain without adding noise. Well-made transformers also provide high common-mode rejection, which helps avoid hum and noise pickup. This is especially important with the low output voltages and long cable runs common with professional microphones. In addition, transformers provide galvanic isolation by electrically insulating the primary circuit from the secondary while allowing signal to pass. While usually unnecessary in microphone applications, this provides a true ground lift, which can eliminate ground loops in certain difficult circumstances. Transformer isolation is also useful when feeding phantom power (a +48 Vdc current-limited voltage to power internal circuitry in the microphone) down the mic cable from the preamp input terminals. Phantom power may be connected through a center tap on the primary to energize the entire primary to +48 Vdc, or supplied through resistors (usually 6.8 k:) to each end of the primary of the transformer. (The latter connection avoids dc currents in the coils, which can lead to premature saturation of the core magnetics.) The galvanic isolation of the transformer avoids any possibility of the 48 Vdc signal from reaching the secondary windings. 12.3.5.2 Active Microphone Preamplifiers Eliminate Input Transformers As is common in electronic design, transformers do have drawbacks. Perhaps the most prominent one is cost: a Jensen Transformer, Inc. JT-115K-E costs approximately $75 US or $3.75 per dB of gain.24 From the point of view of signal, transformers add distortion due to core saturation. Transformer distortion has a unique sonic signature that is considered an asset or a liability—depending on the transformer and whom you ask. Transformers also limit frequency response at both ends of the audio spectrum. Furthermore, they are susceptible to picking up hum from stray electromagnetic fields. Well-designed active transformerless preamplifiers can avoid these problems, lowering cost, reducing distortion, and increasing bandwidth. However, transformerless designs require far better noise performance from the active circuitry than transformer-based preamps do. Active mic preamps usually require capaci-

tors (and other protection devices) to block potentially damaging effects of phantom power.25

12.3.5.3 The Evolution of Active Microphone Preamplifier ICs Active balanced-input microphone preamplifier ICs were not developed until the early 1980s. Early IC fabrication processes did not permit high-quality low-noise devices, and semiconductor makers were uncertain of the demand for such products. Active transformerless microphone preamplifiers must have fully differential inputs because they interface to balanced microphones. The amplifiers described here, both discrete and IC, use a current feedback CFB topology with feedback returned to one (or both) of the differential input transistor pair’s emitters. Among its many attributes, current feedback permits differential gain to be set by a single resistor. Current feedback amplifiers have a history rooted in instrumentation amplifiers. The challenges of amplifying low-level instrumentation signals are very similar to microphones. The current feedback instrumentation amplifier topology, known at least since Demrow’s 1968 paper, 26 was integrated as early as 1982 as the Analog Devices AD524 developed by Scott Wurcer.27 A simplified diagram of the AD524 is shown in Fig. 12-55. Although the AD524 was not designed as an audio preamp, the topology it used later became a de facto standard for IC microphone preamps. Demrow and Wurcer both used a bias scheme and fully balanced topology in which they wrapped op-amps around each of the two input transistors to provide both ac and dc feedback. Gain is set by a single resistor connected between the emitters (shown as 40 :, 404 :and 4.44 k:), and feedback is provided by two resistors (R56 and R 57 ). The input stage is fully symmetrical and followed by a precision differential amplifier to convert the balanced output to single ended. Wurcer’s AD524 required laser-trimmed thin film resistors with matching to 0.01% for an 80 dB common mode rejection ratio at unity gain. Audio manufacturers, using variations on current feedback and the Demrow/Wurcer instrumentation amp, produced microphone preamps based on discrete low-noise transistor front ends as early as 1978; an e x a m p le i s t h e H a r r is on P C 1 0 41 m o d u le . 2 8 In December of 1984, Graeme Cohen also published his discrete transistor topology; it was remarkably similar to the work of Demrow, Wurcer, and the Harrison preamps.29

Tubes, Discrete Solid State Devices, and Integrated Circuits +VS I2 I1 V 50μA B 50μA R52 R53 20 k7 Sense C4 C3 20 k7 A3 R55 VO R 20k7 56 R54 R55 Q , Q 20 k7 –In Q1, Q3 2 4 20 k7 4.44 k7 Reference 20k7 RG1 404 7 RG2 = 100 G +In I3 I4 40 7 G = 1000 50μA 50μA A1

–VS

Figure 12-55. AD524 block diagram. Courtesy Analog Devices, Inc.

Solid State Music, or SSM, which later became Solid State Microtechnology, developed the first active microphone preamp IC for professional audio around 1982.30 SSM specialized in producing niche-market semiconductors aimed at the professional audio business. The SSM2011 was almost completely self-contained, requiring only a handful of external resistors and capacitors to provide a complete preamp system. One unique feature of the SSM2011 was an on-chip LED overload and signal presence indicator. SSM later produced the SSM2015 and the SSM2016 designed by Derek Bowers.31 The SSM2016, and the SSM2011 and 2015 that preceded it, did not use a fully balanced topology like Wurcer ’s AD524 and the Harrison PC1041. The SSM parts used an internal op-amp to convert the differential stage output to single-ended. This allowed external feedback resistors to be used, eliminating the performance penalty of on-chip diffused resistors. The SSM2016 was highly successful but required external precision resistors and up to three external trims. SSM was later acquired by Precision Monolithics and eventually by Analog Devices (ADI). The SSM2016 was extremely suc cessful and, after its disc ontinuanc e in the mid-1990s, became highly sought after. Analog Devices introduced the SSM2017 self contained preamp, also designed by Bowers, as a replacement for the SSM2016. The SSM2017 used internal laser-trimmed thin-film resistors that permitted the fully balanced topology of the AD524 and discrete preamps to be realized as an IC. Analog Devices manufactured the SSM2017 until about 2000 when it was discontinued. A year or two later, ADI released the 2019 which is available today. The Burr Brown division of Texas Instruments offered the INA163, which had similar performance to

351

the SSM2017, but was not pin compatible with it. After the 2017 was discontinued, TI introduced its INA217 in the SSM2017 pinout. Today, TI produces a number of INA-family instrumentation amplifiers suitable for microphone preamps including the INA103, INA163, INA166, INA217, and the first digitally gain-controlled preamp: the PGA2500. In 2005, THAT Corporation introduced a series of microphone preamplifiers in pinouts to match the familiar SSM2019/INA217 as well as the INA163. The THAT1510 and the performance-enhanced THAT1512 use dielectric isolation to provide higher bandwidth than the junction-isolated INA and SSM series products. (Dielectric isolation is explained in the section on audio VCAs.) While all offer relatively high performance, the three different families of parts have different strengths and weaknesses. Differences exist in gain bandwidth, noise floor, distortion, gain structure, and supply consumption. The optimum part for any given application will depend on the exact requirements of the designer. A designer considering any one of these parts should compare their specs carefully before finalizing a new design. 12.3.5.4 Integrated Circuit Mic Preamplifier Application Circuits The THAT1510 series block diagram is shown in Fig. 12-57. Its topology is similar to those of the TI and ADI parts. A typical application circuit is shown in Fig. 12-58. The balanced mic-level signal is applied to the input pins, In+ and In. A single resistor (R G ), connected between pins RG1 and RG2, sets the gain in conjunction with the internal resistors RA and RB. The input stage consists of two independent low-noise amplifiers in a balanced differential amplifier configuration with both ac and dc feedback returned to the emitters of the differential pair. This topology is essentially identical to the AD524 current feedback amplifier as described by Wurcer et al. The output stage is a single op-amp differential amplifier that converts the balanced output of the gain stage into single-ended form. The THAT1500 series offers a choice of gains in this stage: 0 dB for the 1510, and 6 dB for the 1512. Gain is controlled by the input-side resistor values: 5 k: for the 1510 and 10 k: for the 1512. The gain equations for the THAT1510 are identical to that of the SSM2017/2019 and the INA217. The INA163 and THAT 1512 have unique gain equations.

352

V+

Chapter 12

Input Stage

Output Stage –AV

+In –In RG1 RG2

–AV

5 k7 (10 k7)

5 k7 +

Out

5 k7 (10 k7)

RA 5 k7

5 k7 Ref

RB 5 k7

V–

Figure 12-56. THAT1510/1512 block diagram. Courtesy THAT Corporation.

For the THAT 1510, SSM 2019, and INA217 the equation is 10 k: Av = 1 + --------------RG

(12-65) –In C1 470 pF

(12-66)

R1 1 k7

In RG1 CG

C6 V+ Out Out

For the THAT1512 it is k:Av = 0.5 + 5----------RG

+15 100 nF

For the INA163 it is 6 k: Av = 1 + -----------RG

gains. Differences in noise performance begin to show up at lower gains, with the THAT 1512 offering the best performance ~34 nV e Hz at 0 dB gain) of the group. These parts are all generally optimized for the relatively low source impedances of dynamic microphones with typically a few hundred ohm output impedance. Fig. 12-57 provides an application example for direct connection to a dynamic microphone. Capacitors C1–C3 filter out radio frequencies that might cause interference (forming an RFI filter). R1 and R2 provide a bias current path for the inputs and terminate the microphone output. RG sets the gain as defined in the previous equation. CG blocks dc in the input stage feedback loop, limiting the dc gain of this stage to unity and avoiding output offset change with gain. C 6 and C 9 provide power supply bypass.

+In

(12-67)

where, Av is the voltage gain of the circuit. All these parts can reach unity gain but the value of RG required varies considerably. For the 1510, 2017, 2019, 163, and 217, gain is 0 dB (Av = 1) when RG is open: this is the minimum gain of all these ICs. For the 1512, gain is 6 dB (Av = 0.5) with RG open. To go from 60 dB to 0 dB gain, RG must span a large range: 10 ȍ to 10 kȍ for the 1510 and its equivalents. RG is typically a reverse log potentiometer (or set of switched resistors) to provide smooth rotational control of gain. In many applications, and, as shown in Fig. 12-57, a large value capacitor is placed in series with RG to limit the dc gain of the device, thus preventing shifts in output dc-offset with gain changes. For 60 dB of gain with the THAT1512, RG = 5 ȍ (6 : in the case of the INA163). Because of this, CG must be quite large, typically ranging from 1000 μF to 6800 μF to preserve low frequency response. Fortunately, CG does not have to support large voltages: 6.3 V is acceptable. Parts from all manufacturers exhibit excellent voltage noise performance of ~1 nV e Hz at high

C2 470 pF C3 47 pF

RG2 +In R2 1k

Ref V

U1 THAT 1510/1512

100 nF C9

–15

Figure 12-57. THAT1510/1512 Basic Application. Courtesy THAT Corporation.

Fig. 12-58 shows the THAT1512 used as a preamp capable of being used with phantom power. C 1 –C 3 provide RFI protection. R5 and R6 feed phantom power to the microphone. R9 terminates the microphone. C4 and C 5 block 48 Vdc phantom potential from the THAT1512. R3, R4, and D1–D4 provide current limiting and overvoltage protection from phantom power faults. R 1 and R 2 are made larger than previously shown to reduce the loading on C4 and C5. Many variations are possible on these basic circuits, including digital control of gain, dc servos to reduce or eliminate some of the ac-coupling needed, and exotic power supply arrangements that can produce response down to dc. For more information on possible configurations, see application notes published by Analog Devices, Texas Instruments, and THAT Corporation. (All available at their respective web sites: www.analog.com, www.ti.com, www.thatcorp.com.)

Tubes, Discrete Solid State Devices, and Integrated Circuits

353

+48 V +15 V C6

R6 –In

6k8 C1 470p

+In

C2 470p

C4 47u R9 2k7

100n

4R7

R5 6k8

C3 47p

C5 47u

D3 1N4004 D4 1N4004

D1 1N4004 D2 1N4004

4R7

R1 10k

In RG1

V+

Out Out

Ref RG2 V +In

U1 THAT1512 C9

R2 10k

100n +15

–15

Figure 12-58. THAT preamp circuit with phantom power. Courtesy THAT Corporation.

Modern IC microphone preamplifiers provide a simple building block with performance equaling discrete solutions without a costly input transformer. 12.3.6 Balanced Line Interfaces In professional audio, interconnections between devices frequently use balanced lines. These are especially important when analog audio signals are sent over long distances, where the ground references for the send and receive ends are different or where noise and interference may be picked up in the interconnection cables. Differences in signal ground potentials arise as a result of current flowing into power-line safety grounds. These currents, flowing through finite ground impedances between equipment, can produce up to several volts potential difference between the ground references within a single building. These currents, usually at the power line frequency and its harmonics, produce the all-too-familiar hum and buzz known to every sound engineer. Two other forms of interference, electrostatic and magnetic, also create difficulty. Cable shielding reduces electrostatic interference from fields, typically using braided copper, foil wrap, or both. Magnetic interference from fields is much harder to prevent via shielding. The impact of magnetic fields in signal cables is reduced by balanced cable construction using twisted pair cable. Balanced circuits benefit from the pair’s twist by ensuring that magnetic fields cut each conductor equally. This in turn ensures that the currents produced by these fields appear in common mode, wherein the voltages produced appear equally in both inputs. The balanced line approach comes out of telephony, in which voice communications are transmitted over

many miles of unshielded twisted pair cables with reasonable fidelity and freedom from hum and interference pickup. Two principles allow balanced lines to work. First, interference—whether magnetic or electrostatic—is induced equally in both wires in the twisted paired-conductor cable, and second, the circuits formed by the source and receiver, plus the two wires connecting them form a balanced bridge,32 Fig. 12-59. Interfering signals appear identically (in common-mode) at the two (+ and ) inputs, while the desired audio signal appears as a difference (the differential signal) between the two inputs. Driver

Rcm-

Rcm+

Signal (differential)

Vcm _

Rcm-

Rcm+

Receiver

Figure 12-59. Balanced bridge. Courtesy THAT Corporation.

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A common misconception in the design of balanced interfaces is that the audio signals must be transmitted as equal and opposite polarity on both lines. While this is desirable to maximize headroom in many situations, it is unnecessary to preserve fidelity and avoid noise pickup. It is enough if the bridge formed by the combination of the circuit’s two common-mode source impedances (not the signals) working against the two common-mode load impedances remains balanced in all circumstances. In telephony, and in early professional audio systems, transformers were used at both the inputs and outputs of audio gear to maintain bridge balance. Wellmade output transformers have closely matched common-mode source impedances and very high common-mode impedance. (Common-mode impedance is the equivalent impedance from one or both conductors to ground.) The floating connections of most transformers—whether used for inputs or outputs—naturally offer very large common-mode impedance. Both of these factors, matched source impedances for output transformers, and high commonmode impedance (to ground) for both input and output transformers, work together to maintain the balance of the source/load impedance bridge across a wide range of circumstances. In addition, transformers offer galvanic isolation, which is sometimes helpful when faced with particularly difficult grounding situations. On the other hand, as noted previously in the section on preamplifiers, transformers have drawbacks of high cost, limited bandwidth, distortion at high signal levels, and magnetic pickup. 12.3.6.1 Balanced Line Inputs Transformers were used in early balanced line input stages, particularly in the days before inexpensive op-amps made it attractive to replace them. The advent of inexpensive op-amps, especially compared to the cost of transformers, motivated the development of active transformerless inputs. As the state of the art in op-amps improved, transformer-coupled inputs were replaced by less expensive, high-performance active stages based on general-purpose parts like the Texas Instruments TL070 and TL080 series, the National Semiconductor LF351 series, and the Signetics NE5534. As with microphone preamplifiers, common-mode rejection is an important specification for line receiver inputs. The most common configuration for active balanced line input stages used in professional audio is the simple circuit shown in Fig. 12-60. To maintain high common-mode rejection (CMR), the four resistors used

must match very closely. To maintain a 90 dB CMR, for example, the resistor ratio R 1 /R 2 must match that of R 3 /R 4 within 0.005%. The requirement for precision-matched resistors to provide high CMR drove the development of specialized line receiver ICs. To maintain the high CMR potential of precision balanced line receivers, the interconnections between stages must be made through low-resistance connections, and the impedances in both lines of the circuit must be very nearly identical. A few ohms of contact resistance external to the line driver and receiver (due, for example, to oxidation or poor contact) or any imbalance in the driving circuit, can significantly reduce CMR by unbalancing the bridge circuit. The imbalance can be at the source, in the middle at a cable junction, or near the input of the receiving equipment. Although many balanced line receivers provide excellent CMR under ideal conditions, few provide the performance of a transformer under less-than-ideal real world circumstances. V cc In

Sense R2

V out R4

R3 In+

Ref V ee

Part no. THAT1240 THAT1243 THAT1246

Gain

R1 , R3

R2 , R4

0 dB –3 dB –6 dB

9 k7 10.5 k7 12 k7

9 k7 7.5 k7 6 k7

F i g u r e 1 2- 6 0 . 1 2 4 0 b a s i c c i r c u i t . C o u r t e s y T H A T Corporation.

12.3.6.2 Balanced Line Outputs Transformers were also used in early balanced output stages, for the same reasons as they are used in inputs. However, to drive 600 : loads, an output transformer must have more current capacity than an input transformer that supports the same voltage levels. This increased the cost of output transformers, requiring more copper and steel than input-side transformers and putting pressure on designers to find alternative outputs. Early active stages were either discrete or used discrete output transistors to boost the current available from

Tubes, Discrete Solid State Devices, and Integrated Circuits op-amps. The NE5534, with its capability to directly drive a 600 : load, made it possible to use op-amps without additional buffering as output stages. One desirable property of transformer-coupled output stages was that the output voltage was the same regardless of whether the output was connected differentially or in single-ended fashion. While professional audio gear has traditionally used balanced input stages, sound engineers commonly must interface to consumer and semi-pro gear that use single-ended input connections referenced to ground. Transformers behave just as well when one terminal of their output winding is shorted to the ground of a subsequent single-ended input stage. On the other hand, an active-balanced output stage that provides equal and opposite drive to the positive and negative outputs will likely have trouble if one output is shorted to ground. This led to the development of a cross-coupled topology by Thomas Hay of MCI that allowed an active balanced output stage to mimic this property of transformers.33 When loaded equally by reasonable impedances (e.g., 600 : or more) Hay’s circuit delivers substantially equal—and opposite-polarity voltage signals at either output. However, because feedback is taken differentially, when one leg is shorted to ground, the feedback loop automatically produces twice the voltage at the opposing output terminal. This mimics the behavior of a transformer in the same situation. While very clever, this circuit has at least two drawbacks. First, its resistors must be matched very precisely. A tolerance of 0.1% (or better) is often needed to ensure stability, minimize sensitivity to output loading, and maintain close matching of the voltages at either output. (Though, as noted earlier, this last requirement is unnecessary for good performance.) The second drawback is that the power supply voltage available to the two amplifiers limits the voltage swing at each output. When loaded differentially, the output stage can provide twice the voltage swing than it can when driving a single-ended load. But this means that headroom is reduced 6 dB with single-ended loads. One way to ensure the precise matching required by Hay’s circuit is to use laser-trimmed thin-film resistors in an integrated circuit. SSM was the first to do just that when they introduced the SSM2142, a balanced line output driver with a cross-coupled topology. 12.3.6.3 Integrated Circuits for Balanced Line Interfaces Instrumentation amplifier inputs have similar requirements to those of an audio line receiver. The INA105, originally produced by Burr Brown and now Texas

355

Instruments, was an early instrumentation amplifier that featured laser-trimmed resistors to provide 86 dB common-mode rejection. Although its application in professional audio was limited due to the performance of its internal op-amps, the INA105 served as the basis for the modern audio-balanced line receiver. In 1989, the SSM Audio Products Division of Precision Monolithics introduced the SSM2141 balanced line receiver and companion SSM2142 line driver. The SSM2141 was offered in the same pinout as the INA105 but provided low noise and a slew rate of almost 10 V/μs. With a typical CMR of 90 dB, the pro-audio industry finally had a low-cost, high-performance replacement for the line input transformer. The SSM2142 line driver, with its cross-coupled outputs, became a low-cost replacement for the output transformer. Both parts have been quite successful. Today, Analog Devices (which acquired Precision Monolithics) makes the SSM2141 line receiver and the SSM2142 line driver. The SSM2143 line receiver, designed for 6 dB attenuation, was introduced later to offer increased input headroom. It also provides overall unity gain operation when used with an SSM2142 line driver, which has 6 dB of gain. The Burr Brown division of Texas Instruments now produces a similar family of balanced line drivers and receivers, including dual units. The INA134 audio differential line receiver is a second source to the SSM2141. The INA137 is similar to the SSM2143 and also permits gains of ±6 dB. Both devices owe their pinouts to the original INA105. Dual versions of both parts are available as the INA2134 and 2137. TI also makes cross-coupled line drivers known as the DRV134 and DRV135. THAT Corporation also makes balanced line drivers and receivers. THAT’s 1240 series single and 1280 series dual balanced line receivers use laser-trimmed resistors to provide high common rejection in the familiar SSM2141 (single) and INA2134 (dual) pinouts. For lower cost applications, THAT offers the 1250- and 1290-series single and dual line receivers. These parts eliminate laser trimming, which sacrifices CMR to reduce cost. Notably, THAT offers both dual and single line receivers in the unique configuration of ±3 dB gain, which can optimize dynamic range for many common applications. THAT Corporation also offers a unique line receiver, the THAT1200 series, based on technology licensed from William E. Whitlock of Jensen Transformers, Inc. (U.S. Patent 5,568,561).34 This design, dubbed InGenius (a trademark of THAT Corporation), bootstraps the common-mode input impedance to raise it into the

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megohm range of transformers. This overcomes the loss of common-mode rejection when the impedances feeding the line receiver are slightly unbalanced and permits transformer like operation. The InGenius circuit will be discussed in a following section. THAT also offers the THAT1646 balanced line driver, which has identical pinout to the SSM2142 and DRV134/135. THAT’s 1606 balanced line driver is unique among these parts in that it provides not only a differential output, but also a differential input— enabling a more direct connection to digital to analog converters. The THAT1646 and 1606 use a unique output topology unlike conventional cross-coupled outputs which THAT calls “OutSmarts” (another trademark). OutSmarts is based on U.S. Patent 4,979,218 issued to Chris Strahm, then of Audio Teknology Incorporated.35 Conventional cross-coupled outputs lose common-mode feedback when one output is shorted to ground to accommodate a single-ended load. This allows large signal currents to flow into ground, increasing crosstalk and distortion. Strahm’s circuit avoids this by using an additional feedback loop to provide current feedback. Application circuits for the THAT1646 will be described in the section “Balanced Line Outputs.”

–In

In– R 1

U1 1240 9k R2

5 Sense 6

Output

Vout +In

In+ R3

9k VEE 4

1 Ref

Figure 12-61. THAT1240 with 0 dB gain. Courtesy THAT Corporation.

attenuation. These parts accommodate up to +27 dBu inputs without clipping their outputs when running from bipolar 15 V supplies. The THAT1243, and THAT’s other ±3 dB parts (the 1253, 1283, and 1293) are unique with their 0.707 attenuation. This permits a line receiver that accommodates +24 dBu inputs but avoids additional attenuation that increases noise. A 3 dB line receiver is shown in Fig. 12-62.

–In

10.5k

7 VCC

U1 1243 7.5k

5 Sense

In–

12.3.6.4 Balanced Line Input Application Circuits Conventional balanced line receivers from Analog Devices, Texas Instruments, and THAT Corporation are substantially equivalent to the THAT1240 circuit shown in Fig. 12-61. Some variations exist in the values of R 1 –R 4 from one manufacturer to the other that will influence input impedance and noise. The ratio of R1/R3 to R2/R4 establishes the gain with R1 = R3 and R2 = R4. Vout is normally connected to the sense input resistor with the reference pin grounded. Line receivers usually operate at either unity gain (SSM2141, INA134, THAT1240, or THAT1250) or in attenuation (SSM2143, INA137, THAT1243, or THAT1246, etc.). When a perfectly balanced signal (with each input line swinging ½ the differential voltage) is converted from differential to single-ended by a unity gain receiver, the output must swing twice the voltage of either input line for a net voltage gain of +6 dB. With only +21 dBu output voltage available from a line receiver powered by bipolar 15 V supplies, additional attenuation is often needed to provide headroom to accommodate pro audio signal levels of +24 dBu or more. The ratios R1/R2 and R3/R4 are 2:1 in the SSM2143, INA137, and THAT1246 to provide 6 dB

7 VCC

Output

Vout +In

10.5k

7.5k

1 Ref

In+ VEE 4

Figure 12-62. THAT1243 with 3 dB attenuation. Courtesy THAT Corporation.

The ±6 dB parts from all three manufacturers (and the ±3 dB parts from THAT) may be configured for gain instead of attenuation. To accomplish this, the reference and sense pins are used as inputs with the In– pin connected to Vout and the In+ pin connected to ground. A line receiver configured for 6 dB gain is shown in Fig. 12-63. Balanced line receivers may also be used to provide sum-difference networks for mid-side (M/S or M-S) encoding/decoding as well as general-purpose applications requiring precise difference amplifiers. Such applications take advantage of the precise matching of resistor ratios possible via monolithic, laser-trimmed

Tubes, Discrete Solid State Devices, and Integrated Circuits

357

Common Mode Rejection versus Imbalance

–In

U1 1246

7 VCC

5 Sense

In–

Output

Vout

+In 12k

3 In+

1 Ref

VEE 4

Figure 12-63. THAT 1246 with 6 dB gain. Courtesy THAT Corporation.

resistors. In fact, while these parts are usually promoted as input stages, they have applications to many circuits where precise resistor ratios are required. The typical 90 dB common-mode rejection advertised by many of these manufacturers requires ratio matching to within 0.005%. Any resistance external to the line receiver input appears in series with the highly matched internal resistors. A basic line receiver connected to an imbalanced circuit is shown in Fig. 12-64. Even a slight imbalance, one as low as 10 from connector oxidation or poor contact, can degrade common-mode rejection. Fig. 12-65 compares the reduction in CMR for low common-mode impedance line receivers versus the THAT1200 series or a transformer. Rimbalance

Vin– R1

– Vdiff + 2 + Vdiff – 2

–

Vout

+ R3

Vin+

Figure 12-64. Balanced circuit with imbalance. Courtesy THAT Corporation.

The degradation of common-mode rejection from impedance imbalance comes from the relatively low-impedance load of simple line receivers interacting with external impedance imbalances. Since unwanted hum and noise appear in common-mode (as the same signal in both inputs), common-mode loading by common-mode input impedance is often a significant source of error. (The differential input impedance is the load seen by differential signals; the common-mode input impedances is the load seen by common-mode

Common mode rejection ratio–dB

12k

100 90 InGenius Line Receiver

80 70 60

Conventional Line Receiver

50 40 30 20

100 200 300 400 500 600 Differential source resistance error–Ohms

Figure 12-65. CMR imbalance versus source. Courtesy THAT Corporation.

signals.) To reduce the effect of impedance imbalance, the common-mode input impedance, but not the differential impedance, must be made very high. 12.3.6.5 Balanced Line Receivers with the Common-Mode Performance of a Transformer The transformer input stage has one major advantage over most active input stages: its common-mode input impedance is extremely high regardless of its differential input impedance. This is because transformers offer floating connections without any connection to ground. Active stages, especially those made with the simple SSM2141-type IC have common-mode input impedances of approximately the same value as their differential input impedance. (Note that for simple differential stages such as these, the common-mode and differential input impedances are not always the same.) Op-amp input bias current considerations generally make it difficult to use very high impedances for these simple stages. A bigger problem is that the noise of these stages increases with the square root of the impedances chosen, so large input impedances inevitably cause higher noise. Noise and op-amp requirements led designers to choose relatively low impedances (10 k~25 k:). Unfortunately, this means these stages have relatively low common-mode input impedance as well (20 k~50 k:). This interacts with the common-mode output impedance (also relative to ground) of the driving stage, and added cable or connector resistance. If the driver, cable, or connectors provide an unequal, nonzero common-mode output impedance, the input stage loading will upset the natural balance of any

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common-mode signal, converting it from common-mode to differential. No amount of precision i n t h e i n p u t s t a g e ’s r e s i s t o r s w i l l r e j e c t t h i s common-mode-turned-to-differential signal. This can completely spoil the apparently fine performance available from the precisely matched resistors in simple input stages. An instrumentation amplifier, Fig. 12-66, may be used to increase common-mode input impedance. Input resistors Ri1 and Ri2 must be present to supply a bias current return path for buffer amplifiers OA1 and OA2. Ri1 and Ri2 can be made large—in the M range—to minimize the effect of impedance imbalance. While it is possible to use this technique to make line receivers with very high common-mode input impedances, doing so requires specialized op-amps with bias-current compensation or FET input stages. In addition, this requires two more op-amps in addition to the basic differential stage (OA3). In– Ri1

+ OA1 –

– OA2 +

In+

– OA3 + R4

Out

Ri2

Figure 12-66. Instrumentation amplifier. Courtesy THAT Corporation.

With additional circuitry, even higher performance can be obtained by modifying the basic instrumentation amplifier circuit. Bill Whitlock of Jensen Transformers, Inc.developed and patented (U.S. Patent 5,568,561) a method of applying bootstrapping to the instrumentation amplifier in order to further raise common-mode input impedance.34 THAT Corporation incorporated this technology in its InGenius series of input stage ICs. 12.3.6.6 InGenius High Common-Mode Rejection Line Receiver ICs Fig. 12-67 shows the general principle behind ac bootstrapping in a single-ended connection. By feeding the ac component of the input into the junction of Ra and R b , the effective value of R a (at ac) can be made to appear quite large. The dc value of the input impedance (neglecting Rs being in parallel) is Ra + Rb. Because of bootstrapping, Ra and Rb can be made relatively small

values to provide op-amp bias current, but the ac load on Rs (Zin ) can be made to appear to be extremely large relative to the actual value of Ra. Vin

Zin

[(R5 + R7)||(R8 + R9)] Cb A [R5]

G=1

Figure 12-67. Single ended bootstrap. Courtesy THAT Corporation.

A circuit diagram of an InGenius balanced line receiver using the THAT1200 is shown in Fig. 12-68. (All the op-amps and resistors are internal to the IC.) R5 –R9 provides dc bias to internal op-amps OA1 and OA2. Op-amp OA4, along with R10 and R11 extract the common-mode component at the input and feed the ac common-mode component back through Cb to the junction of R7 and R8. Because of this positive feedback, the effective values of R7 and R 8 —at ac—are multiplied into the M range. In its data sheet for the 1200 series ICs, THAT cautions that Cb should be at least 10 μf to maintain common-mode input impedance (ZinCM) of at least 1 M: at 50 Hz. Larger capacitors can increase ZinCM at low power-line frequencies up to the IC’s practical limit of ~10 M: . This limitation is due to the precision of the gain of the internal amplifiers.

In–

R6 R7

OA1 +1 R10 24K

OA4

OA3 – +

+1 R8 In+

R11 24K +1 OA2

R4 R5

Vout

REF

24K CM Out

CM In Cb

Figure 12-68. Balanced line receiver. Courtesy THAT Corporation.

The outputs of OA1 and OA2 contain replicas of the positive and negative input signals. These are converted to single-ended form by a precision differential ampli-

Tubes, Discrete Solid State Devices, and Integrated Circuits fier OA3 and laser-trimmed resistors R1–R4. Because OA1 and OA2 isolate the differential amplifier, and the positive common-mode feedback ensures very high common-mode input impedance, a 1200-series input stage provides 90 dB CMR even with high levels of imbalance. It took Bill Whitlock and Jensen Transformers, Inc. to provide an active input as good as a transformer operating under conditions likely to be found in the real world. A basic application circuit using the THAT1200 series parts is shown in Fig. 12-69.

Vin 50 7 +Out force

+Out sense 10 k7

–Out force

Cb + Vcc

In–

In+

In–

–Out sense

50 7

All resistors 30 k7 unless otherwise indicated

220 uF

359

10 k7

Gnd

C3 100 nF

Figure 12-70. SSM2142 cross coupled output. Courtesy Analog Devices, Inc.

7 CM U1 Out V cc 6 5 CM Out In 120X Vee Ref C4 3 100 nF 4 In+ 1

+15 V +15 V

Out Vin 4

SSM 3 2142

Vee

Figure 12-69. InGenius basic application. Courtesy THAT Corporation.

12.3.6.7 Balanced Line Drivers The Analog Devices SSM2142 and Texas Instruments DRV series balanced line drivers use a cross-coupled method to emulate a transformer’s floating connection and provide constant level with both single-ended (grounded) terminations and fully balanced loads. A block diagram of a cross-coupled line driver is shown in Fig. 12-70. The force and sense lines are normally connected to each output either directly or through small electrolytic coupling capacitors. A typical application of the SSM2142 driving an SSM2141 (or SSM2143) line receiver is provided in Fig. 12-71. If one output of the cross-coupled line driver outputs is shorted to ground in order to provide a single-ended termination, the full short-circuit current of the device will flow into ground. Although this is not harmful to the device, and is in fact a recommended practice, large clipped signal currents will flow into ground, which can produce crosstalk within the product using the stage, as well as in the output signal line itself.

Vout SSM 5 6 2141/ 2 2143 1

8 1

Shielded twisted-pair cable

–15 V

Figure 12-71. SSM2142 driving a SSM2141 line receiver. Courtesy Analog Devices, Inc.

THAT Corporation licensed a patented technology developed by Chris Strahm of Audio Teknology Incorporated. U.S. Patent 4,979,218, issued in December 1990, describes a balanced line driver that emulates a floating transformer output by providing a current-feedback system where the current from each output is equal and out of phase to the opposing output.35 THAT trademarked this technology as OutSmarts and introduced its THAT1646 line driver having identical pinout and functionality to the SSM2142. THAT also offers a version of the 1646 with differential inputs known as the THAT1606. Fig. 12-72 is a simplified block diagram of the THAT1646. The THAT1646 OutSmarts internal circuitry differs from other manufacturer’s offerings. Outputs Dout and Dout+ supply current through 25 : build-out resistors. Feedback from both sides of these resistors is returned into two internal common-mode feedback paths. The driven side of the build-out resistors are fed back into the common-mode C in input while the load side of the build-out resistors, through the sense– and sense+ pins,

360

Chapter 12

Vcc

THAT 1646 10k

Vcc

Out–

CExt

Sns– 5k In+

Gnd

10k Din+ DoutCin+ Cin– A D & AC Din– Dout+ 10k

10k

10p

20k

10k

20k CExt

10k

3 Sns+

Vee

C4 100n

Out+

C5 100n

Vcc In

7 Sns+

10u NP 8

Out+ Gnd Sns- Out– 1 Vee 2 U1 THAT1646 5 C2 Vee

XLR (M) 1

2 3

10u NP

Figure 12-72. THAT 1646 block diagram. Courtesy THAT Corporation.

Figure 12-74. THAT 1646 CMR offset reduction circuit. Courtesy THAT Corporation.

provide feedback into the Cin+ input. A current feedback bridge circuit allows the 1646 to drive one output shorted to ground to allow a single-ended load to be connected. The output short increases gain by 6 dB, similarly to conventional cross-coupled topologies. However, it does so without loss of the common-mode feedback loop. The resulting current feedback prevents large, clipped signal currents flowing into ground. This reduces the crosstalk and distortion produced by these currents.

THAT’s 1606 version of OutSmarts provides a differential input for easier connection to a digital-to-analog converter’s output. A typical application of the THAT1606 is shown in Fig. 12-75. Another advantage to the 1606 is that it requires only a single low-value capacitor (typically a film type) versus the two larger capacitors required by the THAT1646, SSM2142, or DRV134.

A typical application circuit for the THAT1646 is shown in Fig. 12-73. Vcc C4 100n In

7 Vcc Sns+ In

XLR (M) 8

Out+ 3 Gnd Sns- Out– 1 Vee 2 U1 THAT1646 5

Active balanced line drivers and receivers offer numerous advantages over transformers providing lower cost, weight, and distortion, along with greater bandwidth and freedom from magnetic pickup. When used properly, active devices perform as well as, and in many ways better than, the transformers they replace. With careful selection of modernIC building blocks from several IC makers, excellent performance is easy to achieve.

C5 100n Vee

Figure 12-73. THAT 1646 application. Courtesy THAT Corporation.

To reduce the amount of common-mode dc offset, the circuit in Fig. 12-74 is recommended. Capacitors C1 and C 2 , outside the primary signal path, minimize common-mode dc gain, which reduces common-mode output offset voltage and the effect of OutSmarts at low frequencies. Similar capacitors are used in the ADI and TI parts to the same effect, although OutSmarts’ current feedback does not apply.

12.3.7 Digital Integrated Circuits Digital ICs produce an output of either 0 or 1. With digital circuits, when the input reaches a preset level, the output switches polarity. This makes digital circuitry relatively immune to noise. Bipolar technology is characterized by very fast propagation time and high power consumption, while MOS technology has relatively slow propagation times, low power consumption, and high circuit density. Fig. 12-76 shows typical circuits and characteristics of the major bipolar logic families. Table 12-4 gives some of the terminology common to digital circuitry and digital ICs.

Tubes, Discrete Solid State Devices, and Integrated Circuits

361

Vcc C1

C4 100n In+

In–

100n

4 Vcc 14 In+ Cap1 6 In– Out+ 5 Gnd Cap2Out– 3 Vee 13 U1 11 THAT1606 7

C5 100n

D4 1N4004

1M0 D3 1N4004 D5 1N4004 D6 1N4004

XLR (M)

1 C8 100p

Ferrite Bead L2 Ferrite Bead

2 3

C3 100p

Vee

Figure 12-75. THAT 1606 application. Courtesy THAT Corporation.

Table 12-4. Digital Circuit Terminology Adder

Switching circuits that generate sum and carry bits.

Address

A code that designates the location of information and instructions.

AND

A Boolean logic operation that performs multiplication. All inputs must be true for the output to be true.

Asynchronous

A free-running switching network that triggers successive instructions.

Bit

Abbreviation for binary digit; a unit of binary information.

Buffer

A noninverting circuit used to handle fan-out or convert input and output levels.

Byte

A fixed-length binary-bit pattern (word).

Clear

To restore a device to its standard state.

Clock

A pulse generator used to control timing of switching and memory circuits.

Clock rate

The frequency (speed) at which the clock operates. This is normally the major speed of the computer.

Counter

A device capable of changing states in a specified sequence or number of input signals.

Counter, binary

A single input flip-flop. Whenever a pulse appears at the input, the flip-flop changes state (called a T flip-flop).

Counter, ring

A loop or circuit of interconnected flip-flops connected so that only one is on at any given time. As input signals are received, the position of the on state moves in sequence from one flip-flop to another around the loop.

Fan-in

The number of inputs available on a gate.

Fan-out

The number of gates that a given gate can drive. The term is applicable only within a given logic family.

Flip-flop

A circuit having two stable states and the ability to change from one state to the other on application of a signal in a specified manner.

Flip-flop, D

D stands for delay. A flip-flop whose output is a function of the input that appeared one pulse earlier; that is, if a 1 appears at its input, the output will be a 1 a pulse later.

Flip-flop, JK

A flip-flop having two inputs designated J and K. At the application of a clock pulse, a 1 on the J input will set the flip-flop to the 1 or on state; a 1 on the K input will reset it to the 0 or off state; and 1s simultaneously on both inputs will cause it to change state regardless of the state it had been in.

Flip-flop, RS

A flip-flop having two inputs designated R and S. At the application of a clock pulse, a 1 on the S input will set the flip-flop to the 1 or on state, and a 1 on the R input will reset it to the 0 or off state. It is assumed that 1s will never appear simultaneously at both inputs.

Flip-flop, R, S, T

A flip-flop having three inputs, R, S, and T. The R and S inputs produce states as described for the RS flip-flop above; the T input causes the flip-flop to change states.

Flip-flop, T

A flip-flop having only one input. A pulse appearing on the input will cause the flip-flop to change states.

Gate

A circuit having two or more inputs and one output, the output depending on the combination of logic signals at the inputs. There are four gates: AND, OR, NAND, NOR. The definitions below assume positive logic is used.

Gate, AND

All inputs must have 1-state signals to produce a 0-state output.

Gate, NAND

All inputs must have 1-state signals to produce a 1-state output.

Gate, NOR

Any one or more inputs having a 1-state signal will yield a 0-state output.

Gate, OR

Any one or more inputs having a 1-state signal is sufficient to produce a 1-state output.

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Table 12-4. Digital Circuit Terminology (Continued) Inverter

The output is always in the opposite logic state as the input. Also called a NOT circuit.

Memory

A storage device into which information can be inserted and held for use at a later time.

NAND gate (D = ABC for positive inputs)

The simultaneous presence of all inputs in the positive state generates an inverted output.

Negative logic

The more negative voltage (or current) level represents the 1-state; the less negative level represents the 0-state.

NOR gate The presence of one or more positive inputs generates an inverted output. (D = A + B + C for positive inputs) NOT

A boolean logic operator indicating negation. A variable designated NOT will be the opposite of its AND or OR function. A switching function for only one variable.

A boolean operator analogous to addition (except that two truths will only add up to one truth). Of two variables, only one need be true for the output to be true.

Parallel operator

Pertaining to the manipulation of information within computer circuits in which the digits of a word are transmitted simultaneously on separate lines. It is faster than serial operation but requires more equipment.

Positive logic

The more positive voltage (or current) level represents the 1-state; the less positive level represents the 0-state.

Propagation delay

A measure of the time required for a change in logic level to spread through a chain of circuit elements.

Pulse

A change of voltage or current of some finite duration and magnitude. The duration is called the pulse width or pulse length; the magnitude of the change is called the pulse amplitude or pulse height.

A device used to store a certain number of digits in the computer circuits, often one word. Certain registers may also include provisions for shifting, circulating, or other operations.

Rise time

A measure of the time required for a circuit to change its output from a low level (zero) to a high level (one).

Serial operation

The handling of information within computer circuits in which the digits of a word are transmitted one at a time along a single line. Though slower than parallel operation, its circuits are much less complex.

Shift register

An element in the digital family that uses flip-flops to perform a displacement or movement of a set of digits one or more places to the right or left. If the digits are those of a numerical expression, a shift may be the equivalent of multiplying the number by a power of the base.

Skew

Time delay or offset between any two signals.

Synchronous timing Operation of a switching network by a clock pulse generator. Slower and more critical than asynchronous timing but requires fewer and simpler circuits. Word

An assemblage of bits considered as an entity in a computer.

Tubes, Discrete Solid State Devices, and Integrated Circuits

Symbol

Circuit Diagram

Speed*

Power*

Fan-Out*

Noise Immunity*

Trade Name

363

Remarks

+V DCTL

Medium

Low

Series 53

Variations in input characteristics result in base current “hogging” problems. Proper operation not always guaranteed. More susceptibile to noise because of low operating and signal voltages.

Low

RTL

Very similar to DCTL. Resistors resolve current “hogging” problem and reduce power dissipation. However,operating speed is reduced.

Low

Series 51

Though capacitors can increase speed capability, noise immunity is affected by capacitive coupling of noise signals.

Medium

Medium Medium to high

930 DTL

Use of pull-up resistor and charge-control technique improves speed capabilities. Many variations of this circuit exist, each having specific advantages.

High

Medium

Medium Medium to high

SUHL Very similar to DTL. Has lower parasitic Series 54/74 capacity at inputs. With the many existing variations, this has become very

High

MECL ECCSL

High

Medium Medium CTML

C1 High

Low

High

+V RTL

+V RCTI

DTL

TTL

+V CML (ECL)

Medium to high

Similar to a differential amplifier, the reference voltage sets the threshold voltage. High-speed, high-fan-out operation is possible with associated high power dissipation. Also known as emitter-coupled logic (ECL).

+V CTL

More difficult manufacturing process results in compromises of active device characteristics and higher cost.

+V I2L

Medium

I 2L

*Low = Medium = High =

Provides smallest and most dense bipolar gate. Simple manufacturing process and higher component packing density than the MOS process. Also known as merged-transistor logic (MTL).

500 mV

Figure 12-76. Typical digital circuits and their characteristics for the major logic families. (Adapted from Reference 4.)

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Chapter 12

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

Gilbert, “A precise Four Quadrant Multiplier with Subnanosecond Response,” IEEE J. of Solid State Circuits, Vol. SC-3, no. 4, December 1968. Blackmer, “RMS Circuits with Bipolar Logarithmic Converter,” United States Patent 3,681,618, August 1, 1972. Blackmer, “Multiplier Circuits,” United States Patent 3,714,462, January 30, 1973. “Solid State Music Dual Linear-Antilog Voltage Controlled Amplifier,” SSM2000 Data Sheet, September, 1976. Frey, “An Integrated Generalized Voltage Controlled Building Block”, J. Audio Eng Soc., Preprint No. 2403, November 1986. Curtis Electro Music Website, http://curtiselectromusic.com/Doug_Curtis.html. Baskind, Rubens et al, “The Design and Integration of A High Performance Voltage Controlled Attenuator,” J. Audio Eng Soc., Preprint No. 1555, November 1979. Welland, “Compensation for VCA Op-Amp Errors,” United States Patent 4,434,380, February 28,1984 Analog Devices, “SSM2018T Trimless Voltage Controlled Amplifiers,” SSM2018T Datasheet, July 2002. Blackmer, “Multiplier Circuits,” United States Patent 3,714,462, January 30, 1973. Frey, “An Integrated Generalized Voltage Controlled Building Block,” J. Audio Eng Soc., Preprint No. 2403, November 1986. Frey, “Voltage-controlled element,” United States Patent 4,471,320, September 11, 1984. Frey, “Monolithic Voltage-Controlled Element,” United States Patent 4,560,947, December 24, 1985. Rubens, and Baskind, “Voltage Controlled Attenuator,” United States Patent 4,155,047, May 15, 1979. “Solid State Music-Dual Linear-Antilog Voltage Controlled Amplifier,” SSM2000 Data Sheet, September 1976. IEEE Std 152-1991-IEEE Standard for Audio Program Level Measurement, June 22, 1992. Blackmer, “RMS Circuits with Bipolar Logarithmic Converter,” United States patent 3,681,618, August 1, 1972. Chapel and Gurol, “Thermally Isolated Monolithic Semiconductor Die,” United States Patent 4,346,291, August 24, 1982. Analog Devices, AD636 Datasheet. Adams, “Networks for the Log Domain,” United States Patent 4,430,626, February 7, 1984. THAT Corporation, “Adaptive Attack and Release Rates Using THAT Corporation RMS Detectors,” Design Note DN-114, 2000. Jensen, “JE-990 Discrete Operational Amplifier,” J. Audio Eng Soc., January/February 1980. Jung, IC Op-Amp Cookbook, No. 20969, Howard W. Sams, 1974. www.jensentransformers.com, May 2008. Hebert and Thomas, “The 48 Volt Phantom Menace,” Audio Engineering Society Convention Paper 5335, May 2001. Demrow, “Evolution From Operational Amplifier To Data Amplifier,” Analog Devices, 1968. Wurcer, “A Programmable Instrumentation Amplifier for 12b Resolution Systems,” International Solid State Circuits Conference, February 1982. See also Analog Devices, Analog Dialog, Vol. 30 No. 2, 1996. Harrison Systems, PC1041 Microphone Preamp Schematic, 1978. Cohen, “Double Balanced Microphone Amplifier,” Audio Engineering Society Preprint 2106, September 1984. Solid State Music, SSM2011 Datasheet, 1982. Bowers, “An Ultra-Low-Noise Monolithic Microphone Preamplifier,” Audio Engineering Society Preprint 2495, 1987. Whitlock, “A New Balanced Audio Input Circuit For Maximum Common-Mode Rejection In Real-World Environments,” www.jensen-transformers.com. 1996. Hay, “Differential Technology In Recording Consoles And The Impact Of Transformerless Circuitry On Grounding Technique,” Audio Engineering Society Preprint 1723, October 1980. Whitlock, “Differential Line Receiver With Common-Mode Bootstrapping,” US patent 5,568,561, October 22, 1996. Strahm, “Balanced Line Output Circuit,” United States Patent 4,979,218, December, 18, 1990.

Chapter

Heatsinks and Relays by Glen Ballou and Henry Villaume 13.1 Heatsinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 13.1.1 Thermal Management of Today’s Audio Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 13.1.1.1 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 13.1.1.2 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 13.1.1.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 13.1.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 13.1.2 New Technologies to Make Things Fit More Easily. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 13.1.3 How Heatsinks Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 13.1.3.1 Thermal Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 13.1.3.2 Heatsink Materials and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 13.2 Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 13.2.1 Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 13.2.2 Contact Characteristics6,7,8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 13.2.3 Relay Loads8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 13.2.3.1 The Effects of Various Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 13.2.4 Electromechanical Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 13.2.4.1 Dc Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 13.2.4.2 Ac Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 13.2.5 Reed Relays6,7,8,11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 13.2.5.1 Contact Resistance and Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 13.2.5.2 Magnetic Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 13.2.5.3 Environmental Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 13.2.5.4 Dry Reed Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 13.2.5.5 Mercury-Wetted Contact Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 13.2.5.6 RF Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 13.2.5.7 Dry Reed Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 13.2.6 Solid-State Relays9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 13.2.6.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 13.2.6.2 Disadvantages and Protection4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 13.2.6.3 High-Peak-Transient-Voltage Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 13.2.6.4 Low Load Current Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 13.2.6.5 Optically Coupled Solid-State Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 13.2.6.6 Transformer-Coupled Solid-State Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 13.2.6.7 Direct-Coupled Solid-State Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 13.2.6.8 Solid-State Time-Delay Relays10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

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Heatsinks and Relays 13.1 Heatsinks 13.1.1 Thermal Management of Today’s Audio Systems By Henry Villaume, Villaume Associates, LLC Today’s audio systems, like all electronic systems are being powered by smaller devices, packaged in smaller systems that are generating more heat. We need to increase our level of understanding on all of the latest techniques for the management of this added heat in as effective a means as possible. Let’s first start with the understanding of the three methods of heat transfer— specifically, convection, conduction, and radiation as all three methods of heat transfer contribute to the complete thermal management provided by the heatsinks installed in an audio system. 13.1.1.1 Convection Convection is the transfer of heat from a solid surface to the surrounding gas, which is always air in the case of a typical audio system. This method of heat transfer drives the amount of required fin surface area that is accessible to the surrounding air so that it may heat up the surrounding air, allow it to move away, and make room for the process to repeat itself. This process can be greatly accelerated with the use of a fan to provide more energy to the moving of the air than just the natural buoyant force of the heated air. Natural convection is when there is no external fan and the heat transfer occurs with very low air flow rates, typically as low as 35 linear feet per minute (lfm) for obstructed natural convection to 75 lfm for optimum unobstructed vertical natural convection. Natural convection is never zero air flow rate because without air movement there would be no heat transfer. Think of the closed cell plastic foam insulation. It works as an insulator because the closed cell prevents the air from moving away. Forced convection is when a system fan imparts a velocity to the air surrounding the heatsink fins. The fan may be physically attached to the convective fin surface area of the heatsink to increase the air velocity over the fin surfaces. There is impingement flow—fan blows down from on top of the fins—and through flow—fan blows from the side across the fin set. Forced convection thermal systems are most generally significantly smaller (50% or more) than their natural convection equivalents. The penalties for the

367

smaller size are the added power to operate the fan, an added failure mechanism, the added cost, and the noise from the fan. Fan noise is probably the most important consideration when applying them in audio systems.

13.1.1.2 Conduction Conduction is the transfer of heat from one solid to the next adjacent solid. The amount and thermal gradient of heat transfer are dependent on the surface finishes —flatness and roughness—and the interfacial pressure generated by the attachment system. This mechanically generated force is accomplished by screws, springs, snap assemblies, etc. The thermal effectiveness of a conductive interface is measured by the resultant temperature gradient in °C. This may be calculated from the interface thermal resistance at the mounted pressure times the watts of energy moving across the joint divided by the cross-sectional area. These temperature gradients are most significant for high wattage components in small packages—divisors less than 1.0 are, in actual effect, multipliers. Good thermal solutions have a ttac hme nt sy ste ms t hat ge nerat e pressu re s of 25–50 psi. Table 13-1 compares the thermal performance of most of the common interface material groups with a dry joint—this makes amply clear why it is never acceptable to specify or default through design inaction to a dry joint. Table 13-1. Thermal Performance of Common Interface Materials Interface Material Thermal Group Performance Range in °C in²/W Dry Mating Surfaces Gap Fillers

3.0-12.0

Electrically Insulating High Performance Pads Phase Change Pads

0.2- 1.5

Low Performance Grease High Performance Grease

0.4-4.0

0.09-0.35 0.02-0.14 0.04-0.16 0.009-0.04

Comments

Too much uncertainty to use. Too big a thermal gradient Minimize thickness required Spring mechanical load Maximize mechanical loads Minimize thickness Maximize mechanical loads Must follow application method Spring mechanical load Screen apply Spring mechanical load Must Screen apply Spring mechanical load Best at high loads(> 50 psi)

368

Chapter 13

The primary heat transfer driving force is the temperature difference between Tmaxcase and Tmaxambient modified by the conductive delta T losses in the interface and any extraordinary hot spot offsets and spreading losses. If heatsinks are mounted over spread hot spots these last conductive losses are not sufficiently large to consider. They really only become significant when considering very unusual arrangements—high-watt density loads such as typical LEDs.

the heat transfer without exceeding the application temperature limits.

13.1.1.3 Radiation

The range of technologies, materials, and fabrication processes available to the thermal designer today is quite impressive. The primary goal when employing these advanced technologies, materials, and fabrication processes is to increase the effective density of the of the resultant heat transfer system. Technically, we are increasing the volumetric efficiency of the thermal solution proposed for a given application. In “man speak” the required heatsink gets much smaller in size and therefore fits more easily into the ever-shrinking product envelope. A smaller heatsink has a decreased conductive thermal spreading resistance and therefore a smaller conductive temperature gradient. In this section we are going to assume that we have a convective solution defined for a baseline heatsink. The baseline heatsink is fabricated from an extruded aluminum alloy (6063-T5). The following paragraphs will describe a technology, material or fabrication process and give a volume ratio or range of volume ratios that can be applied to the existing solution to quickly see the benefit of applying this technology, material, or fabrication process to the audio application at hand. Ratios that are less than 1.00 are indicating a reduction in heatsink volume.

Radiation is the third and least important method of heat transfer for audio system heatsinks. Radiation has a maximum 20–25% impact in natural convection applications with a negligible impact after 200 lfm applications. Radiation is a function of the fourth power of the absolute temperature difference between the hot side and surrounding cooler surfaces that look at each other and their respective emissivities. In the real world in which we live, these are not significant enough to suggest a lot of effort to understand and optimize. Aluminum extruded heatsinks were typically made black in an anodizing process at a significant cost to get an emissivity of 0.95 (dimensionless). The typical aluminum surface forms an oxide film in less than a second after machining with an emissivity of about 0.30–0.40. Nominally, almost half the benefit will come free so that our advice is “Leave the radiation effects alone.” What you get beneficially you were going to largely get anyway, free from Mother Nature. In review, heatsinks use all three methods of heat transfer to produce the desired effect of cooling the typical electronic component in the typical audio system. 13.1.1.4 Summary Convection is usually the most significant method, and it depends on having sufficient fin surface area in direct contact with the surrounding air and design features to minimize the insulating effects of boundary films. Aerodynamic shapes and adequate open fin spacing that allows free air movement are critical design issues. Conduction is the first step in the heat transfer chain in that conduction transfers the heat from the device into heatsink, then through the heatsink to the fin surface where convection takes over. Some heatsinks need conduction enhancements such as heat pipes to keep the conduction temperature gradients to a value that is low enough to allow the convection to complete

Radiation is a secondary level effect that is always present, marginally significant in natural convection, but not economical to control.

13.1.2 New Technologies to Make Things Fit More Easily

Thermal solution problem solving is an iterative process balancing the application boundary specifications against the affordable technologies/materials/fabrication processes until a system compromise solution is defined. 1 For example; marketing has directed that only a natural convection solution is acceptable but the heatsink is too big. One solution might require the Tmaxambient be reduced by 5°C and the heatsink be fabricated from copper, C110 soldered together. This could reduce the size of the heatsink by 25–35%. The penalties would be the weight would increase between to and three times and the unit cost of the heatsink increase by three to four times. There are software systems 2 that specialize in defining these trade-offs rapidly, allowing a real-time compromise to be made, even during the design review meeting with marketing.

Heatsinks and Relays

369

Table 13-2 summarizes the thermal solution benefits possible with the proper application of new technologies, materials and fabrication processes.

great success. The air flow was fully contained and no leakage occurred. And so the audio cooling tube was born.

Extruded heatsinks have fin thicknesses that are much greater, thicker than required thermally. They are thicker to accommodate the strength requirements of the die, which is close to the melting point of aluminum during the extrusion process.

There should always be a space—0.5–0.8 inches along the axis of the fan—between the fan outlet and the fin set that is fully shrouded to force the air to pass over the convective fin surfaces. This is called the plenum. Its function is to allow the upstream pressure generated by the fan to reach an equilibrium and thereby equalize the air flow through each fin opening.

Bonded fin and folded fin heatsink designs use sheet stock for the fins so that they may be optimally sized as required to carry the thermal load without regard to the mechanical requirements of the extrusion process. These heatsinks can, therefore, without compromising the required open fin spacing, have a greater number of fins and be convectively much more volumetrically effective. These sheet metal fins are attached to the heatsink bases with either thermal epoxy adhesives or solders. Since this joint only represents ~3 % of the total thermal resistance of the heatsink, the adhesive choice is never critical. Air flow management is the most critical parameter to control in optimizing the convective heat transfer for any thermal solution. Baffles, shrouds, and fan sizing are all very critical in making the most of the convective portion of the heat transfer thermal solution. Some months ago we were confronted with an audio amplifier that had two rows of very hot components. With two facing extrusions that formed a box shape, we mounted a fan at the end and blew the air down the chute with

Audio systems that require fans need to be carefully designed to have an air flow path that is well defined so that the fan may be operated at a minimal speed. This results in the fan generating a minimum of noise. High-velocity fans are noisy. Noise abatement is very expensive and seldom truly satisfactory, therefore, the best solution is to minimize the fan generated noise.

13.1.3 How Heatsinks Work by Glen Ballou Heatsinks are used to remove heat from a device, often the semiconductor junction. To remove heat, there must be a temperature differential ('T) between the junction and the air. For this reason, heat removal is always after the fact. Unfortunately, there is also resistance to heat transfer between the junction and its case, any insulating material, the heatsink, and the air, Fig. 13-1.

Table 13-2. Thermal Solutions with New Technology, Materials, and Fabrication Processes Technology/ Material/ Fabrication

Title

Volumetric Ratio Range

Copper C110

Molded Plastic Conductive 0.97 (200 LFM) 1.07 (>500 LFM) Base-Mounted Heat Pipes3 1 Heat Pipe 0.79 2 Heat Pipe 0.73 Base-Mounted Heat Pipes3 1 Heat Pipe 0.71 2 Heat Pipe 0.66 0.69 Al Base-Mounted Vapor 0.58 Cu Chamber3 Graphite 0.72

TM TM TM M TM FM

0.8

0.75 Solid-State Heat Pipes (TPG)4 Bonded Fin and Folded Fin 0.90 Al 0.76 Cu

Cost Range

Comments

3.5 ×

Volumetric ratios are even lower for conduction=limited applications Weight almost triples (3 ×)

0.5–0.7 After Saves weight and finishing3 tooling if not Hybrids—molded base metal fins a standard 1.5–2.0 Aluminum base 4.0–4.5

Copper base

2.5 Al 4.8 Cu 6–8 ×

Achieves optimum spreading

3.6 Al 5.4 Cu 2× 3.6 ×

Relatively fragile 35% reduction in weight Eliminates burnout as a failure mode More convective fin surface per unit volume fin shapes break up boundary film layers for performance gains

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Chapter 13

J (Junction)

C (Case)

S (Sink)

A (Ambient)

QSA TC TA TS TJ QCS QJC Case Sink Ambient Junction temperature temperature temperature temperature

Figure 13-1. Series thermal resistance/temperature circuit. A. Small heat sinks used with diodes and transistors. Their diameter is less than a dime.

13.1.3.1 Thermal Resistance The total thermal resistance between the junction and the air is the sum of the individual thermal resistances 6T = T JC + T CI + T IS + T SA

(13-1)

where, I is the thermal resistance in degrees Celsius per watt (°C/W), JC is the junction to case, CI is the case to insulator, IS is the insulator to heatsink, SA is the heatsink to air. The temperature at the junction can be determined from the ambient temperature, the thermal resistance between the air and the junction, and the power dissipated at the junction. T J = T A + T JA P D

(13-2)

where, TA is the temperature of the air, TJA is the thermal resistance from the air to the junction, PD is the power dissipated. If the junction temperature was known, then the power dissipated at the junction can be determined 'T P D = ------6T where, 'T is TJ TA.

(13-3)

B. Large heat sink for use with heavy current rectifiers. The stud of the rectifier is screwed into the center fin of the sink.

Figure 13-2. Conduction type heatsinks used for cooling diodes and transistors. Courtesy Wakefield Engineering Co.

where, Q is the rate of heat flow, K is the thermal conductivity of material, A is the cross-sectional area, 'T is the temperature difference, L is the length of heat flow.

Heatsinks are generally made from extruded aluminum or copper and are painted black, except for the areas in which the heat-producing device is mounted. The size of heatsinks will vary with the amount of heat to be radiated and the ambient temperature and the maximum average forward current through the element. Several different types of heatsinks are pictured in Fig. 13-2. The rate of heat flow from an object is

For best conduction of heat, the material should have a h i g h t h e r m a l c o n d u c t i v i t y a n d h a v e a l a rg e cross-sectional area. The ambient or material temperature should be maintained as low as possible, and the thermal path should be short. The heat may also be transferred by convection and radiation. When a surface is hotter than the air about it, the density of the air is reduced and rises, taking heat with it. The amount of heat (energy) radiated by a body is dependent on its surface area, temperature, and emissivity. For best results, the heatsink should:

Q = KA'T --------------L

• Have maximum surface area/volume (hence the use of vertical fins).

13.1.3.2 Heatsink Materials and Design

(13-4)

Heatsinks and Relays

1.335 1.370

Chassis insulating spacer 4.625 4.690

Figure 13-3. Typical heatsink for mounting two transistors. Courtesy Delco Electronics Corp.

Temperature differential—°C (mounting stud to ambient air)

The overall effectiveness of a heatsink is dependent to a great extent on the intimacy of the contact between the device to be cooled and the surface of the heatsink. Intimacy between these two is a function of the degree of conformity between the two surfaces and the amount of pressure that holds them together. The application of a silicone oil to the two surfaces will help to minimize air gaps between the surfaces, improving conduction. The use of a mica washer between the base of the device to be cooled and the heatsink will add as much as 0.5°C/W to the thermal resistance of the combination. Therefore, it is recommended that (whenever possible) an insulating washer be used to insulate the entire heatsink from the chassis to which it is to be mounted. This permits the solid-state device to be mounted directly to the surface of the hea tsink (without the mica washer). In this way, the thermal resistance of the mica washer is avoided. Today high thermal conductive/high electrical insulation materials are available to electrically insulate the transistor case from the heatsink. They come in the form of silicon rubber insulators, hard-coat-anodized finish aluminum wafers, and wafers with a high beryllium content. A typical heatsink is shown in Fig. 13-3. This sink has 165 in2 of radiating surface. The graph in Fig. 13-4 shows the thermal characteristics of a heatsink with a transistor mounted directly on its surface. A silicone oil is used to increase the heat transfer. This graph was made with the heatsink fins in a vertical plane, with air flowing from convection only. Fig. 13-5 shows the effect of thermal resistance with forced air blown along the length of the fin. A transistor mounting kit is shown in Fig. 13-6. Several different types of silicon fluids are available to improve heat transfer from the device to the heatsink. The fluid is applied between the base of the transistor and the surface of the heatsink or, if the transistor is insulated from the heatsink, between the base and the mica washer and the mica washer and the heatsink. For diodes pressed into a heatsink, the silicone fluid is applied to the surface of the diode case before pressing

3.000 3.125

Cooling fins

60 40 20 0

10 15 20 Power dissipation—W

Figure 13-4. Thermal characteristics for the heatsink shown in Fig. 13-3, with forced air cooling. Courtesy of Delco Electronics Corp.

Thermal resistance—°C/W

• Be made of a high thermal conductivity material. • Have material of high emissivity (painted aluminum or copper). • Have proper ventilation and location (should be below, not above, other heat radiators). • Be placed so that the lowest power device is below the higher power devices, and all devices should be as low as possible on the heatsink.

371

20W constant dissipation

2.0

1.5

1.0 50

100 150 Velocity of air flow—ft/min

200

Figure 13-5. Thermal characteristics for the heatsink shown in Fig. 13-3, with forced air cooling. Courtesy of Delco Electronics Corp.

it into the heatsink. The purpose of the silicone fluid is to provide good heat transfer by eliminating air gaps. Thermally conductive adhesives can also be used. These adhesives offer a high heat transfer, low shrinkage, and a coefficient of thermal expansion comparable to copper and aluminum. The thermal capacity of a cooling fin or heatsink must be large compared to the thermal capacity of the

372

Chapter 13 Table 13-3. Specific Thermal Resistance p of Interface Materials, °C in/W

Transistor

Material

MICA insulator 11/8 in2 × 0.001 in to 0.002 in thick Insulating bushings use one for mounting on material 1/8 in to 15/64 in thick. Use two for material of ½ in or greater thickness Copper or aluminum heat sink or chassis MICA insulator Metal washer Solder lug #10-32 hex. nut

#4-40 ×½ R.H. screw (2) Transistor

MICA insulator Copper or aluminum heat sink or chassis Insulating bushing (2) Lockwasher Solder lug #4-40 nut (2) Figure 13-6. Transistor/heatsink mounting kits. Courtesy Delco Electronics Corp.

device and have good thermal conductivity across its entire area. The specific thermal resistance U of interface materials used for heatsinks and insulating devices is shown in Table 13-3. The thermal resistance T for these materials can be determined by the equation T = Ut ----A where, U is the specific thermal resistance, t is the material thickness in inches, A is the area in square inches.

(13-5)

For instance, a square copper plate 4 inches per side and 1 » 8 inch thick would have a T of 0.00078°C/W,

Still air Mylar film Silicone grease Mica Wakefield Type 120 Compound Wakefield Delta Bond 152 Anodize Aluminum Copper Courtesy of Wakefield Engineering, Inc.

U 1200 236 204 66 56 47 5.6 0.19 0.10

while a mica insulator 0.003 inch thick with a diameter of 1 inch would have a T of 0.25°C/W. If the semiconductor dissipates 100 W, the temperature drop across the copper plate would be 0.07°C (0.13°F) and across the mica washer it would be 25°C (45°F). In transistor replacement in older equipment, it would be best to replace the mica insulator with a new type of insulator. In the selection of a heatsink material, the thermal conductivity of the material must be considered. This determines the thickness required to eliminate thermal gradients and the resultant reduction in emissivity. An aluminum fin must be twice as thick as a comparable copper fin, and steel must be eight times as thick as copper. Except for the smallest low-current solid-state devices, most devices must use a heatsink, either built in or external. Space for heatsinks is generally limited, so the minimum surface area permissible may be approximately calculated for a flat aluminum heat plate by W 2 A = 133 ------- in 'T

(13-6)

where, W is the power dissipated by the device, 'T is the temperature differences between the ambient and case temperature in qC. The approximate wattage dissipated by the device can be calculated from the load current and the voltage drop across it W = IL VD where, IL is the load current, VD is the voltage drop across the device.

(13-7)

Heatsinks and Relays

'T = T case – T ambient = 75qC – 25qC = 50qC Using Eq. 13-7 W = VD IL

$T/W = Q

10 7 6 5 4

Model A

20 15 Model B

5 20 30 40 50 60 70 TC case temperature–C°

1.5 2 2.5 3 4 5 6 7 8 9 10 Side dimension of square plate—inches

In restricted areas, forced-convection cooling may be necessary to reduce the effective thermal resistance of the heatsink. When forced air cooling is used to cool the component, the cubic feet per minute (cfm or ft3/min) required is determined by

It is important that the case temperature, Tcase, does not exceed the maximum allowed for a given load current, IL (see typical derating curves in Fig. 13-70).

IL Rms on-state current–A

Figure 13-8. Thermal resistance for a vertically mounted 1 e16 inch aluminum plate of various dimensions.

W 2 A = 133 ------- in 'T 22.5 = 133 u ---------50

0 0 10

Using Eq. 13-6

Thickness: 1/16 inch finish: bare position: vertical TC TA: 50oC

2.5

= 22.5 W

= 1.5 u 15

= 59.85 in

QThermal resistance—oC/W

For a triac, VD is about 1.5 V; for SCRs, about 0.7 V. For transistors it could be from 0.7 V to more than 100 V. The following is an example of how to determine the minimum surface area required for a flat aluminum heatsink to keep the case temperature of 75°C (167°F) for a triac while delivering a load current of 15 A, at 25°C (77°F) ambient and a voltage drop across the triac of 1.5 V

373

Btu e h cmf = ---------------- u 0.02 temperature rise 60 (13-8) = 1.76Q --------------'TK where, 1 W is 3.4 Btu, temperature rise is in °C, Q is the heat dissipated in watts, 'T is the heatsink mounting temperature minus the ambient temperature, K is the coupling efficiency (0.2 for wide spaced fins, 0.6 for close spaced fins).

80 90 100

Figure 13-7. A typical derating curve for solid state devices.

13.2 Relays

Eq. 13-6 gives the surface area needed for a vertically mounted heatsink. With free air convection, a vertically mounted heatsink, Fig. 13-8, has a thermal resistance approximately 30% lower than with horizontal mounting.

A relay is an electrically operated switch connected to or actuated by a remote circuit. The relay causes a second circuit or group of circuits to operate. The relay may control many different types of circuits connected to it. These circuits may consist of motors, bells, lights, audio circuits, power supplies, and so on, or the relay

374

Chapter 13

may be used to switch a number of other circuits at the same time or in sequence from one input. Relays may be electromechanical or solid state. Both have advantages and disadvantages. Only a few years ago relays were big and cumbersome and required either an octal-type socket or were externally wired. Today relays are very compact and come in many layouts. A few are given below. Solder Connectors. C o n n e c t o r s v a r y i n s i z e a n d spacing, depending on the current carrying capacity. Octal Sockets. Plug into standard 8 pin and 11 pin sockets. Rectangular Sockets. Plug into a 10 pin, 11 pin, 12 pin, 14 pin, 16 pin, 22 pin, or 28 pin socket. DIP Relays. Designed to mount directly on a printed circuit board on a 0.1 inch spacing. Sockets can be 8 pin or 16 pin. SIP 4 Pin Relay. Plug into a SIP socket or mount on a printed circuit board on a 0.2 inch in-line spacing. 13.2.1 Glossary of Terms This glossary was compiled from NARM Standard RS-436, MIL STD 202, and MIL STD R5757. Actuate Time. The time measured from coil energization to the stable contact closure (Form A) or stable contact opening (Form B) of the contact under test. (See also Operate Time.) Ampere Turns (AT). The product of the number of turns in an electromagnetic coil winding and the current in amperes passing through the winding. Bandwidth. The frequency at which the RF power insertion loss of a relay is 50%, or 3 dB. Bias, Magnetic. A steady magnetic field applied to the magnetic circuit of a switch to aid or impede its operation in relation to the coil’s magnetic field. Bounce, Contact. Intermittent and undesired opening of closed contacts or closing of opened contacts usually occurring during operate or release transition. Breakdown Voltage. The maximum voltage that can be applied across the open switch contacts before electrical breakdown occurs. In reed relays it is primarily dependent on the gap between the reed switch contacts and the type of gas fill used. High AT switches within a given switch family have larger gaps and higher breakdown voltage. It is also affected by the shape of the

contacts, since pitting or whiskering of the contact surfaces can develop regions of high electric field gradient that promote electron emission and avalanche breakdown. Since such pitting can be asymmetric, breakdown voltage tests should be performed with forward and reverse polarity. When testing bare switches, ambient light can affect the point of avalanche and should be controlled or eliminated for consistent testing. Breakdown voltage measurements can be used to detect reed switch capsule damage. See Paschen Test. Carry Current. The maximum continuous current that can be carried by a closed relay without exceeding its rating. Coaxial Shield. Copper alloy material that is terminated to two pins of a reed relay within the relay on each side of the switch. Used to simulate the outer conductor of a coaxial cable for high-frequency transmission. Coil. An assembly consisting of one or more turns of wire around a common form. In reed relays, current applied to this winding generates a magnetic field that operates the reed switch. Coil AT. The coil ampere turns (AT) is the product of the current flowing through the coil (and therefore directly related to coil power) and the number of turns. The coil AT exceeds the switch AT by an appropriate design margin to ensure reliable switch closure and adequate switch overdrive. Sometimes abbreviated as NI, where N is the number of turns and I is the coil current. Coil Power. The product, in watts, of the relay’s nominal voltage and current drawn at that voltage. Cold Switching. A circuit design that ensures the relay contacts are fully closed before the switched load is applied. It must take into account bounce, operate and release time. If technically feasible, cold switching is the best method for maximizing contact life at higher loads. Contact. The ferromagnetic blades of a switch often plated with rhodium, ruthenium, or tungsten material. Contact Resistance, Dynamic. Variation in contact resistance during the period in which contacts are in motion after closing. Contact Resistance, Static. The dc resistance of closed contacts as measured at their associated contact terminals. Measurement is made after stable contact closure is achieved.

Heatsinks and Relays

375

Crosstalk (Crosstalk Coupling). W h e n a p p l i e d t o multichannel relays, the ratio, expressed in dB, of the signal power being emitted from a relay output contact to the power being applied to an adjacent input channel at a specified frequency.

at higher frequencies, resulting in lower isolation at higher frequencies. Conversely, increasing inductive reactance at higher frequencies causes the impedance of a closed relay to rise, increasing the insertion loss at higher frequencies.

Duty Cycle. A ratio of energized to de-energized time.

Impedance Discontinuity. A d e v i a t i o n f r o m t h e nominal RF impedance of 50 : at a point inside a reed relay. Impedance discontinuities cause signal absorption and reflectance problems resulting in higher signal losses. They are minimized by designing the relay to have ideal transmission line characteristics.

Electrostatic Shield. Copper alloy material terminated to one pin within the reed relay. Used to minimize coupling and electrostatic noise between the coil and contacts. Form-A. Contact configuration that has one single pole–single throw normally open (SPST n.o.) contact. Form-B. Contact configuration that has one single pole–single throw normally closed (SPST n.c.) contact. Form-C. Contact configuration that has one single pole–double throw (SPDT) contact. (One common point connected to one normally open and one normally closed contact.) Sometimes referred to as a transfer contact. Hard Failure. Permanent failure of the contact being tested. Hermetic Seal. An enclosure that is sealed by fusion to ensure a low rate of gas leakage. In a reed switch, a glass-to-metal seal is employed. Hot Switching. A ci r c ui t d e s i g n th a t a p p li e s th e switched load to the switch contacts at the time of opening and closure. Hysteresis. When applied to reed relays, the difference between the electrical power required to initially close the relay and the power required to just maintain it in a closed state. (Usually expressed in terms of the relay’s pull-in voltage and drop-out voltage.) Some degree of hysteresis is desirable to prevent chatter and is also an indicator of adequate switch contact force. Impedance (Z). The combined dc resistance and ac reactance of a relay, at a specified frequency and if found with the equation Z = R + jX where, R is the dc resistance, 1 -, X is 2SfL – -----------2SfC f is the frequency.

(13-9)

Because of the small residual capacitance across the open contacts of a reed relay, the impedance decreases

Insertion Loss. The ratio of the power delivered from an ac source to a load via a relay with closed contacts, compared to the power delivered directly, at a specified frequency, and is found with the equation V Insertion Loss = – 20 log -----t Vi

(13-10)

where, Vt is the transmitted voltage, Vi is the incident voltage. Insertion loss, isolation and return loss are often expressed with the sign reversed; for example, the frequency at which 50% power loss occurs may be quoted as the 3 dB point. Since relays are passive and always produce net losses, this does not normally cause confusion. Inrush Current. Generally, the current waveform immediately after a load is connected to a source. Inrush current can form a surge flowing through a relay that is switching a low-impedance source load that is typically a highly reactive circuit or one with a nonlinear load characteristic such as a tungsten lamp load. Such abusive load surges are sometimes encountered when relays are inadvertently connected to test loads containing undischarged capacitors or to long transmission lines with appreciable amounts of stored capacitive energy. Excessive inrush currents can cause switch contact welding or premature contact failure. Insulation Resistance. The dc resistance between two specified test points. Isolation. The ratio of the power delivered from a source to a load via a relay with open contacts, compared to the power delivered directly, at a specified frequency. If Vi is the incident voltage and V t is the transmitted voltage, then isolation can be expressed in decibel format as

376 V Isolation = – 20 log -----t Vi

Chapter 13

(13-11)

where, Vt is the transmitted voltage, Vi is the incident voltage. Latching Relay. A bistable relay, typically with two coils, that requires a voltage pulse to change state. When pulse is removed from the coil, the relay stays in the state in which it was last set. Life Expectancy. The average number of cycles that a relay will achieve under specified load conditions before the contacts fail due to sticking, missing or excessive contact resistance. Expressed as mean cycles before failure (MCBF).

Operate Voltage. The coil voltage measured at which a contact changes state from its unenergized state. Overdrive. The fraction or percentage by which the voltage applied to the coil of a relay exceeds its pull-in voltage. An overdrive of at least 25% ensures adequate closed contact force and well-controlled bounce times, which result in optimum contact life. For instance, Coto Technology’s relays are designed for a minimum of 36% overdrive so a relay with a nominal coil voltage of 5 V will pullin at no greater than 3.75 V. When using reed relays, the overdrive applied to the relay should not drop below 25% under field conditions. Issues such as power supply droop and voltage drops across relay drivers can cause a nominally acceptable power supply voltage to drop to a level where adequate overdrive is not maintained.

Low Thermal Emf Relay. A relay designed specifically for switching low-voltage level signals such as thermocouples. These types of relays use a thermally compensating ceramic chip to minimize the thermal offset voltage generated by the relay.

Release Time. The time value measured from coil de-energization to the time of the contact opening, Form-A or first contact closure, Form-B.

Magnetic Interaction. The tendency of a relay to be influenced by the magnetic field from an adjacent energized relay. This influence can result in depression or elevation of the pull-in and dropout voltage of the affected relay, possibly causing them to fall outside their specification. Magnetic interaction can be minimized by alternating the polarity of adjacent relay coils, by magnetic shielding, or by placing two relays at right angles to each other.

Return Loss. The ratio of the power reflected from a relay to that incident on the relay, at a specified frequency and can be found with the equation

Magnetic Shield. A ferromagnetic material used to minimize magnetic coupling between a relay and external magnetic fields. Mercury Wetted Contact. A form of reed switch in which the reeds and contacts are wetted by a film of mercury obtained by a capillary action from a mercury pool encapsulated within the reed switch. The switch in this type of relay must be mounted vertically to ensure proper operation. Missing (Contacts). A reed switch failure mechanism, whereby an open contact fails to close by a specified time after relay energization. Nominal Voltage. The normal operating voltage of the relay. Operate Time. The time value measured from the energization of the coil to the first contact closure, Form A, or the first contact open, Form B.

Release Voltage. The coil voltage measured at which the contact returns to its de-energized state.

V Return loss = – 20 log -----r Vi

(13-12)

where, Vr is the reflected voltage, Vi is the incident voltage. Signal Rise Time. The rise time of a relay is the time required for its output signal to rise from 10– 90% of its final value, when the input is changed abruptly by a step function signal. Shield, Coaxial. A conductive metallic sheath surrounding a reed relay’s reed switch, appropriately connected to external pins by multiple internal connections, and designed to preserve a 50 : impedance environment within the relay. Used in relays designed for high-frequency service to minimize impedance discontinuities. Shield, Electrostatic. A conductive metallic sheath surrounding a reed relay’s reed switch, connected to at least one external relay pin, and designed to minimize capacitive coupling between the switch and other relay components, thus reducing high-frequency noise pickup. It is similar to a coaxial shield, but not designed to maintain a 50 : RF impedance environment.

Heatsinks and Relays Shield, Magnetic. An optional plate or shell constructed of magnetically permeable material such as nickel-iron or mu-metal, fitted external to the relay’s coil. Its function is to reduce the effects of magnetic interaction between adjacent relays and to improve the efficiency of the relay coil. A magnetic shell also reduces the influence of external magnetic fields, which is useful in security applications. Magnetic shields can be fitted externally or may be buried inside the relay housing. Soft Failure. Intermittent self-recovering failure of a contact. Sticking (Contacts). A switch failure mechanism, whereby a closed contact fails to open by a specified time after relay de-energization. Can be subclassified as hard or soft failures. Switch AT. The ampere turns required to close a reed switch, pull-in AT, or just to maintain it closed, drop-out AT, and is specified with a specific type and design of coil. Switch AT depends on the length of the switch leads and increases when the reed switch leads are cropped. This must be taken into account when specifying a switch for a particular application. Switching Current. The maximum current that can be hot-switched by a relay at a specified voltage without exceeding its rating. Switching Voltage. The maximum voltage that can be hot-switched by a relay at a specified current without exceeding its rating. Generally lower than breakdown voltage, since it has to allow for any possible arcing at the time of contact breaking. Transmission Line. In relay terms an interruptible waveguide consisting of two or more conductors, designed to have a well-controlled characteristic RF impedance and to efficiently transmit RF power from source to load with minimum losses, or to block RF energy with minimum leakage. Structures useful within RF relays include microstrips, coplanar waveguides, and coaxial transmission line elements. VSWR (Voltage Standing Wave Ratio). The ratio of the maximum RF voltage in a relay to the minimum voltage at a specified frequency and calculated from VSWR = 1 + U e 1 – U

(13-13)

where, Uis the the voltage reflected back from a closed relay terminated at its output with a standard reference impedance, normally 50 : .

377

13.2.2 Contact Characteristics6,7,8 Contacts may switch either power or dry circuits. A power circuit always has current flowing, while a dry circuit has minimal or no current flowing, such as an audio circuit. A dry or low-level circuit typically is less than 100 mV or 1 mA. The mechanical design of the contact springs is such that when the contacts are closed, they slide for a short distance over the surfaces of each other before coming to rest. This is called a wiping contact, and it ensures good electrical contact. Contacts are made of silver, palladium, rhodium, or gold and may be smooth or bifurcated. Bifurcated contacts have better wiping and cleaning action than smooth contacts and, therefore, are used on dry circuits. There are various combinations of contact springs making up the circuits that are operated by the action of the relay. Typical spring piles are shown in Fig. 13-9. As contacts close, the initial resistance is relatively high, and any films, oxides, and so on further increase the contact resistance. Upon closing, current begins to flow across the rough surface of the contacts, heating and softening them until the entire contact is mating, which reduces the contact resistance to milliohms. When the current through the circuit is too low to heat and soften the contacts, gold contacts should be used since the contacts do not oxidize and, therefore, have low contact resistance. On the other hand, gold should not be used in power circuits where current is flowing. The contact current specified is the maximum current, often the make-or-break current. For instance, the make current of a motor or capacitor may be 10–15 times as high as its steady-state operation. Silver cadmium oxide contacts are very common for this type of load. The contact voltage specified is the maximum voltage allowed during arcing during break. The break voltage of an inductor can be 50 times the steady-state voltage of the circuit. To protect the relay contacts from high transient voltages, arc suppression should be used. For dc loads, this may be in the form of a reverse-biased diode (rectifier), variable resistor (varistor), or RC network, as shown in Fig. 13-10. The R and C in an RC circuit are calculated with the following equations: 2

I C = ------ μF 10

(13-14)

378

Chapter 13

A. Make, single-pole, single-throw, normally open (Form A).

J. Make, make, break.

B. Break, single-pole, single-throw, normally closed (Form B).

K. Single-pole, doublethrow, center off.

C. Break, make (transfer) (Form C). L. Break, make, make. D. Make, break (continuity transfer). M. Double-make, contact on arm (Form U). E. Break, make, break. N. Double-break, contact on arm (Form V). F. Make, make. O. Double-break, doublemake, contact on arm (Form W). G. Break, break. P. Double-make (Form X).

H. Break, break, make. Q. Double-break (Form Y).

I. Make, break, make. R. Double-break, doublemake (Form Z).

Figure 13-9. Various contact arrangements of relays. (From American National Standard Definitions and Terminology for Relays for Electronics Equipment C83.16-1971.)

0.01 VR = ---------------I

(13-15)

When using a rectifier, the rectifier is an open circuit to the power source because it is reverse biased; however, when the circuit breaks, the diode conducts. This technique depends on a reverse path for the diode to conduct; otherwise, it will flow through some other part of the circuit. It is important that the rectifier have a voltage rating equal to the transient voltage.

Contact bounce occurs in all mechanical-type relays except the mercury-wetted types that, because of the thin film of mercury on the contacts, do not break during make. Bounce creates noise in the circuit, particularly when switching audio where it acts as a dropout. 13.2.3 Relay Loads8 Never assume that a relay contact can switch its rated current no matter what type of load it sees. High in-rush currents or high induced back electromotive force (emf) like those of Fig. 13-11 can quickly erode or weld elec-

Peak current can reach 15 × normal

Load R

C¾

Current

Relay contact

Load R

B. Resistor, ac/dc. Relay contact

Load

C. Diodes, dc. Relay contact

Load

D. Diode and Zener, dc.

Load

E. Diode and Resistor, dc. Relay contact

Relay contact Load

Load R

VAR

F. Varistor, ac.

Relay contact

G. Resistor-capacitor-diode network, dc. Relay contact R

Load

Max in-rush current = V/R

Time Capacitor load

A. Resistor capacitor network (Use C or C['] as preferred), ac/dc. Relay contact

379

Current

Heatsinks and Relays

In-rush current 3 to 6 × running current

Incandescent lamps Starting Running Induction motor load

Figure 13-11. High in-rush current on turn-on can damage relays.

currents as much as 15 times the steady-state current. This is why lamp burnout almost always occurs during turn on. Capacitive Loads. The initial charging current to a capacitive circuit can be extremely high, since the capacitor acts as a short circuit, and current is limited only by the circuit resistance. Capacitive loads may be long transmission lines, filters for electromagnetic interference (emi) elimination, and power supplies. Motor Loads. High in-rush current is drawn by most motors, because at standstill their input impedance is very low. This is particularly bad when aggravated by contact bounce causing several high-current makes and breaks before final closure. When the motor rotates, it develops an internal back emf that reduces the current. Depending on the mechanical load, the starting time may be very long and produce a relay-damaging in-rush current. Inductive Loads. In-rush current is limited by inductance; however, when turned off, energy stored in magnetic fields must be dissipated.

Figure 13-10. Methods of suppressing transients across contacts. Courtesy Magnecraft Electric Co.

Dc Loads. These are harder to turn off than ac loads because the voltage never passes through zero. When electromagnetic radiation (emr) contacts open, an arc is struck that may be sustained by the applied voltage, burning contacts.

tromechanical relay contacts and destroy solid-state relays.

13.2.4 Electromechanical Relays

Load H. Back-to-back diode I. Capacitor-diode-resistor (zener or avalanche), ac. for ac suppression.

13.2.3.1 The Effects of Various Loads Incandescent Lamps. The cold resistance of a tungsten-filament lamp is extremely low, resulting in in-rush

Regardless of whether the relay operates on ac or dc, it will consist of an actuating coil, a core, an armature, and a group of contact springs that are connected to the circuit or circuits to be controlled. Associated with the armature are mechanical adjustments and springs. The

380

Chapter 13

mechanical arrangement of the contacts may be such that when the relay is at rest, certain circuits are either open or closed. If the contacts are open when the relay is at rest (not energized) they are called normally open contacts. Relays are wound in many different manners, Fig. 13-12. Among them are the single wound, double wound, trifilar wound, bifilar wound, and two coil, which are nonelectromagnetic. 1

A. Single. 3

B. Double.

Noninductive Magnet 135

246

C. Trifilar. 13

In the quick-operate type, the armature is attracted immediately to the pole piece of the electromagnet when the control circuit is closed. Slow-operate relays have a time-delay characteristic; that is, the armature is not immediately attracted to the pole piece of the electromagnet when the control circuit is closed. To accomplish this a copper collar is placed around the armature end of the pole piece. They differ from the slow-release variety in that the latter type has the copper collar around the end of the pole piece opposite from the armature. A polarized relay is designed to react to a given direction of current and magnitude. Polarized relays use a permanent magnet core. Current in a given direction increases the magnetic field, and in the opposite direction it decreases the field. Thus, the relay will operate only for a given direction of current through the coil. A latching relay is stable in both positions. One type of latching relay contains two separate actuating coils. Actuating one coil latches the relay in one position where it remains until it is unlatched by energizing the other coil. A second and more modern type is a bistable magnetic latching relay. This type is available in singleor dual-coil latching configurations. Both are bistable and will remain in either state indefinitely. The coils are designed for intermittent duty: 10 s maximum on-time. The relay sets or resets on a pulse of 100 ms or greater. Fig. 13-13 shows the various contact and coil forms. 13.2.4.2 Ac Relays

D. Bifilar. 1

E. Two coil.

Figure 13-12. Types of relay coil windings.

13.2.4.1 Dc Relays Direct current (dc) relays are designed to operate at various voltages and currents by varying the dc resistance of the actuating coils, and may vary from a few to several thousand ohms. Dc relays may operate as marginal, quick-operate, slow-operate, or polarized. A marginal relay operates when the current through its winding reaches a specified value, and it releases when the current falls to a given value.

Alternating-current (ac) relays are similar in construction to the dc relays. Since ac has a zero value every half cycle, the magnetic field of an ac-operated relay will have corresponding zero values in the magnetic field every half cycle. At and near the instants of zero current, the armature will leave the core, unless some provision is made to hold it in position. One method consists of using an armature of such mass that its inertia will hold it in position. Another method makes use of two windings on separate cores. These windings are connected so that their respective currents are out of phase with each other. Both coils effect a pull on the armature when current flows in both windings. A third type employs a split pole piece of which one part is surrounded by a copper ring acting as a shorted turn. Alternating current in the actuating coil winding induces a current in the copper coil. This current is out of phase with the current in the actuating coil and does not reach the zero value at the same instant as the

Heatsinks and Relays

+ Reset

Set +

13.2.5 Reed Relays6,7,8,11

+ Reset

Set +

B. Dc single coil, 2 Form C contacts.

A. Dc single coil, 1 Form C contact 3

+ Reset

Reset

Set +

D. Ac coil, 1 Form C contact.

Reset

8 A

Com

Reed relays were developed by the Bell Telephone Laboratories in 1960 for use in the Bell System central offices. The glass envelope is surrounded by an electromagnetic coil connected to a control circuit. Although originally developed for the telephone company, such devices have found many uses in the electronics industry. The term reed relay covers dry reed relays and mercury-wetted contact relays, all of which use hermetically sealed reed switches. In both types, the reeds (thin, flat blades) serve multiple functions, as conductor, contacts, springs, and magnetic armatures. Reed relays are usually soldered directly onto a circuit board or plugged into a socket that is mounted onto a circuit board.

Set

Com

C. Dc dual coil, 2 Form C contacts.

381

Set

E. Ac coil, 2 Form C contacts.

Figure 13-13. Various types and pin connections for latching relays. Courtesy Magnecraft Electric Co.

current in the actuating coil. As a result, there is always enough pull on the armature to hold it in the operating position. An ac differential relay employs two windings exactly alike, except they are wound in opposite directions. Such relays operate only when one winding is energized. When both windings are energized in opposite directions, they produce an aiding magnetic field, since the windings are in opposite directions. When the current through the actuating coils is going in the same direction, the coils produce opposite magnetic fields. If the current through the two coils is equal, the magnetic fields neutralize each other and the relay is nonoperative. A differential polar relay employs a split magnetic circuit consisting of two windings on a permanent magnet core. A differential polar relay is a combination of a differential and a polarized relay.

13.2.5.1 Contact Resistance and Dynamics Reed relays have much better switching speed than electromechanical relays. The fastest Coto Technology switching reed relay is the 9800 series, with a typical actuate time of 100 ȝs. Release time is approximately 50 ȝs. Actuate time is defined as the period from coil energization until the contact is closed and has stopped bouncing. After the contacts have stopped bouncing, they continue to vibrate while in contact with one another for a period of about 1 ms. This vibration creates a wiping action and variable contact pressure. Static contact resistance (SCR) is the resistance across the contact terminals of the relay after it has been closed for a sufficient period of time to allow for complete settling. For most reed relays, a few milliseconds is more than adequate, but the relay industry uses 50 ms to define the measurement. Another contact resistance measurement that has provided great insight into the overall quality of the relay is contact resistance stability (CRS). CRS measures the repeatability of successive static contact resistance measurements.

13.2.5.2 Magnetic Interaction Reed relays are subject to external magnetic effects including the earth’s magnetic field (equivalent to approximately 0.5 AT and generally negligible), electric motors, transformers external magnets, etc., which may change performance characteristics. Such magnetic sources include one common source of an external magnetic field acting on a relay or another relay oper-

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ating in close proximity. The potential for magnetic coupling must be taken into account when installing densely packed single- or multichannel relays. An example of magnetic interaction is shown in Fig. 13-14 where two relays, K1 and K2, with identical coil polarities are mounted adjacent to each other. When K2 is “off”, relay K1 operates at its designed voltage. When K2 is activated, the magnetic fields oppose so the effective magnetic flux within K1 is reduced, requiring an increase in coil voltage to operate the reed switch. For closely packed relays without magnetic shields, a 10–20% increase in operate voltage is typical, which can drive the relays above their specified limits. The opposite effect occurs if K1 and K2 are polarized in opposite directions making the operating voltage for K1 less.

13.2.5.3 Environmental Temperature Effects The resistance of the copper wire used in reed relay coils increases by 0.4% /1°C rise in temperature. Reed relays are current-sensitive devices so their operate and release levels are based on the current input to the coil. If a voltage source is used to drive the relays, an increase in coil resistance causes less current to flow through the coil, so the voltage must be increased to compensate and maintain current flow. Industry standards define that relays are typically specified at 25°C ambient. If the relay is used in higher ambient conditions or near external sources of heat, this must be carefully considered. For example, a standard relay nominally rated at 5 Vdc has a 3.8 Vdc maximum operate value at 25°C as allowed by the specifications. If the relay is used in a 75°C environment, the 50°C temperature rise increases the operate voltage by 50 × 0.4%, or 20%. The relay now will operate at 3.8 Vdc + (3.8 Vdc × 20%), or 4.56 Vdc. If there is more than a 0.5 Vdc drop in supply voltage due to a device driver or sagging power supply, the relay may not operate. Under these conditions there will be increases in operate and release timing to approximately the same 20%. 13.2.5.4 Dry Reed Relays

Relay K1

Relay K2

Figure 13-14. Adverse magnetic interaction. Courtesy Coto Technology.

There are several ways to reduce magnetic interaction between relays: • Specify relays that incorporate an internal or external magnetic shield. • Apply an external magnetic shield to the area where the relays are mounted. A sheet of mu-metal or other high-magnetic-permeability ferrous alloy 2–5 mils thick is effective. • Provide increased on-center spacing between relays. Each doubling of this distance reduces the interaction effect by a factor of approximately four. • Avoid simultaneous operation of adjacent relays. • Provide alternating coil polarities for relays used in a matrix.

Because of the tremendous increases in low-level logic switching, computer applications, and other business machine and communication applications, dry reed relays have become an important factor in the relay field. They have the great advantage of being hermetically sealed, making them impervious to atmospheric contamination. They are very fast in operation and when operated within their rated contact loads, they have a very long life. They can be manufactured automatically and therefore are relatively inexpensive. A typical dry reed switch capsule is shown in Fig. 13-15.

Supporting terminal

Normally open contacts

Glass Supporting capsule terminal

Figure 13-15. Construction of a switch capsule of a typical dry reed relay—Form A. Courtesy Magnecraft Electric Co.

In this basic design, two opposing reeds are sealed into a narrow glass capsule and overlap at their free ends. At the contact area, they are plated with rhodium over gold to produce a low contact resistance when they

Heatsinks and Relays meet. The capsule, surrounded by an electromagnetic coil, is made of glass and filled with a dry inert gas. When the coil is energized in the basic Form A contact combination, the normally open contacts are brought together; when the field is removed the reeds separate by their own spring tension. Some may contain permanent magnets for magnetic biasing to achieve normally closed contacts (Form B). Single-pole, double-throw contact combinations (Form C) are also available. Current rating, which is dependent on the size of the reed and the type and amount of plating, may range from low level to 1 A. Effective contact protection is essential in most applications unless switching is done dry. Relay packages using up to four Form C and six Form A dry reed switches are common, providing multiple switching arrangements. The reed relay may be built for a large variety of operational modes such as pulse relay, latch relay, crosspoint relay, and logic relay. These relays may also be supplied with electrostatic or magnetic shields. The relay in Fig. 13-16 has two Form C contacts.

383

efficiency decreases and power input increases. This can lead to a practical limitation. On the other hand, the increase in power required to operate one more switch capsule is usually less than the total required if the assembly were split in two. The single contact relay is the most frequently used but relays with four or more switches in a single coil are quite common. Sensitivity. The power input required to operate dry reed relays is determined by the sensitivity of the particular reed switch used, by the number of switches operated by the coil, by the permanent magnet biasing (if used), and by the efficiency of the coil and the effectiveness of its coupling to the reeds. The minimum input required to effect closure ranges from milliwatts for a single capsule sensitive unit to several watts for a multipole relay. Operate Time. Coil time constant, overdrive, and the characteristics of the reed switch determine operate time. With maximum overdrive, reed relays will operate in approximately 200 μs or less. Drive at rated voltage usually results in a 1 ms operate time. Release Time. With the relay coil unsuppressed, dry reed switch contacts release in a fraction of a millisecond. Form A contacts open in as little as 50 μs. Magnetically biased Form B contacts and normally closed contacts of Form C switches reclose from 100 μs to 1 ms, respectively. If the relay coil is suppressed, release times are increased. Diode suppression can delay release for several milliseconds, depending on coil characteristics, drive level, and reed release characteristics.

Figure 13-16. Coto Technology 2342 multipole relay, Courtesy Coto Technology.

Reed switches have the following characteristics: • A high degree of reliability stemming from their controlled contact environment. • Consistency of performance resulting from a minimum number of parts. • Long operational life. • Ease of packaging as a relay. • High-speed operation. • Small size. • Low cost. Number of Switches. There appears to be no limit to the number of switches that can be actuated by a common coil. However, as the number increases, coil

Bounce. As with the other hard contact switches, dry reed contacts bounce on closure. The duration of bounce is typically quite short and is in part dependent on drive level. In some of the faster devices, the sum of operate time and bounce is relatively constant so as drive is increased, the operate time decreases and bounce increases. While normally closed contacts of a Form C switch bounce more than normally open contacts, magnetically biased Form B contacts exhibit essentially the same bounce as Form A. Contact Resistance. Because the reeds in a dry reed switch are made of a magnetic material that has a high volume resistivity, terminal-to-terminal resistance is somewhat higher than in some other types of relays. Typical specification limit for initial maximum resistance of a Form A reed relay is 0.200 : .

384

Chapter 13

13.2.5.5 Mercury-Wetted Contact Relays Mercury-wetted contact relays are a form of reed relays consisting of a glass-encapsulated reed with its base immersed in a pool of mercury and the other end capable of moving between one or two stationary contacts. The mercury flows up to the reed by capillary action and wets the contact surface of the moving end of the reed as well as the contact surfaces of the stationary contacts. Thus a mercury-to-mercury contact is maintained in a closed position. The mercury-wetted relay is usually actuated by a coil around the capsule. Aside from being extremely fast in operation and having relatively good load-carrying capacity, mercury-wetted contact relays have extremely long life since the mercury films are reestablished at each contact closure and contact erosion is eliminated. Since the films are “stretchable,” there is no contact bounce. Contact interface resistance is extremely low. Three disadvantages of this type of reed relays are: 1. 2. 3.

The freezing point of mercury is (–38.8°C or –37.8°F). They have poor resistance to shock and vibration. Some type need to mount in a near vertical position.

These relays are available in a compact form for printed-circuit board mounting. Multipole versions can be provided by putting additional capsules inside the coil. They are used for a great variety of switching applications such as are found in computers, business machines, machine tool control systems, and laboratory instruments. Mercury-wetted switches can also come as a nonposition sensitive, mercury-wetted, reed relay that combines the desirable features of both dry reed and mercury-wetted capsules. This allows the user to place the reed relay in any position and is capable of withstanding shock and vibration limits usually associated with dry reed capsules. On the other hand, they retain the principal advantages of other mercury-wetted switches—no contact bounce and low stable contact resistance. Operation of the nonposition-sensitive switch is made possible by the elimination of the pool of mercury at the bottom of the capsule. Its design captures and retains the mercury on contact and blade surfaces only. Due to the limited amount of mercury film, this switch should be restricted for use at low-level loads. Mercury-wetted reed relays are a distinct segment of the reed relay family. They are different from the dry reed relays in the fact that contact between switch elements is made via a thin film of mercury. Thus, the

most important special characteristics of mercury-wetted relays are: • Contact resistance is essentially constant from operation to operation throughout life. • Contacts do not exhibit bounce. The amount of mercury at the contacts is great enough to both cushion the impact of the underlying members and to electrically bridge any mechanical bounce that remains. • Life is measured in billions of operations, due to constant contact surface renewal. • Contacts are versatile. The same contacts, properly applied, can handle relatively high-power and low-level signals. • Electrical parameters are constant. With contact wear eliminated, operating characteristics remain the same through billions of operations. To preserve these characteristics, the rate of change of voltage across the contacts as they open must be limited to preclude damage to the contact surface under the mercury. For this reason, suppression should be specified for all but low-level applications. Mounting Position. To ensure that distribution of mercury to the relay contacts is proper, position sensitive types should be mounted with switches oriented vertically. It is generally agreed that deviation from vertical by as much as 30° will have some effect on performance. The nonposition-sensitive mercurywetted relay, which is the most common type today, is not affected by these limitations. Bounce. Mercury-wetted relays do not bounce if operated within appropriate limits. However, if drive rates are increased, resonant effects in the switch may cause rebound to exceed the level that can be bridged by the mercury, and electrical bounce will result. Altered distribution of mercury to the contacts, caused by the high rate of operation, may also contribute to this effect. Contact Resistance. Mercury-wetted relays have a terminal-to-terminal contact resistance that is somewhat lower than dry reed relays. Typical specification limit for maximum contact resistance is 0.150 : . 13.2.5.6 RF Relays RF relays are used in high-frequency applications, usually in a 50 : circuit. The RF coaxial shielded relay in Fig. 13-17 can switch up to 200 Vdc at 0.5 A.

Heatsinks and Relays

385

Return loss is calculated from the reflection coefficient (ȡ), which is the ratio of the magnitude of signal power being reflected from a closed relay to the power input at a specified frequency Return loss = – 20 log U

Figure 13-17. Coto Technology 9290 RF reed relay. Courtesy Coto Technology.

Insertion and Other Losses. In the past, the typical parameters used to quantify RF performance of reed relays were Insertion loss, isolation, and return loss ( s o m e t i m e s c a l l e d r e f l e c ti o n l o s s ) . T h e s e a r e frequency-related vector quantities describing the relative amount of RF power entering the relay and either being transmitted to the output or being reflected back to the source. For example, with the relay’s reed switch closed and 50% power being transmitted through the relay, the insertion loss would be 0.5 or í3 dB. The frequency at which a í3 dB rolloff occurs is a convenient scalar (single-valued) quantity for describing insertion loss performance. Isolation. The RF isolation of the reed relay can be determined by injecting an RF signal of known power amplitude with the reed switch open (coil unactivated). Sweeping the RF frequency and plotting the amount of RF energy exiting the relay allows the isolation curve to be plotted on a dB scale. At lower frequencies, the isolation may be í40 dB or greater, indicating that less than 0.01% of the incident power is leaking through the relay. The isolation decreases at higher frequencies, because of capacitive leakage across reed switch contacts. Return Loss. Return loss represents the amount of RF power being reflected back to the source with the reed switch closed and the output terminated with a standard impedance, normally 50 ȍ. If the relay was closely matched to 50 ȍ at all frequencies, the reflected energy would be a very small fraction of the incident energy from low to high frequencies. In practice, return loss increases (more power is reflected) as frequency increases. High return loss (low reflective energy) is desirable for high-speed pulse transmission, since there is less risk of echoing signal collisions that can cause binary data corruption and increased bit error rates.

(13-16)

To determine the RF performance of a reed relay involves injecting a swept frequency RF signal of known power into the relay and measuring the amount of RF energy transmitted through or reflected back from it. These measurements can be conveniently made using a Vector Network Analyzer (VNA). These test instruments comprise a unified RF sweep frequency generator and quantitative receiver/detector. In the case of a Form A relay, the device is treated as a network with one input and one output port, and the amount of RF energy entering and being reflected from each port is recorded as a function of frequency. Thus a complete characterization of a Form A relay comprises four data vectors, designated as follows: S11 power reflected from input port. S12 power transmitted to input port from output port. S21 power transmitted to output port from input port. S22 power reflected from output port. Voltage Standing Wave Ratio (VSWR). V S W R i s a measurement of how much incident signal power is reflected back to the source when an RF signal is injected into a closed relay terminated with a 50 : impedance. It represents the ratio of the maximum amplitude of the reflected signal envelope amplitude divided by the minimum at a specified frequency. A VSWR of 1 indicates a perfect match between the source, relay, and output load impedance and is not achievable. VSWR at any particular frequency can be converted from y-axis return loss using Table 13-2. Table 13-4. Return Loss Versus VSWR Return Loss VSWR (dB)

VSWR

50 40 30 20 10 3

1.01 1.02 1.07 1.22 1.93 5.85

Rise Time. The rise time of a reed relay is the time required for its output signal to rise from 10% to 90% of its final value, when the input is changed abruptly by a step function signal. The relay can be approximated by

386

Chapter 13

a simple first-order low-pass filter. The rise time is approximately 90% T r = RC u ln ----------10%

(13-17)

combination of coplanar waveguide and coaxial structures with very little impedance discontinuity through the relays. The Coto B10 and B40 reed relays, Fig. 13-18 achieve bandwidths greater than 10 GHz and rise times of 35 ps or less.

= 2.3RC Substituting into the equation for the 50% roll-off frequency f – 3 dB = 1 e 2SRC yields the relationship 0.35 T r = ------------- . f – 3 dB

(13-18)

Therefore the relay’s rise time can be simply estimated from the S21 insertion loss curve by dividing the –3 dB rolloff frequency into 0.35. For example, the Coto Technology B40 ball grid relay has f3 dB = 11.5 GHz, from which the rise time can be estimated as 30 ps. Effect of Lead Form on High Frequency Performance. Surface mount (SMD) relays give better RF performance than those with through hole leads. SMD leadforms comprise gullwing, J-bend, and axial forms. Each has its advantages and disadvantages, but the RF performance point of view, axial relays generally have the best RF performance in terms of signal losses, followed by J-bend and gullwing. The straight-through signal path of axial relays minimizes capacitive and inductive reactance in the leads and minimizes impedance discontinuities in the relay, resulting in the highest bandwidth. However, the axial leadform requires a cavity in the printed circuit board to receive the body of the relay. An advantage is the effective reduced height of the axial relay, where space is at a premium. J-bend relays provide the next-best RF performance and have the advantages of requiring slightly less area on the PCB. The gullwing form is the most common type of SMD relay. It has the longest lead length between the connection to the PCB pad and the relay body which results in slightly lower RF performance than the other lead types. Initial pick-and-place soldering is simple, as is rework, resulting in a broad preference for this lead type unless RF performance is critical. Coto Technology’s new leadless relays have greatly enhanced RF performance. They do not have traditional exposed metal leads; instead, the connection to the user’s circuit board is made with ball-grid-array (BGA) attachment, so that the devices are essentially leadless. In the BGA relays, the signal path between the BGA signal input and output is designed as an RF transmission line, with an RF impedance close to 50 ȍ throughout the relay. This is achieved using a matched

Figure 13-18. Coto Technology B40 Ball Grid surface mount 4-channel reed relay. Courtesy Coto Technology.

Skin Effect in Reed Relays. At high frequencies, RF signals tend to travel near the surface of conductors rather than through the bulk of the material. The skin effect is exaggerated in metals with high magnetic permeability, such as the nickel-iron alloy used for reed switch blades. In a reed switch, the same metal has to carry the switched current and also respond to a magnetic closure field. Skin effect does not appreciably affect the operation of reed relays at RF frequencies because the increase in ac resistance due to skin effect is proportional to the square root of frequency, whereas the losses due to increasing reactance are directly proportional to L and inversely proportional to C. Also the external lead surfaces are coated with tin or solder alloys for enhanced solder-ability which helps to reduce skin effect losses. Selecting Reed Relays for High Frequency Service. High-speed switching circuits can be accomplished with reed relays, electromechanical relays (EMRs) specifically designed for high-frequency service, solid-state relays (SSRs), PIN diodes, and microelectromechanical systems (MEMS) relays. In many cases, reed relays are an excellent choice, particularly with respect to their unrivalled RC product. RC is a figure of merit expressed in pF·ȍ, where R is the closed contact resistance and C is the open contact capacitance. The lower this figure is, the better the high-frequency performance. The RC product of a Coto Technology B40 relay for example, is approximately 0.02 pF•ȍ. SSRs have pF•ȍ products equal to about 6, almost 300 times

Heatsinks and Relays higher, plus, the breakdown voltage at these pF•ȍ levels is much lower than that of a reed switch. The turn-off time for SSRs is also longer than the 50 ȝs needed by a reed relay to reach its typical 10 12 ȍ off resistance. Some feel that the reliability of reed relays compared to solid-state devices is largely unjustified, due to continuous technological improvements. Many reed relays have demonstrated MCBF values of several hundred million to several billion closure cycles at typical signal switching levels. PIN diodes are occasionally used for HF switching. However, PIN diodes require relatively complex drive circuitry compared to the simple logic circuitry that drives reed relays. PIN diodes typically have a lower frequency cut-on of about 1 MHz, while a reed relay can switch from dc to its useful cut-off frequency. The high junction capacitance of PIN diodes results in lower RF isolation than a reed relay when the PIN diode is biased open. When biased closed, the higher on-resistance of the PIN diode can lead to Q-factor damping in the circuit to which it is connected. PIN diodes can exhibit significant nonlinearity, leading to gain compression, harmonic distortion, and intermodulation distortion, while reed relays are linear switching devices. Electromechanical relays (EMRs) have been developed with bandwidths to about 6 GHz, and isolation of about 20 dB at that frequency. This isolation is better than that of a reed relay, since the contacts can be designed with bigger spacing, resulting in lower capacitive leakage. This advantage must be weighed against the increased size and cost of EMRs and lower reliability. The EMR has a complex structure with more moving parts than the simple blade flexure involved in closing a reed switch, resulting in a lower mechanical life. If higher isolation is required with a reed relay solution, two relays can be cascaded together with a combined reliability that is still higher than that of a typical EMR. MEMS switches (relays) are being developed based on two technologies, electrostatic closure and pulsed magnetic toggling between open and closed states. They offer potential advantages in terms of small and low loss high-frequency switching. However, adequate contact reliability has not been demonstrated at the switching loads required by automated test equipment (ATE) applications. At present, though, MEMS relay technology is too immature for use in most applications addressed by reed relays.

387

13.2.5.7 Dry Reed Switches A dry reed switch is an assembly containing ferromagnetic contact blades that are hermetically sealed in a glass envelope and are operated by an externally generated magnetic field. The field can be a coil or a permanent magnet. The switches in Figs. 13-19A and 13-19B can switch up to 175 Vdc at 350 mA or 140 Vac at 250 ma. The switch in Fig. 13-19C can switch 200 Vdc at 1 A or 140 Vac at 1 A.

A. RI-80 SMD SPST 5 W switch. B. RI-80 SPST 5W switch.

C. RI-25 SPST 25 W switch.

Figure 13-19. Coto Technology dry reed switches. Courtesy Coto Technology.

A. A dry-reed switch mounted within a coil.

N Ic

B. A dry-reed switch mounted outside a coil. N

S Ic

C. A dry-reed switch biased by a permanent magnet and operated by a coil.

Figure 13-20. Energizing a dry-reed switch with a coil. Courtesy Coto Technology.

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Chapter 13

X 90o

Hold

+Y Hold

Off

Hold

180o

180o On

B. Rotational movement with a bar-shaped permanent magnet.

+Y On

A. Movement with the magnetic field parallel to the dry-reed switch.

S X

S S

N N

S Off

Off

Hold

Off

N S

Off

C. Movement with the magnetic field perpendicular to the dry-reed switch.

D. Rotational movement with two or more ring magnets.

Figure 13-21. Energizing a dry-reed switch with a permanent magnet. Courtesy Coto Technology.

Fig. 13-20 shows three methods of operating a reed switch using a coil. Fig. 13-21 shows four ways to operate a reed switch using permanent magnets. 13.2.6 Solid-State Relays9 Solid-state relays (SSRs) utilize the on–off switching properties of transistors and SCRs for opening and closing dc circuits. They also use triacs for switching ac circuits.

includes a lamp or light-emitting diode that shines on a phototransistor serving as the actuating device. In other types of SSRs, a small reed relay or transformer may serve as the actuating device. A third type is direct coupled and therefore not actually an SSR because there is no isolation between input and output. These are better called an amplifier. All three types are shown in Fig. 13-22. Ac relays turn on and off at zero crossing; therefore, they have reduced dv/dt. However, this does slow down the action to the operating frequency.

13.2.6.1 Advantages SSRs have several advantages over their electromechanical counterparts: no moving parts, arcing, burning, or wearing of contacts; and the capacity for high-speed, bounceless, noiseless operation. Many SSRs are available that feature optical coupling; thus, the signal circuit

13.2.6.2 Disadvantages and Protection4 Solid-state relays also have some inherent problems as they are easily destroyed by short circuits, high surge current, high dv/dt, and high peak voltage across the power circuit.

Heatsinks and Relays

Photo transistor Control circuit

Trigger circuit

Triac

Power circuit

Light emitting diode

ac line

A. Optically coupled. dc control circuit

dc to ac converter

Trigger circuit

Triac

Power circuit

Transformer

389

L is the inductance in henrys, V is the line voltage, dv/dt is the maximum permissible rate of change of voltage in volts per microsecond, I is the load current, PF is the load power factor, C is the capacitance in microfarads, R1, R2 are the resistance in ohms, f is the line frequency. RC networks are often internal to SSRs. if Supply voltage V

ac line B. Transformer coupled.

Trigger circuit

Control circuit

Triac

l Power circuit

Solid-state switch

C Snubber R1

ac line C. Direct coupled.

Figure 13-22. Various types of solid-state relays.

Short-circuit and high-surge current protection is performed with fast blow fuses or series resistors. A standard fuse normally will not blow before the SCR or triac is destroyed since the fuses are designed to withstand surge currents. Fast blow fuses will act on high in-rush currents and usually protect solid-state devices. Using a current-limiting resistor will protect the SSR; however, it creates a voltage drop that is current dependent and, at high current, dissipates high power. A common technique for protecting solid-state switching elements against high dv/dt transients is by shunting the switching element with an RC network (snubber), as shown in Fig. 13-23. The following equations provide effective results: L dv R 1 = --- u -----V dt

(13-19)

Load Snubber protection

Figure 13-23. Snubber circuit for solid-state relay protection.

13.2.6.3 High-Peak-Transient-Voltage Protection Where high-peak-voltage transients occur, effective protection can be obtained by using metal-oxide varistors (MOVs). The MOV is a bidirectional voltagesensitive device that becomes low impedance when its design voltage threshold is exceeded. Fig. 13-24 shows how the proper MOV can be chosen. The peak nonrepetitive voltage (VDSM) of the selected relay is transposed to the MOV plot of peak voltage versus peak amperes. The corresponding current for that peak voltage is read off the chart. Using this value of current (I) in

1 – PF dv R 2 = ---------------------------- u -----2Sf dt

(13-20)

V DSM = V p – IR

4L C = -----2 R2

(13-21)

where, I is the current, Vp is the peak instantaneous voltage transient, R is the load plus source resistance.

4 V 1 – PF C = -------2- u --- u ----------------------I 2SF R2 where,

(13-22)

(13-23)

It is important that the VDSM peak nonrepetitive voltage of the SSR is not exceeded. The energy rating of the MOV must not be exceeded by the value of

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Chapter 13

E = V DSM u I u t

(13-24) Manufacturer’s max volt-ampere characteristics

Vp VDSM Peak volts Vnom max Vnom rms T

I–Apeak IR R

VP VDSM MOV

I Metal-oxide varistor surge suppression SSR

IR > VP VDSM Energy > VDSM × l × T

Figure 13-24. Metal-oxide varistor peak transient protector.

13.2.6.4 Low Load Current Protection If the load current is low, it may be necessary to take special precautions to ensure proper operation. Solid-state relays have a finite off-state leakage current. SSRs also need a minimum operating current to latch the output device. If the off-state voltage across the load is very high, it could cause problems with circuit dropout and component overheating. In these applications a low-wattage incandescent lamp in parallel with the load offers a simple remedy. The nonlinear characteristics of the lamp allow it to be of lower resistance in the off state while conserving power in the on state. It must be remembered to size the SSR for the combined load.

The light-emitting diode requires only 1.5 V to energize and has very rapid response time. The power circuit consists of a high-speed phototransistor and an SCR for dc power source, as well as a triac for ac application. The relay not only responds with high speed but is also capable of very fast repetitious operation and provides very brief delays in turnoff. In some applications, the photocoupler housing provides a slotted opening between the continuously lit light-emitting diode and the phototransistor. On–off control is provided by a moving arm, vane, or other mechanical device that rides in the slot and interrupts the light beam in accordance with some external mechanical motion. Typical optically coupled SSRs have the following characteristics: Turn-on control voltage Isolation dv/dt Pickup control voltage Dropout control voltage One-cycle surge (rms) 1 second overload Maximum contact voltage drop

3–30 Vdc 1500 Vac 100 V/μs 3 Vdc 1 Vdc 7–10 times nominal 2.3 times nominal 1.5–4 V

13.2.6.6 Transformer-Coupled Solid-State Relays In Fig. 13-22B, the dc control signal is changed to ac in a converter circuit, the output of which is magnetically coupled to the triac trigger circuit by means of a transformer. Since there is no direct electrical connection between the primary and secondary of the transformer, control/power-circuit isolation is provided up to the voltage withstanding limit of the primary/secondary insulation.

13.2.6.5 Optically Coupled Solid-State Relays The optically coupled solid-state relay arrangement (SSR) shown in Fig. 13-22A is capable of providing the highest control/power-circuit isolation—many thousands of volts in compact, convenient form. The triac trigger circuit is energized by a phototransistor, a semiconductor device (encapsulated in transparent plastic) whose collector-emitter current is controlled by the amount of light falling on its base region. A phototransistor is mounted in a light-tight chamber with a light-emitting diode, the separation between them being enough to give high isolation (thousands of volts) between the control and power circuit.

13.2.6.7 Direct-Coupled Solid-State Relays The circuit shown in Fig. 13-22C cannot truly be called a solid-state relay because it does not have isolation between input and output. It is the simplest configuration; no coupling device is interposed between the control and actuating circuits, so no isolation of the control circuit is provided. This circuit would be better called an amplifier. One other variation of these solid-state circuits is occasionally encountered—the Darlington circuit. A typical arrangement is shown in Fig. 13-25. Actually a pair of cascaded power transistors, this circuit is used in

Heatsinks and Relays many solid-state systems to achieve very high power gain—1000 to 10,000 or more. Now marketed in single-transistor cases, it can be obtained as what appears to be a single transistor with high operating voltage ratings that control high amperage loads with only a few volts at the base connection and draw only a few milliamperes from the control circuit. It can be used for relay purposes in a dc circuit the same way, either by direct control signal coupling or with intermediate isolation devices like those described. It is not usable in ac power circuits.

391

Control power Delay Output switching A. On delay. Continuous power Control switch Delay

Output switching

B. Nontotalizer. Control signal

Load

Continuous power Control switch

Figure 13-25. Darlington direct-coupled solid-state relay.

Output switching D D D D C. Totalizer/preset counter.

13.2.6.8 Solid-State Time-Delay Relays10 Solid-state time-delay relays, Fig. 13-26, can operate in many different modes since they do not rely on heaters or pneumatics. Simple ICs allow the relays to do standard functions plus totaling, intervals, and momentary action as described in the following. On-Delay. Upon application of control power, the time-delay period begins. At the end of time delay, the output switch operates. When control power is re moved, the output sw itch returns to normal, Fig. 13-26A. Nontotalizer. Upon the opening of the control switch, the time-delay period begins. However, any control switch closure prior to the end of the time delay will immediately recycle the timer. At the end of the time-delay period, the output switch operates and remains operated until the required continuous power is interrupted, as shown in Fig. 13-26B. Totalizer/Preset Counter. T h e o u t p u t s w i t c h w i l l operate when the sum of the individual control switch closure durations equal the preset time-delay period. There may be interruptions between the control switch closures without substantially altering the cumulative timing accuracy. The output switch returns to normal when the continuous power is interrupted, as shown in Fig. 13-26C. Off-Delay. Upon closure of the control switch, the output switch operates. Upon opening of the control

Continuous power Control switch Output switching Delay D. Off delay. Control power Output switching Delay E. Interval. Continuous power Control switch Output switching Delay F. Momentary actuation.

Figure 13-26. Types of time-delay relays.

switch, the time-delay period begins. However, any control switch closure prior to the end of the time-delay period will immediately recycle the timer. At the end of the time-delay period, the output switch returns to

392

Chapter 13

normal. Continuous power must be furnished to this timer, as shown in Fig. 13-26D. Interval. Upon application of the control power, the output switch operates. At the end of the time-delay period, the output switch returns to normal. Control power must be interrupted in order to recycle, as shown in Fig. 13-26E.

programmable timing ranges from 0.1 s to 120 min and the relay has 10 A DPDT contacts. An eight position DIP switch is used to program the timing function and a calibrated knob is used to set the timing.

Momentary Actuation. Upon closure of the control switch, the output switch operates, and the time-delay period begins. The time-delay period is not affected by duration of the control switch closure. At the end of the time-delay period, the output switch returns to normal. Continuous power must be furnished to this timer, as shown in Fig. 13-26F. Programmable Time-Delay Relay. P r o g r a m m a b l e time-delay relays are available where the time and functions can be programmed by the user. The Magnecraft W211PROGX-1 relay in Fig. 13-27 is an example of this type. It plugs into an octal socket, has ±0.1% repeatability and four input voltage ranges. It has four programmable functions, On Delay, Off Delay, One Shot, and On Delay and Off Delay. There are 62

Figure 13-27. A programmable time delay relay. Courtesy Magnecraft Electric Co.

References 1.

Logan Hedin, TenHex and Gary Arnold, Thermal Design of an LED Commercial Florescent Tube, Cool Polymers; Presented at IMAPs New England 2008 35th Symposium.

Solver-Calc©, An Excel Spreadsheet Program for Rapid Thermal Management Calculations, by Villaume Associates, LLC, www.thermalseminars.com.

Heat pipes have become increasingly useful in spreading heat loads and moving heat to an area where the convective fin surface area may be more effectively positioned in the available air flow path. “Google” for vendors as there are quite a few suppliers of this component in a thermal solution.

TPG is a product designator for highly oriented pyrolytic graphite offered by Momentive Performance Materials in Ohio. The in plane thermal conductivity is ~1750 W/m°K. It can perform in high watt density (> 80 W/in²) applications without suffering “burn-out” failures that are possible with regular heat pipes.

Two major suppliers; Wakefield Thermal Solutions, Pelham, N.H., and Cool Options Inc., Warwick, R.I.

Designer’s Handbook and Catalog of Reed and Mercury Wetted Contact Relays, Chicago: Magnecraft Electric Co.

“Relay Loads” Electronic Design 26, December 20, 1978.

Solid-State Relays, Chicago: Magnecraft Electric Co.

10. Designer's Handbook and Catalog of Time-Delay Relays, Chicago: Magnecraft Electric Co. 11. Coto Technology Reed Relays and Dry Reed Switches, Coto Technology.

14 Transmission Techniques: Wire and Cable Chapter

by Steve Lampen and Glen Ballou 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 Resistance and Wire Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.2 Calculating Wire Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.3 Resistance and Gage Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.4 Drawing and Annealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.5 Plating and Tinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.6 Conductor Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.6.1 Stranded Cables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.7 Pulling Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.8 Skin Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.9 Current Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.9.1 Wire Current Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.1 Plastics and Dielectric Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2 Wire Insulation Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 Jackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.1 Vinyl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.2 Polyethylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.3 Teflon® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.4 Polypropylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6 Thermoset Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.1 Silicone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.2 Neoprene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.3 Rubber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.4 EPDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.7 Single Conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.8 Multiconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.8.1 Multiconductor Insulation Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9 Pairs and Balanced Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.1 Multipair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.2 Analog Multipair Snake Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3 High Frequency Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.1 DVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.2 HDMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.3 IEEE -1394 or FireWire Serial Digital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

393

397 397 397 397 398 399 399 399 400 401 402 402 403 403 403 405 405 405 405 405 406 406 406 406 406 406 406 406 407 407 407 408 408 409 409 410 410

14.9.3.4 USB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.5 DisplayPort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6 Premise/Data Category Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.1 Cabling Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.2 Structured Cabling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.3 Types of Structured Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.4 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.5 Critical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.6 Terminating Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.7 Baluns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.8 Adaptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.9 Power Over Ethernet (PoE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.9.3.6.10 Power Over Ethernet Plus (PoE Plus) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10 Coaxial Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.1 History of Coaxial Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.2 Coaxial Cable Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.2.1 CCTV Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.2.1.1 CCTV Distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.2.2 CATV Broadband Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.3 Coaxial Cable Installation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.3.1 Indoor Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.3.2 Outdoor Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.4 Coaxial Cable Termination Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.4.1 Soldering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.4.2 Crimping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.4.3 Twist-On Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.4.4 Compression Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.5 Return Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.6 Video Triaxial Cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.7 S-Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.8 RGB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.10.9 VGA and Family. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11 Digital Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11.1 Digital Signals and Digital Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11.2 Coax and SDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11.3 Cables and SDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11.4 Receiver Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.11.5 Serial Digital Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.12 Radio Guide Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.13 Velocity of Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14 Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.1 Serve or Spiral Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.2 Double Serve Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.3 French BraidTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.4 Braid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.5 Foil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.6 Combination Shields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.6.1 Foil + Serve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.6.2 Foil + Braid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.14.6.3 Foil + Braid + Foil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

394

411 411 412 412 412 412 413 414 416 416 417 417 417 418 418 418 419 419 419 419 419 420 420 420 420 420 420 420 421 421 421 422 422 422 422 422 423 423 424 424 425 425 425 426 426 426 426 427 427 427

14.14.6.4 Foil + Braid + Foil + Braid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.15 Shield Current Induced Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.16 Grounds of Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.16.1 Ground Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.16.2 Telescopic Grounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.17 UTP and Audio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.17.1 So Why Shields? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.18 AES/EBU Digital Audio Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.18.1 AES/EBU Digital Coaxial Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.19 Triboelectric Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.20 Conduit Fill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.21 Long Line Audio Twisted Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.22 Delay and Delay Skew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.23 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.24 Characteristic Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.25 Characteristic Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.26 Twisted-Pair Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.26.1 Transmission Line Termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.27 Loudspeaker Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.27.1 Damping Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.27.2 Crosstalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28 National Electrical Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.1 Designation and Environmental Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.2 Cable Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.3 NEC Substitution Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.4 Final Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.5 Plenum Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.6 Power Distribution Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.6.1 Ground-Fault Interrupters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.7 AC Power Cords and Receptacles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.8 Shielded Power Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.28.9 International Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

395

427 427 427 428 428 429 429 430 430 430 431 431 431 432 432 433 434 435 435 437 437 438 439 440 440 440 441 442 442 443 444 445 448 448

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Transmission Techniques: Wire and Cable 14.1 Introduction It was not long ago that wire was the only method to inexpensively and reliably transmit sound or pictures from one place to another. Today we not only have wire, but we also have fiber optics, and wireless radio frequency (RF) transmission from Blu-tooth to wireless routers, cell phones, and microwave and satellite delivery. RF transmission is discussed briefly in Chapter 16.10, Wireless Microphones. This chapter will discuss the various forms of wire and cable used in audio and video. Wire is a single conductive element. Wire can be insulated or uninsulated. Cable, on the other hand, is two or more conductive elements. While they theoretically could be uninsulated, the chance of them touching each other and creating a short circuit requires that they are usually both insulated. A cable can be multiple insulated wires, called a multiconductor cable, or wires that are twisted together, called a twisted pair cable, or cables with one wire in the center, surrounded by insulation and then a covering of metal used as another signal path, called coaxial cable.

14.2 Conductors Wire and cable are used to connect one circuit or component to another. They can be internal, connecting one circuit to another inside a box, or externally connecting one box to another. 14.2.1 Resistance and Wire Size Wire is made of metal, or other conductive compounds. All wire has resistance which dissipates power through heat. While this is not apparent on cables with small signals, such as audio or video signals, it is very apparent where high power or high current travels down a cable, such as a power cord. Resistance is related to the size of the wire. The smaller the wire, the greater the resistance. 14.2.2 Calculating Wire Resistance The resistance for a given length of wire is determined by: KL (14-1) R = ------2 d where, R is the resistance of the length of wire in ohms,

397

K is the resistance of the material in ohms per circular mil foot, L is the length of the wire in feet, d is the diameter of the wire in mils. The resistance, in ohms per circular mil foot (:/cir mil ft), of many of the materials used for conductors is given in Table 14-1. The resistance shown is at 20°C (68°F), commonly called room temperature. Table 14-1. Resistance of Metals and Alloys Material Silver Copper Gold Chromium Aluminum Tungsten Molybdenum High-brass Phosphor-bronze Nickel, pure Iron Platinum Palladium Tin Tantalum Manganese-nickel Steel Lead Nickel-silver Alumel Arsenic Monel Manganin Constantan Titanium Chromel Steel, manganese Steel, stainless Chromax Nichrome V Tophet A Nichrome Kovar A

Symbol Ag Cu Au Cr Al W Mo Cu-Zn Sn-P-Cu Ni Fe Pt Pd Sn Ta Ni-Mn C-Fe Pb Cu-Zn-Ni Ni-Al-Mn-Si As Ni-Cu-Fe-Mn Cu-Mn-Ni Cu-Ni Ti Ni-Cr Mn-C-Fe C-Cr-Ni-Fe Cr-Ni-Fe Ni-Cr Ni-Cr Ni-Fe-Cr Ni-Co-Mn-Fe

Resistance

:/cir mil ft) 9.71 10.37 14.55 15.87 16.06 33.22 34.27 50.00 57.38 60.00 60.14 63.80 65.90 69.50 79.90 85.00 103.00 134.00 171.00 203.00 214.00 256.00 268.00 270.00 292.00 427.00 427.00 549.00 610.00 650.00 659.00 675.00 1732.00

When determining the resistance of a twisted pair, remember that the length of wire in a pair is twice the length of a single wire. Resistance in other construc-

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tions, such as coaxial cables, can be difficult to determine from just knowing the constituent parts. The center conductor might be easy to determine but a braid or braid + foil shield can be difficult. In those cases, consult the manufacturer. Table 14-1 show the resistance in ohms (ȍ) per foot per circular mil area for various metals, and combinations of metals (alloys). Of the common metals, silver is the lowest resistance. But silver is expensive and hard to work with. The next material, copper, is significantly less expensive, readily available, and lends itself to being annealed, which is discussed in Section 14.2.4. Copper is therefore the most common material used in the manufacture of wire and cable. However, where price is paramount and performance not as critical, aluminum is often used. The use of aluminum as the conducting element in a cable should be an indication to the user that this cable is intended to be lower cost and possibly lower performance. One exception to this rule might be the use of aluminum foil which is often used in the foil shielding of even expensive high-performance cables. Another exception is emerging for automobile design, where the weight of the cable is a major factor. Aluminum is significantly less weight than copper, and the short distances required in cars means that resistance is less of a factor. Table 14-1 may surprise many who believe, in error, that gold is the best conductor. The advantage of gold is its inability to oxidize. This makes it an ideal covering for articles that are exposed to the atmosphere, pollution, or moisture such as the pins in connectors or the connection points on insertable circuit boards. As a conductor, gold does not require annealing, and is often used in integrated circuits since it can be made into very fine wire. But, in normal applications, gold would make a poor conductive material, closer to aluminum in performance than copper. One other material on the list commonly found in cable is steel. As can be seen, this material is almost ten times the resistance of copper, so many are puzzled by its use. In fact, in the cables that use steel wires, they are coated with a layer of copper, called copper-clad steel and signal passes only on the copper layer, an effect called skin effect that will be discussed in Section 14.2.8. Therefore, the steel wire is used for strength and is not intended to carry signals. Copper-clad steel is also found in cables where cable pulling strength (pulling tension) is paramount. Then a stranded conductor can be made up of many copper-clad steel strands to maximize strength. Such a

cable would compromise basic resistive performance. As is often the case, one can trade a specific attribute for another. In this case, better strength at the cost of higher resistance.

14.2.3 Resistance and Gage Size

In the United States, wire is sized by the American Wire Gage (AWG) method. AWG was based on the previous Brown and Sharpe (B & S) system of wire sizes which dates from 1856. AWG numbers are most common in the United States, and will be referred to throughout this book. The wire most often used in audio ranges from approximately 10 AWG to 30 AWG, although larger and smaller gage sizes exist. Wire with a small AWG number, such as 4 AWG, is very heavy, physically strong but cumbersome, and has very low resistance, while wire of larger numbers, such as 30 AWG can be very light weight and fragile, and has high resistance. Resistance is an important factor in determining the appropriate wire size in any circuit. For instance, if an 8 : loudspeaker is being connected to an amplifier 500 ft away through a #19 wire, 50% of the power would be dropped in the wire in the form of heat. This is discussed in Section 14.25 regarding loudpeaker cable. Each time the wire size changes three numbers, such as from 16 AWG to 19 AWG the resistance doubles. The reverse is also true. With a wire changed from 16 AWG to 13 AWG, the resistance halves. This also means that combining two identical wires of any given gage decreases the total gage of the combined wires by three units, and reduces the resistance. Two 24 AWG wires combined (twisted together) would be 21 AWG, for instance. If wires are combined of different gages, the resulting gage can be easily calculated by adding the circular mil area (CMA) shown in Tables 14-2 and 14-3. For instance, if three wires were combined, one 16 AWG (2583 CMA), one 20 AWG (1022 CMA) and one 24 AWG (404 CMA), the total CMA would be 2583 + 1022 + 404 = 4009 CMA. Looking in Table 14-1, this numbers falls just under 14 AWG. While even number gages are the most common, odd number gages (e.g., 23 AWG) can sometimes be found. There are many Category 6 (Cat 6) premise/data cables that are 23 AWG, for instance. When required, manufacturers can even produce partial gages. There are coaxial cables with 28.5 AWG center conductors. Such specialized gage sizes might require equally special connectors.

Transmission Techniques: Wire and Cable There are two basic forms of wire, solid and stranded. A solid conductor is one continuous piece of metal. A stranded conductor is made of multiple smaller wires combined to make a single conductor. Solid wire has slightly lower resistance, with less flexibility and less flex-life (flexes to failure) than stranded wire.

14.2.4 Drawing and Annealing Copper conductors start life as copper ore in the ground. This ore is mined, refined, and made into bars or rod. Five sixteenth inch copper rod is the most common form used for the making of wire and cable. Copper can be purchased at various purities. These commonly follow the ASTM (American Society for Testing and Materials) standards. Most of the high-purity copper is known as ETP, electrolytic tough pitch. For example, many cable products are manufactured with ASTM B115 ETP. This copper is 99.95% pure. Copper of higher purity can be purchased should the requirement arise. Many consumer audiophiles consider these to be oxygen free, when this term is really a discussion of copper purity and is determined by the number of nines of purity. The cost of the copper rises dramatically with each “9” that is added. To turn 5 / 16 inch rod into usable wire, the copper rod is drawn through a series of dies. Each time it makes the rod slightly smaller. Eventually you can work the rod down to a very long length of very small wire. To take 5 / 16 inch rod down to a 12 AWG wire requires drawing the conductor through eleven different dies. Down to 20 AWG requires fifteen dies. To take that wire down to 36 AWG requires twenty-eight dies. The act of drawing the copper work hardens the material making it brittle. The wire is run through an in-line annealing oven, at speeds up to 7000 feet per minute, and a temperature of 900 to 1000°F (482 to 537°C). This temperature is not enough to melt the wire, but it is enough to let the copper lose its brittleness and become flexible again, to reverse the work hardening. Annealing is commonly done at the end of the drawing process. However, if the next step requires more flexibility, it can be annealed partway through the drawing process. Some manufacturers draw down the wire and then put the entire roll in an annealing oven. In order to reduce oxygen content, some annealing ovens have inert atmospheres, such as nitrogen. This increases the purity of the copper by reducing the oxygen content. But in-line annealing is more consistent than a whole roll in an oven.

399

Lack of annealing, or insufficient annealing time or temperature, can produce a conductor which is stiff, brittle, and prone to failure. With batch annealing, the inner windings in a roll may not be heated as effectively as the outer windings. Cables made in other countries may not have sufficient purity for high-performance applications. Poor--quality copper, or poor annealing, are very hard to tell from initial visual inspection but often shows up during or after installation. 14.2.5 Plating and Tinning Much of the wire manufactured is plated with a layer of tin. This can also be done in-line with the drawing and annealing by electroplating a layer on the wire. Tinning makes the wire especially resistant to pollutants, chemicals, salt (as in marine applications). But such a plated conductor is not appropriate for high-frequency applications where the signal travels on the skin of the conductor, called skin effect. In that case, bare copper conductors are used. The surface of a conductor used for high frequencies is a major factor in good performance and should have a mirror finish on that surface. Wires are occasionally plated with silver. While silver is slightly more conductive, its real advantage is that silver oxide is the same resistance as bare silver. This is not true with copper, where copper oxide is a semiconductor. Therefore, where reactions with a copper wire are predicted, silver plating may help preserve performance. So silver plating is sometimes used for marine cables, or cables used in similar outdoor environments. Some plastics, when extruded (melted) onto wires, can chemically affect the copper. This is common, for instance, with an insulation of extruded TFE (tetrafluoroethylene), a form of Teflon™. Wires used inside these cables are often silver plated or silver-clad. Any oxidizing caused by the extrusion process therefore has no effect on performance. Of course, just the cost of silver alone makes any silver-plated conductor significantly more expensive than bare copper.

14.2.6 Conductor Parameters Table 14-2 shows various parameters for solid wire from 4 AWG to 40 AWG. Table 14-3 shows the same parameters for stranded wire. Note that the resistance of a specific gage of solid wire is lower than stranded wire of the same gage. This is because the stranded wire is not completely conductive; there are spaces (interstices) between

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the strands. It takes a larger stranded wire to equal the resistance of a solid wire.

Table 14-2. Parameters for Solid Wire from 4 AWG to 40 AWG AWG Nominal CMA Diameter (×1000)

Bare lbs/ft

:/100 Current MM2 0 ft

Equivalent

0.2043

41.7

0.12636

0.25

59.57

21.1

0.1819

33.1

0.10020

0.31

47.29

16.8

0.162

26.3

0.07949

0.4

37.57

13.3

0.1443

20.8

0.06301

0.5

29.71

10.6

0.1285

16.5

0.04998

0.63

23.57

8.37

0.1144

13.1

0.03964

0.8

18.71

6.63

0.1019

10.4

0.03143

14.86

5.26

0.0907

8.23

0.02493

1.26

11.76

4.17

0.0808

6.53

0.01977

1.6

9.33

3.31

0.075

5.18

0.01567

2.01

7.40

2.62

0.0641

4.11

0.01243

2.54

5.87

2.08

0.0571

3.26

0.00986

3.2

4.66

1.65

0.0508

2.58

0.00782

4.03

3.69

1.31

0.0453

2.05

0.00620

5.1

2.93

1.04

0.0403

1.62

0.00492

6.4

2.31

0.823

0.0359

1.29

0.00390

8.1

1.84

0.653

0.032

1.02

0.00309

10.1

1.46

0.519

0.0285

0.81

0.00245

12.8

1.16

0.412

0.0254

0.642

0.00195

16.2

0.92

0.324

0.0226

0.51

0.00154

20.3

0.73

0.259

0.0201

0.404

0.00122

25.7

0.58

0.205

0.0179

0.32

0.00097

32.4

0.46

0.162

0.0159

0.253

0.00077

0.36

0.128

0.0142

0.202

0.00061

51.4

0.29

0.102

0.0126

0.159

0.00048

65.3

0.23

0.08

0.0113

0.127

0.00038

81.2

0.18

0.0643

0.01

0.1

0.00030

104

0.14

0.0507

0.0089

0.0797

0.00024

131

0.11

0.0401

0.008

0.064

0.00019

162

0.09

0.0324

0.0071

0.0504

0.00015

206

0.07

0.0255

0.0063

0.0398

0.00012

261

0.06

0.0201

0.0056

0.0315

0.00010

331

0.05

0.0159

0.005

0.025

0.00008

415

0.04

0.0127

0.0045

0.0203

0.00006

512

0.03

0.0103

0.004

0.016

0.00005

648

0.02

0.0081

0.0035

0.0123

0.00004

847

0.02

0.0062

0.003

0.0096

0.00003

1080

0.01

0.0049

14.2.6.1 Stranded Cables. Stranded cables are more flexible, and have greater flex-life (flexes to failure) than solid wire. Table 14-4 shows some suggested construction values. The two numbers (65 × 34, for example) show the number of strands (65) and the gage size of each strand (34) for each variation in flexing. Table 14-3. Parameters for ASTM Class B Stranded Wires from 4 AWG to 40 AWG AWG Nominal CMA Diameter (×1000)

Bare lbs/ft

:/ 1000 ft

Current MM2 A* Equivalent

4 0.232 53.824 0.12936 0.253 59.63 27.273 5 0.206 42.436 0.10320 0.323 47.27 21.503 6 0.184 33.856 0.08249 0.408 37.49 17.155 7 0.164 26.896 0.06601 0.514 29.75 13.628 8 0.146 21.316 0.05298 0.648 23.59 10.801 9 0.13 16.9 0.04264 0.816 18.70 8.563 10 0.116 13.456 0.03316 1.03 14.83 6.818 11 0.103 10.609 0.02867 1.297 11.75 5.376 12 0.0915 8.372 0.02085 1.635 9.33 4.242 13 0.0816 6.659 0.01808 2.063 8.04 3.374 14 0.0727 5.285 0.01313 2.73 5.87 2.678 15 0.0647 4.186 0.01139 3.29 4.66 2.121 16 0.0576 3.318 0.00824 4.35 3.69 1.681 17 0.0513 2.632 0.00713 5.25 2.93 1.334 18 0.0456 2.079 0.00518 6.92 2.32 1.053 19 0.0407 1.656 0.00484 8.25 1.84 0.839 20 0.0362 1.31 0.00326 10.9 1.46 0.664 21 0.0323 1.043 0.00284 13.19 1.16 0.528 22 0.0287 0.824 0.00204 17.5 0.92 0.418 23 0.0256 0.655 0.00176 20.99 0.73 0.332 24 0.0228 0.52 0.00129 27.7 0.58 0.263 25 0.0203 0.412 0.01125 33.01 0.46 0.209 26 0.018 0.324 0.00081 44.4 0.36 0.164 27 0.0161 0.259 0.00064 55.6 0.29 0.131 28 0.0143 0.204 0.00051 70.7 0.23 0.103 29 0.0128 0.164 0.00045 83.99 0.18 0.083 30 0.0113 0.128 0.00032 112 0.14 0.0649 31 0.011 0.121 0.00020 136.1 0.11 0.0613 32 0.009 0.081 0.00020 164.1 0.09 0.041 33 0.00825 0.068 0.00017 219.17 0.07 0.0345 34 0.0075 0.056 0.00013 260.9 0.06 0.0284 35 0.00675 0.046 0.00011 335.96 0.04 0.0233 36 0.006 0.036 0.00008 414.8 0.04 0.0182 37 0.00525 0.028 0.00006 578.7 0.03 0.0142 38 0.0045 0.02 0.00005 658.5 0.02 0.0101 39 0.00375 0.014 0.00004 876.7 0.02 0.0071 40 0.003 0.009 0.00003 1028.8 0.01 0.0046 *For both solid and stranded wire, amperage is calculated at 1 A for each 700 CMA. See also Section 14.2.9.

Transmission Techniques: Wire and Cable

401

Table 14-4. Suggested Conductor Strandings for Various Degrees of Flexing Severity Typical Applications

AWG

19 × 25

19 × 0.455

Solid 19 × 27

19 × 0.361

65 × 30

65 × 0.254

19 × 27 41 × 30

19 × 0.361 41 × 0.254

165 × 0.160

104 × 34

12 AWG Fixed Service (Hook-Up Wire Cable in Raceway) Moderate Flexing (Frequency Disturbed for Maintenance) Severe Flexing (Microphones and Test Prods)

165 × 34

mm 14 AWG

16 AWG

104 × 0.160 18 AWG

Fixed Service (Hook-Up Wire Cable in Raceway)

Solid 19 × 29

19 × 0.287

Solid 7 × 26 16 × 30

7 × 0.404 16 × 0.254

Moderate Flexing (Frequently Disturbed for Maintenance)

19 × 29 26 × 30

19 × 0.287 26 × 0.254

16 × 30 41 × 34

16 × 0.254 41 × 0.160

65 × 34 104 × 36

65 × 0.160 104 × 0.127

41 × 34 65 × 36

41 × 0.160 65 × 0.127

Severe Flexing (Microphones, Test Prods)

20 AWG

22 AWG

Fixed Service (Hook-Up Wire Cable in Raceway)

Solid 7 × 28 10 × 30

7 × 0.320 10 × 0.254

Moderate Flexing (Frequency Distributed for Maintenance)

7 × 28 10 × 30 19 × 32 26 × 34

7 × 0.320 10 × 0.254 19 × 0.203 26 × 0.160

26 × 34 42 × 36

26 × 0.160 42 × 0.127

Severe Flexing (Microphones, Test Prods)

Solid 7 × 30

7 × 0.254

7 × 30

7 × 0.254

19 × 34

19 × 0.160

19 × 34 26 × 36

19 × 0.160 26 × 0.127

24 AWG Fixed Service (Hook-Up Wire Cable in Raceway)

26 AWG Solid 7 × 34

7 × 0.160

7 × 0.203 10 × 0.160

7 × 34

7 × 0.160

19 × 0.127 45 × 0.079

7 × 34 10 × 36

7 × 0.160 10 × 0.127

Solid 7 × 32

7 × 0.203

Moderate Flexing (Frequently Disturbed for Maintenance)

7 × 32 10 × 34

Severe Flexing (Microphones, Test Prods)

19 × 36 45 × 40

Courtesy Belden

14.2.7 Pulling Tension Pulling tension must be adhered to so the cable will not be permanently elongated. The pulling tension for annealed copper conductors is shown in Table 14-5. Multiconductor cable pulling tension can be determined by multiplying the total number of conductors by the appropriate value. For twisted pair cables, there are two wires per pair. For shielded twisted pair cables, with foil shields, there is a drain wire that must be included in the calculations. Be cautious: the drain wire can sometimes be smaller gage than the conductors in the pair. The pulling tension of coaxial cables or other cables that are not multiple conductors is much harder

to calculate. Consult the manufacturer for the required pulling tension. Table 14-5. Pulling Tension for Annealed Copper Conductors 24 AWG

5.0 lbs

22 AWG

7.5 lbs

20 AWG

12.0 lbs

18 AWG

19.5 lbs

16 AWG

31.0 lbs

14 AWG

49.0 lbs

12 AWG

79.0 lbs

402

Chapter 14

14.2.8 Skin Effect

Table 14-6. Skin Depths at Various Frequencies

As the frequency of the signal increases on a wire, the signal travels closer to the surface of the conductor. Since very little of the area of the center conductor is used at high frequencies, some cable is made with a copper clad-steel core center conductor. These are known as copper-clad, copper-covered, or Copperweld™ and are usually used by CATV/broadband service providers. Copper-clad steel is stronger than copper cable so it can more easily withstand pulling during installation, or wind, ice, and other outside elements after installation. For instance, a copper-clad #18 AWG coaxial cable has a pull strength of 102 lbs while a solid copper #18 AWG coax would have a pull strength of 69 lbs. The main disadvantage is that steel is not a good conductor below 50 MHz, between four and seven times the resistance of copper, depending on the thickness of the copper layer. This is a problem where signals are below 50 MHz s u c h a s D O C S I S d a t a d e l i v e r y, o r V O D (video-on-demand) signals which are coming from the home to the provider. When installing cable in a system, it is better to use solid copper cable so it can be used at low frequencies as well as high frequencies. This is also why copper-clad conductors are not appropriate for any application below 50 MHz, such as baseband video, CCTV, analog, or digital audio. Copper-clad is also not appropriate for applications such as SDI or HD-SDI video, and similar signals where a significant portion of the data is below 50 MHz. The skin depth for copper conductors can be calculated with the equation D = 2.61 ---------f where, D is the skin depth in inches, f is the frequency in hertz.

(14-2)

Table 14-6 compares the actual skin depth and percent of the center conductor actually used in an RG-6 cable. The skin depth always remains the same no matter what the thickness of the wire is. The only thing that changes is the percent of the conductor utilized. Determining the percent of the conductor utilized requires using two times the skin depth because we are comparing the diameter of the conductor to its depth. As can be seen, by the time the frequencies are high, the depth of the signal on the skin can easily be microinches. For signals in that range, such as high-definition video signals, for example, this means that the

Frequency Skin Depth in Inches

% Used of #18 AWG Conductor

1 kHz

0.082500

100

10 kHz

0.026100

100

100 kHz

0.008280

1 MHz

0.002610

10 MHz

0.000825

100 MHz

0.000261

4.1 1.3

1 GHz

0.0000825

0.41

10 GHz

0.0000261

0.13

surface of the wire is as critical as the wire itself. Therefore, conductors intended to carry high frequencies should have a mirror finish. Since the resistance of the wire at these high frequencies is of no consequence, it is sometimes asked why larger conductors go farther. The reason is that the surface area, the skin, on a wire is greater as the wire gets larger in size. Further, some conductors have a tin layer to help prevent corrosion. These cables are obviously not intended for use at frequencies above just a few megahertz, or a significant portion of the signal would be traveling in the tin layer. Tin is not an especially good conductor as can be seen in Table 14-1.

14.2.9 Current Capacity For conductors that will carry large amounts of electrical flow, large amperage or current from point to point, a general chart has been made to simplify the current carrying capacity of each conductor. To use the current capacity chart in Fig. 14-1, first determine conductor gage, insulation and jacket temperature rating, and number of conductors from the applicable product description for the cable of interest. These can usually be obtained from a manufacturer’s Web site or catalog. Next, find the current value on the chart for the proper temperature rating and conductor size. To calculate the maximum current rating/conductor multiply the chart value by the appropriate conductor factor. The chart assumes the cable is surrounded by still air at an ambient temperature of 25°C (77°F). Current values are in amperes (rms) and are valid for copper conductors only. The maximum continuous current rating for an electronic cable is limited by conductor size, number of conductors contained within the cable, maximum temperature rating of the insulation on the conductors,

Transmission Techniques: Wire and Cable

limited by the current carrying capacity of the wire but of the termination point.

100 80 60 40 30 Current—A

20 0

10 8 6

g g ing rat ratin ratin °C 0 15

°C

5 10

°C

14.2.9.1 Wire Current Ratings

0°

8 0&

in rat

4 3 2 1 28

403

26 24

Conductor size—AWG # Conductors* Factor # Conductors* Factor 1 1.6 6—15 0.7 2—3 1.0 16—30 0.5 4—5 0.8 * do not count shields unless used as a conductor

Figure 14-1. Current ratings for electronic cable. Courtesy Belden.

and environment conditions such as ambient temperature and air flow. The four lines marked with temperatures apply to different insulation plastics and their melting point. Consult the manufacturer’s Web site or catalog for the maximum insulation or jacket temperature. The current ratings of Fig. 14-1 are intended as general guidelines for low-power electronic communications and control applications. Current ratings for high-power applications generally are set by regulatory agencies such as Underwriters Laboratories (UL), Canadian Standards Association (CSA), National Electrical Code (NEC), and others and should be used before final installation. Table 310-15(b)(2)(a) of the NEC contains amperage adjustment factors for whenever more than three current carrying conductors are in a conduit or raceway. Section 240-3 of the NEC provides requirements for overload protection for conductors other than flexible cords and fixture wires. Section 240-3(d), Small Conductors, states that #14 to #10 conductors require a maximum protective overcurrent device with a rating no higher than the current rating listed in the 60°C column. These currents are 15 A for #14 copper wire, 20 A for #12 copper wire, and 30 A for #10 copper wire. These values are familiar as the breaker ratings for commercial installations. When connecting wire to a terminal strip or another wire etc., the temperature rise in the connections must also be taken into account. Often the circuit is not

Current carrying capacity of wire is controlled by the NEC, particularly in Table 310-16, Table 31015(b)(2)(a), and Section 240-3. Table 310-16 of the NEC shows the maximum current carrying capacity for insulated conductors rated from 0 to 2000 V, including copper and aluminum conductors. Each conductor amperage is given for three temperatures: 60°C, 75°C, and 90°C. Copper doesn’t melt until almost 2000q so the current limit on a copper wire is not the melting point of the wire but the melting point of the insulation. This number is listed by most manufacturers in their catalog or on their Web site. For instance, PVC (polyvinyl chloride) can be formulated to withstand temperatures from 60qC to as high as 105qC. The materials won’t melt right at the specified temperature, but may begin to fail certain tests, such as cracking when bent.

14.3 Insulation Wire can be bare, often called bus bar or bus wire, but is most often insulated. It is covered with a non-conducting material. Early insulations included cotton or silk woven around the conductor, or even paper. Cotton-covered house wiring can still be found in perfect operating condition in old houses. Today, most insulation materials are either some kind of rubber or some kind of plastic. The material chosen should be listed in the manufacturer’s catalog with each cable type. Table 14-7 lists some of the rubber-based materials with their properties. Table 14-8 lists the properties of various plastics. The ratings in both tables are based on average performance of general-purpose compounds. Any given property can usually be improved by the use of selective compounding.

14.3.1 Plastics and Dielectric Constant Table 14-9 is a list of various insulation materials with details on performance, requirements, and special advantages. Insulation, when used on a cable intended to carry a signal, is often referred to as a dielectric. The performance of any material, its ability to insulate with minimal effect to the signal running on the cable is called the dielectric constant and can be measured in a

404

Chapter 14

Table 14-7. Comparative Properties of Rubber Insulation. (Courtesy Belden) Properties

Rubber

Oxidation Resistance F Heat Resistance F Oil Resistance P Low Temperature Flexibility G Weather, Sun Resistance F Ozone Resistance P Abrasion Resistance E Electrical Properties E Flame Resistance P Nuclear Radiation Resistance F Water Resistance G Acid Resistance F-G Alkali Resistance F-G Gasoline, Kerosene, etc. P (Aliphatic Hydrocarbons) Resistance Benzol, Toluol, etc.(Aromatic P Hydrocarbons) Resistance Degreaser Solvents (Halogenated P Hydrocarbons) Resistance Alcohol Resistance G P = poor, F = fair, G = good, E = excellent, O = outstanding

Neoprene

Hypalon (Chlorosulfonated Polyethylene)

EPDM (Ethylene Propylene Diene Monomer)

Silicone

G G G F-G G G G-E P G F-G E G G G

E E G F E E G G G G G-E E E F

G E F G-E E E G E P G G-E G-E G-E P

E O F-G O O O P O F-G E G-E F-G F-G P-F

P-F

P-G

Table 14-8. Comparative Properties of Plastic Insulation. (Courtesy Belden) Properties

PVC

Low-Density Cellular High-Density Polyethylene Polyurethane Nylon Teflon® Polyethylene Polyethylene Polyethylene

Oxidation Resistance E E Heat Resistance G-E G Oil Resistance F G Low Temperature Flexibility P-G G-E Weather, Sun Resistance G-E E Ozone Resistance E E Abrasion Resistance F-G F-G Electrical Properties F-G E Flame Resistance E P Nuclear Radiation Resistance G G Water Resistance E E Acid Resistance G-E G-E Alkali Resistance G-E G-E Gasoline, Kerosene, etc. (AliP P-F phatic Hydrocarbons) Resistance Benzol, Toluol, etc. (Aromatic P-F P Hydrocarbons) Resistance Degreaser Solvents (HalogeP-F P nated Hydrocarbons) Resistance Alcohol Resistance G-E E P = poor, F = fair, G = good, E = excellent, O = outstanding

E G G E E E F E P G E G-E G-E P-F

E E G-E E E E E E P G E G-E G-E P-F

E E F P E E F-G E P F E E E P-F

E G E G G E O P P G P-G F F G

E E E G E E E P P F-G P-F P-F E G

O O O O O E E E O P E E E E

P-F

Transmission Techniques: Wire and Cable laboratory. Table 14-9 shows some standard numbers as a point of reference. Table 14-9. Dielectric Constant Dielectric Constant

Material

Note

Vacuum

By definition

1.0167

Air

Very close to 1

1.35

Foam, Air-filled Plastic Current technological limit

2.1

Solid Teflon™

Best solid plastic

2.3

Solid Polyethylene

Most common plastic

3.5–6.5

Solid Polyvinyl Chlo- Low price, easy to work ride with

14.3.2 Wire Insulation Characteristics The key difference between rubber compounds and plastic compounds is their recyclability. Plastic materials can be ground up, and re-melted into other objects. Polyethylene, for instance, can be recycled into plastic bottles, grocery bags, or even park benches. And, should the need arise, these objects could themselves be ground up and turned back into wire insulation, or many other uses. The term thermoplastic means changed by heat and is the source of the common term plastic. Rubber compounds, on the other hand, are thermoset. That is, once they are made, they are set, and the process cannot be reversed. Rubber, and its family, is cured in a process sometimes called vulcanizing. These compounds cannot be ground up and recycled into new products. There are natural rubber compounds (such as latex-based rubber) and artificial, chemical-based rubber compounds such as EPDM (ethylenepropylene-diene monomer). The vast majority of wire and cable insulations are plastic-based compounds. Rubber, while it is extremely rugged, is considerably more expensive that most plastics, so there are fewer and fewer manufacturers offering rubber-based products. These materials, both rubber and plastic, are used in two applications with cable. The first application is insulation of the conductor(s) inside the cable. The second is as a jacket material to protect the contents of the cable.

14.4 Jackets The jacket characteristics of cable have a large effect on its ruggedness and the effect of environment. A key consideration is often flexibility, especially at low temperatures. Audio and broadcast cables are manufactured in a

405

wide selection of standard jacketing materials. Special compounds and variations of standard compounds are used to meet critical audio and broadcast application requirements and unusual environmental conditions. Proper matching of cable jackets to their working environment can prevent deterioration due to intense heat and cold, sunlight, mechanical abuse, impact, and crowd or vehicle traffic.

14.5 Plastics Plastic is a shortened version of the term thermoplastic. Thermo means heat, plastic means change. Thermoplastic materials can be changed by heat. They can be melted and extruded into other shapes. They can be extruded around wires, for instance, forming an insulative (nonconductive) layer. There are many forms of plastic. Below is a list of the most common varieties used in the manufacture of wire and cable. 14.5.1 Vinyl Vinyl is sometimes referred to as PVC or polyvinyl chloride, and is a chemical compound invented in 1928 by Dr. Waldo Semon (USA). Extremely high or low temperature properties cannot be found in one formulation, therefore, formulations may have 55°C to +105°C (67°F to +221°F) rating while other common vinyls may have 20°C to +60°C (4°F to +140°F). The many varieties of vinyl also differ in pliability and electrical properties fitting a multitude of applications. The price range can vary accordingly. Typical dielectric constant values can vary from 3.5 at 1000 Hz to 6.5 at 60 Hz, making it a poor choice if high performance is required. PVC is one of the least expensive compounds, and one of the easiest to work with. Therefore, PVC is used with many cables that do not require high performance, or where cost of materials is a major factor. PVC is easy to color, and can be quite flexible, although it is not very rugged. In high-performance cables, PVC is often used as the jacket material, but not inside the cable. 14.5.2 Polyethylene Polyethylene, invented by accident in 1933 by E.W. Fawcett and R.O. Gibson (Great Britain), is a very good insulation in terms of electrical properties. It has a low dielectric constant value over all frequencies and very high insulation resistance. In terms of flexibility, polyethylene can be rated stiff to very hard depending on molecular weight and density. Low density is the most

406

Chapter 14

flexible and high density high molecular weight formulations are very hard. Moisture resistance is rated excellent. Correct brown and black formulations have excellent sunlight resistance. The dielectric constant is 2.3 for solid insulation and as low as 1.35 for gas-injected foam cellular designs. Polyethylene is the most common plastic worldwide.

14.6.1 Silicone Silicone is a very soft insulation which has a temperature range from 80°C to +200°C (112°F to +392°F). It has excellent electrical properties plus ozone resistance, low moisture absorption, weather resistance, and radiation resistance. It typically has low mechanical strength and poor scuff resistance. Silicone is seldom used because it is very expensive.

14.5.3 Teflon® Invented in 1937 by Roy Plunkett (USA) at DuPont, Teflon has excellent electrical properties, temperature range, and chemical resistance. It is not suitable where subjected to nuclear radiation, and it does not have good high voltage characteristics. FEP (fluorinated ethylenepropylene) Teflon is extrudable in a manner similar to vinyl and polyethylene, therefore, long wire and cable lengths are available. TFE (tetrafluoroethylene) Teflon is extrudable in a hydraulic ram-type process and lengths are limited due to amount of material in the ram, thickness of the insulation, and core size. TFE must be extruded over silver-coated or nickel-coated wire. The nickel and silver-coated designs are rated +260°C and +200°C maximum (500°F and 392°F), respectively, which is the highest temperature for common plastics. The cost of Teflon is approximately eight to ten times more per pound than vinyl insulations. The dielectric constant for solid Teflon is 2.1, the lowest of all solid plastics. Foam Teflon (FEP) has a dielectric constant as low as 1.35. Teflon is produced by and a trademark of DuPont Corporation.

14.5.4 Polypropylene Polypropylene is similar in electrical properties to polyethylene and is primarily used as an insulation material. Typically, it is harder than polyethylene, which makes it suitable for thin wall insulations. UL maximum temperature rating may be 60°C or 80°C (140°F or 176°F). The dielectric constant is 2.25 for solid and 1.55 for cellular designs.

14.6.2 Neoprene Neoprene has a maximum temperature range from 55°C to +90°C (67°F to +194°F). The actual range depends on the formulation used. Neoprene is both oil and sunlight resistant making it ideal for many outdoor applications. The most stable colors are black, dark brown, and gray. The electrical properties are not as good as other insulation material; therefore, thicker insulation must be used for the same insulation. 14.6.3 Rubber The description of rubber normally includes natural rubber and styrene-butadiene rubber (SBR) compounds. Both can be used for insulation and jackets. There are many formulations of these basic materials and each formulation is for a specific application. Some formulations are suitable for 55°C (67°F) minimum while others are suitable for +75°C (+167°F) maximum. Rubber jacketing compounds feature exceptional durability for extended cable life. They withstand high-impact and abrasive conditions better than PVC and are resistant to degradation or penetration by water, alkali, or acid. They have excellent heat resistant properties, and also provide greater cable flexibility in cold temperatures. 14.6.4 EPDM EPDM stands for ethylene-propylene-diene monomer. It was invented by Dr. Waldo Semon in 1927 (see Section 14.5.1). It is extremely rugged, like natural rubber, but can be created from petroleum byproducts ethylene and propylene gas.

14.6 Thermoset Compounds As the name implies, thermoset compounds are produced by heat (thermo) but are set. That is, the process cannot be reversed as in thermoplastics. They cannot be recycled into new products as thermoplastic materials can.

14.7 Single Conductor Single conductor wire starts with a single wire, either solid or stranded. It can be bare, sometimes called buss bar, or can be jacketed. There is no actual limit to how

Transmission Techniques: Wire and Cable small, or how large, a conductor could be. Choice of size (AWG) will be based on application and the current or wattage delivery required. If jacketed, the choice of jacket can be based on performance, ruggedness, flexibility, or any other requirement. There is no single conductor plenum rating because the NEC (National Electrical Code) only applies to cables, more than one conductor. However, Articles 300 and 310 of the NEC are sometimes cited when installing single co nductor w ire for grounds and sim ilar applications.

14.8 Multiconductor Bundles of two or more insulated wires are considered multiconductor cable. Besides the requirements for each conductor, there is often an overall jacket, chosen for whatever properties would be appropriate for a particular application. There are specialized multiconductor cables, such as power cordage used to deliver ac power from a wall outlet (or other source) to a device. There are UL safety ratings on such a cable to assure users will not be harmed. There are other multiconductor applications such as VFD (variable frequency drive) cables, specially formulated to minimize standing waves and arcing discharge when running variable frequency motors. Since a multiconductor cable is not divided into pairs, resistance is still the major parameter to be determined, although reactions between conductors (as in VFD) can also be considered.

407

14.8.1 Multiconductor Insulation Color Codes The wire insulation colors help trace conductors or conductor pairs. There are many color tables; Table 14-10 is one example.

14.9 Pairs and Balanced Lines Twisting two insulated wires together makes a twisted pair. Since two conductive paths are needed to make a circuit, twisted pairs give users an easy way to connect power or signals from point to point. Sometimes the insulation color is different to identify each wire in each pair. Pairs can have dramatically better performance than multiconductor cables because pairs can be driven as a balanced line. A balanced line is a configuration where the two wires are electrically identical. The electrical performance is referred to ground, the zero point in circuit design. Balanced lines reject noise, from low frequencies, such as 50/60 Hz power line noise, up to radio frequency signals in the Megahertz, or even higher. When the two conductors are electrically identical, or close to identical, there are many other parameters, besides resistance, that come into play. These include capacitance, inductance, and impedance. And when we get to high-frequency pairs, such as data cables, we even measure the variations in resistance (resistance unbalance), variations in capacitance (capacitance unbalance, or even variations in impedance (return loss). Each of these has a section farther on in this chapter.

Table 14-10. Color Code for Nonpaired Cables per ICEA #2 and #2R Conductor

Color

Conductor

Color

Conductor

Color

Conductor

Color

1st

Black

14th

Green/White

27th

Blue/Blk/Wht

40th

Red/Wht/Grn

2nd

White

15th

Blue/White

28th

Blk/Red/Grn

41st

Grn/Wht/Blue

3rd

Red

16th

Black/Red

29th

Wht/Red/Grn

42nd

Org/Red.Grn

4th

Green

17th

White/Red

30th

Red/Blk/Grn

43rd

Blue/Red/Grn

5th

Orange

18th

Orange/Red

31st

Grn/Blk/Org

44th

Blk/Wht/Blue

6th

Blue

19th

Blue/Red

32nd

Org/Blk/Grn

45th

Wht/Blk/Blue

7th

White/Black

20th

Red/Green

33rd

Blue/Wht/Org

46th

Red/Wht/Blue

8th

Red/Black

21st

Orange/Green

34th

Blk/Wht/Org

47th

Grn/Orn/Red

9th

Green/Black

22nd

Blk/Wht/Red

35th

Wht/Red/Org

48th

Org/Red/Blue

10th

Orange/Black

23rd

Wht/Blk/Red

36th

Org/Wht/Blue

49th

Blue/Red/Org

50th

Blk/Org/Red

11th

Blue/Black

24th

Red/Blk/Wht

37th

Wht/Red/Blue

12th

Black/White

25th

Grn/Blk/Wht

38th

Blk/Wht/Grn

13th

Red/White

26th

Org/Blk/Wht

39th

Wht/Blk/Grn

Courtesy Belden

408

Chapter 14

Balanced lines work because they have a transformer at each end, a device made of two coils of wire wound together. Many modern devices now use circuits that act electrically the same as a transformer, an effect called active balancing. The highest-quality transformers can be extremely expensive, so high-performing balanced-line chips have been improving, some getting very close to the coils-of-wire performance. It should be noted that virtually all professional installations use twisted pairs for audio because of their noise rejection properties. In the consumer world, the cable has one hot connection and a grounded shield around it and is called an unbalanced cable. These cables are effective for only short distances and have no other inherent noise rejection besides the shield itself. 14.9.1 Multipair As the name implies, multipair cables contain more than one pair. Sometimes referred to as multicore cables, these can just be grouped bare pairs, or each pair could be individually jacketed, or each pair could be shielded (shielding is outlined below), or the pairs could even be individually shielded and jacketed. All of these options are easily available. Where there is an overall jacket, or individual jackets for each pair, the jacket material for each pair is chosen with regard to price, flexibility, ruggedness, color, and any other parameter required. It should be noted that the jackets on pairs, or the overall jacket, has almost no effect on the performance of the pairs. One could make a case that, with individually jacketed pairs, the jacket moves the pairs apart and therefore improves crosstalk between pairs. It is also possible that poorly extruded jackets could leak the chemicals that make up the jacket into the pair they are

protecting, an effect called compound migration, and therefore affect the performance of the pair. Table 14-11 shows a common color code for paired cables where they are simply a bundle of pairs. The color coding is only to identify the pair and the coloring of the insulation has no effect on performance. If this cable were individually jacketed pairs, it would be likely that the two wires in the pair would be identical colors such as all black-and-red, and the jackets would use different colors to identify them as shown in Table 14-12. 14.9.2 Analog Multipair Snake Cable Originally designed for the broadcast industry, hard-wire multipair audio snake cables feature individually shielded pairs, for optimum noise rejection, and sometimes with individual jackets on each pair for improved physical protection. These cables are ideal, carrying multiple line-level or microphone-level signals. They will also interconnect audio components such as multichannel mixers and consoles for recording studios, radio and television stations, postproduction facilities, and sound system installations. Snakes offer the following features: • A variety insulation materials, for low capacitance, ruggedness, or fire ratings. • Spiral/serve, braid, French BraidTM, or foil shields. • Jacket and insulation material to meet ruggedness or NEC flame requirements. • High temperature resistance in some compounds. • Cold temperature pliability in some compounds. • Low-profile appearance, based mostly on the gage of the wires, but also on the insulation.

Table 14-11. Color Codes for Paired Cables (Belden Standard) Pair No.

Color Combination

1 Black/Red 2 Black/White 3 Black Green 4 Black/Blue 5 Black/Yellow 6 Black/Brown 7 Black/Orange 8 Red/White 9 Red/Green 10 Red/Blue Courtesy Belden

Pair No. 11 12 13 14 15 16 17 18 19 20

Color Combination Red/Yellow Red/Brown Red/Orange Green/White Green/Blue Green/Yellow Green/Brown Green/Orange White/Blue White/Yellow

Pair No. 21 22 23 24 25 26 27 28 29 30

Color Combination White/Brown White/Orange Blue/Yellow Blue/Brown Blue/Orange Brown/Yellow Brown/Orange Orange/Yellow Purple/Orange Purple/Red

Pair No. 31 32 33 34 35 36 37

Color Combination Purple/White Purple/Dark Green Purple/Light Blue Purple/Yellow Purple/Brown Purple/Black Gray/White

Transmission Techniques: Wire and Cable • Some feature overall shields to reduce crosstalk and facilitate star grounding. • Allows easier and cheaper installs than using multiple single channel cables. Snakes come with various terminations and can be specified to meet the consumer’s needs. Common terminations are male or female XLR (microphone) connectors and ¼ inch male stereo connectors on one end, and either a junction box with male or female XLR connectors and ¼ inch stereo connectors or pigtails with female XLR connectors and ¼ inch connectors on the other end. For stage applications, multipair individually shielded snake cables feature lightweight and small diameter construction, making them ideal for use as portable audio snakes. Individually shielded and jacketed pairs are easier to install with less wiring errors. In areas that subscribe to the NEC guidelines, the need for conduit in studios is eliminated when CM-rated snake cable is used through walls between rooms. Vertically between floors, snakes rated CMR (riser) do not need conduit. In plenum areas (raised floors, drop ceilings) CMP, plenum rated snake cables can be used without conduit. Color codes for snakes are given in Table 14-12. 14.9.3 High Frequency Pairs Twisted pairs were original conceived to carry low-frequency signals, such as telephone audio. Beginning in the 1970s research and development was producing cables such as twinax that had reasonable performance to the megahertz. IBM Type 1 was the breakthrough

409

product that proved that twisted-pairs could indeed carry data. This led directly to the Category premise/data cable of today. There are now myriad forms of high-frequency, high-data rate cable including DVI, USB, HDMI, IEEE 1394 FireWire, and others. All of these are commonly used to transport audio and video signals, Table 14-13.

14.9.3.1 DVI DVI (Digital Visual Interface) is used extensively in the computer-monitor interface market for flat panel LCD monitors. The DVI connection between local monitors and computers includes a serial digital interface and a parallel interface format, somewhat like combining the broadcast serial digital and parallel digital interfaces. Transmission of the TMDS (transition minimized differential signaling) format combines four differential, high-speed serial connections transmitted in a parallel bundle. DVI specifications that are extended to the dual mode operation allow for greater data rates for higher display resolutions. This requires seven parallel, differential, high-speed pairs. Quality cabling and connections become extremely important. The nominal DVI cable length limit is 4.5 m (15 ft). Electrical performance requirements are signal rise time of 0.330 ns, and a cable impedance of 100 : FEXT is less than 5%, and signal rise time degradation is a maximum of 160 ps (picoseconds). Cable for DVI is application specific since the actual bit rate per channel is 1.65 Gbps.

Table 14-12. Color Codes for Snake Cables Pair Color Pair No. Combination No.

Color Combination

Pair No.

Color Combination

Pair No.

Color Combination

Pair No.

Color Combination

1 Brown

Lt. Gray/Brown stripe 25

Lt. Blue/Brown stripe 37

Lime/Brown stripe 49

2 Red

Lt. Gray/Red stripe

Lt. Blue/Red stripe

Lime/Red stripe

3 Orange

Lt. Gray/Orange stripe 27

Lt. Blue/Orange stripe 39

Lime/Orange stripe 51

Aqua/Orange stripe

4 Yellow

Lt. Gray/Yellow stripe 28

Lt. Blue/Yellow stripe 40

Lime/Yellow stripe 52

Aqua/Yellow stripe

5 Green

Lt. Gray/Green stripe 29

Lt. Blue/Green stripe

Lime/Green stripe

Aqua/Green stripe

6 Blue

Lt. Gray/Blue stripe

Lt. Blue/Blue stripe

Lime/Blue stripe

Aqua/Blue stripe

7 Violet

Lt. Gray/Violet stripe 31

Lt. Blue/Violet stripe

Lime/Violet stripe

Aqua/Violet stripe

8 Gray

Lt. Gray/Gray stripe

Lt. Blue/Gray stripe

Lime/Gray stripe

Aqua/Gray stripe

9 White

Lt. Gray/White stripe 33

Lt. Blue/White stripe

Lime/White stripe

Aqua/White stripe

10 Black

Lt. Gray/Black stripe

Lt. Blue/Black stripe

Lime/Black stripe

Aqua/Black stripe

11 Tan

Lt. Gray/Tan stripe

Lt. Blue/Tan stripe

Lime/Tan stripe

Aqua/Tan stripe

12 Pink

Lt. Gray/Pink stripe

Lt. Blue/Pink stripe

Lime/Pink stripe

Aqua/Pink stripe

Courtesy Belden.

30 32

Aqua/Brown stripe Aqua/Red stripe

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Table 14-13. Comparing Twisted-Pair High-Frequency Formats Standard

Format

Intended Use

D1 component parallel broadcast

Connector Style multipin D

Cable Type

Transmission Distance1

Sample Rate

Data Rate (Mbps)

Guiding Document

multipairs

4.5 m/15 ft

27 MHz

270

ITU-R BT.601-5

serial

professional/ consumer

(see IEEE 1394)

4.5 m/15 ft

20.25 MHz

IEC 61834

IEEE 1394 (FireWire)

serial

professional/ 1394 consumer

6 conductors, 2-STPs/2 pwr

4.5 m/15 ft

n/a

USB 1.1

serial

consumer

USB A&B

4 conductors, 1 UTP/ 2 pwr

5 m/16.5 ft

n/a

USB 1.1 Promoter Group

USB 2.0

serial

professional/ USB consumer A&B

4 conductors, 1-UTP/ 2 pwr

5 m/16.5 ft

n/a

480

USB 2.0 Promoter Group

DVI

serial/ consumer parallel

DVI (multipin D)

Four STPs

10 m/33 ft

To 165 MHz

1650

DDWG; DVI 1.0

HDMI

parallel consumer

HDMI (19 pin) Four STPs + 7 conductors

DisplayPort

parallel consumer

20 pin

Four STPs + 8 conductors

Unspecified 15 m

100, 200, 400 IEEE 1394

To 340 MHz To 10.2 Gbps HDMI LLC To 340 MHz To 10.8 Gbps VESA

1 Transmission distances may vary widely depending on cabling and the specific equipment involved. STP = shielded twisted pair, UTP = unshielded twisted pair, n/a = not applicable

Picture information or even the entire picture can be lost if any vital data is missing with digital video interfaces. DVI cable and its termination are very important and the physical parameters of the twisted pairs must be highly controlled as the specifications for the cable and the receiver are given in fractions of bit transmission. Requirements depend on the clock rate or signal resolution being used. Transferring the maximum rate of 1600 × 1200 at 60 Hz for a single link system means that one bit time or 10 bits per pixel is 0.1 1 e 165 MHz or 0.606 ns. The DVI receiver specification allows 0.40 × bit time, or 0.242 ns intrapair skew within any twisted pair. The pattern at the receiver must be very symmetrical. The interpair skew, which governs how bits will line up in time at the receiving decoder, may only be 0.6 × pixel time, or 3.64 ns. These parameters control the transmission distances for DVI. Also, the cable should be evaluated on its insertion loss for a given length. DVI transmitter output is specified into a cable impedance of 100 : with a signal swing of ±780 mV with a minimum signal swing of ±200 mV. When determining DVI cable, assume minimum performance by the transmitter—i.e., 200 mV—and best sensitivity by the receiver which must operate on signals ±75 mV. Under these conditions the cable attenuation can be no greater than 8.5 dB at 1.65 GHz (10 bits/pixel × 165 MHz clock) which is relatively difficult to maintain on twisted-pair cable. DVI connections combine the digital delivery, described above, with legacy analog component

delivery. This allows DVI to be the transition delivery scheme between analog and digital applications.

14.9.3.2 HDMI HDMI (high definition multimedia interface) is similar to DVI except that it is digital-only delivery. Where DVI has found its way into the commercial space as well as consumer applications, HDMI is almost entirely consumer-based. It is configured into a 19 pin connector which contains four shielded twisted pairs (three pairs data, one pair clock) and seven wire for HDCP (copy protection), devices handshaking, and power. The standard versions of HDMI are nonlocking connector, attesting to its consumer-only focus.

14.9.3.3 IEEE -1394 or FireWire Serial Digital FireWire, or IEEE -1394, is used to upload DV, or digital video, format signals to computers etc. DV, sometimes called DV25, is a serial digital format of 25 Mbps. IEEE 1394 supports up to 400 Mbps. The specification defines three signaling rates, S100 (98.304 Mbps), S200 (196.608 Mbps), and S400 (393.216 Mbps). IEEE 1394 can interconnect up to sixty three devices in a peer-to-peer configuration so audio and video can be transferred from device to device without a computer, D/A, or A/D conversion. IEEE 1394 is hot plugable from the circuit while the equipment is turned on.

Transmission Techniques: Wire and Cable The IEEE 1394 system uses two shielded twisted pairs and two single wires, all enclosed in a shield and jacket, Fig. 14-2. Each pair is shielded with 100% coverage foil and a minimum 60% coverage braid. The outer shield is 100% coverage foil and a minimum 90% coverage braid. Each pair is shielded with aluminum foil and is equal to or greater than 60% braid. The twisted pairs handle the differential data and strobe (assists in clock regeneration) while the two separate wires provide the power and ground for remote devices. Signal level is 265 mV differential into 110 : . Individual shield Signal lines A Shielded twisted pair Power supply 8 V–40 V, 1.5 Adc max. Signal lines A Shielded twisted pair Signal line shield Outer jacket Copper or gold contacts Metal shroud Connector

Figure 14-2. IEEE 1394 cable and connector.

The IEEE 1394 specification cable length is a maximum of 4.5 m (15 ft). Some applications may run longer lengths when the data rate is lowered to the 100 Mbps level. The typical cable has #28 gage copper twisted pairs and #22 gage wires for power and ground. The IEEE 1394 specification provides the following electrical performance requirements: • Pair-to-pair data skew is 0.40 ns. • Crosstalk must be maintained below 26 dB from 1 MHz to 500 MHz. • Velocity of propagation must not exceed 5.05 ns/m. Table 14-14 gives details of the physical interface system for IEEE 1394. 14.9.3.4 USB The USB, universal serial bus, simplifies connection of computer peripherals. USB 1.1 is limited to a communications rate of 12 Mbps, while USB 2.0 supports up to 480 Mbps communication. The USB cable consists of

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one twisted pair for data and two untwisted wires for powering downstream appliances. A full-speed cable includes a #28 gage twisted pair, and an untwisted pair of #28 to #20 gage power conductors, all enclosed in an aluminized polyester shield with a drain wire. Table 14-14. Critical IEEE 1394 Timing Parameters Parameter

100 Mbps

Max Tr/Tf

200 Mbps

400 Mbps 1.20 ns

3.20 ns

2.20 ns

Bit Cell Time

10.17 ns

5.09 ns

2.54 ns

Transmit Skew

0.40 ns

0.25 ns

0.20 ns

Transmit Jitter

0.80 ns

0.50 ns

0.25 ns

Receive End Skew

0.80 ns

0.65 ns

0.60 ns

Receive End Jitter

1.08 ns

0.75 ns

0.48 ns

Nominal impedance for the data pair is 90 : . The maximum cable length is determined by the signal propagation delay which must be less than 26 ns from end to end. Table 14-15 lists some common plastics and the theoretical distance each could go based on 26 ns. With an additional allowance of 4 ns, which is split between the sending device connection and the receiver connection/response function, the entire one-way delay is a maximum of 30 ns. The cable velocity of propagation must be less than 5.2 ns/m and the length and twist of the data pair must be matched so time skew is no more than 0.10 ns between bit polarities. The nominal differential signal level is 800 mV. Table 14-15. Dielectric Constant, Delay, and Transmission Distance of Various Plastics Material

Dielectric Constant

Foam, Air-Filled Plastic Solid Teflon™ Solid Polyethylene Solid Polyvinyl Chloride

Delay ns/ft

Maximum USB Distance

1.35

1.16

22.4 ft

2.1

1.45

18 ft

2.3

1.52

17 ft

3.5–6.5

1.87–2.55

10–14 ft

14.9.3.5 DisplayPort DisplayPort is an emerging protocol for digital video. Its original intention was the transfer of images from a PC or similar device to a display. It has some significant advantages over DVI and HDMI. DisplayPort is by design backward-compatible to single link DVI and HDMI. Those are both severely distance-limited by the delay skew of the three data pairs when compared to the clock pair. With DisplayPort the clock is embedded with

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the video, much as the clock is embedded with the audio bit stream in AES digital audio, so the distance limitations on DisplayPort are less likely to involve clock timing problems. H o w e ve r, d i s p l a y p or t i s a l s o a n on l o c k in g connector, of 20 pins, and is intended for maximum distance 15 m (50 ft). These cables are, like HDMI and DVI, only available in assemblies. Raw cable and connectorization in the field do not currently look like an option for the professional installer. All these factors make it less likely to be embraced by the professional broadcast video arena. 14.9.3.6 Premise/Data Category Cables While premise/data category cables were never intended to be audio or video cables, their high performance and low cost, and their ubiquitous availability, have seen them pressed into service carrying all sorts of nondata signals. It should also be noted that high-speed Ethernet networks are routinely used to transport these audio and video signals in data networks. The emergence of 10GBase-T, 10 gigabit networks, will allow the transport of even multiple uncompressed 1080p/60 video images. The digital nature of most entertainment content, with the ubiquitous video server technology in use today, makes high-bandwidth, high-data-rate networks in audio, video, broadcast, and other entertainment facilities, an obvious conclusion.

version is called Fast Ethernet and 1000 Mbps version is called Gigabit Ethernet. 14.9.3.6.2 Structured Cabling Structured cabling, also called communications cabling, data/voice, low voltage, or limited energy is the standardized infrastructure for telephone and local area network (LAN) connections in most commercial installations. The architecture for the cable is standardized by Electronic Industries Association and Telecommunications Industry Association (EIA/TIA), an industry trade association. EIA/TIA 568, referred to as 568, is the main document covering structured cabling. IEEE 802.3 also has standards for structured cabling. The current standard, as of this writing, is EIA/TIA 568-B.2-10 that covers all active standards up to 10GbaseT, 10 gigabit cabling. 14.9.3.6.3 Types of Structured Cables Following are the types of cabling, Category 1 though Category 7, often referred to as Cat 1 through Cat 7. The standard TIA/EIA 568A no longer recognizes Cat 1, 2, or 4. As of July 2000, the FCC mandated the use of cable no less than Cat 3 for home wiring. The naming convention specified by ISO/IEC 11801 is shown in Fig. 14-3. XX/XXX

14.9.3.6.1 Cabling Definitions • Telcom Closet (TC). Location where the horizontal cabling and backbone cabling are made. • Main Cross-Connect (MXC). Often called the equipment room and is where the main electronics are located. • Intermediate Cross-Connect (IXC). A room between the TC and the MXC are terminated. Rarely used in LANs. • Horizontal Cabling. The connection from the telcom closet to the work area. • Backbone Cabling. The cabling that connect all of the hubs together. • Hub. The connecting electronic box that all of the h ori zon ta l ca bl es co nn ec t to w hic h a re th en connected to the backbone cable. • Ethernet. A 10, 100, or 1000 Mb/s LAN. The 10 Mbps version is called 10Base-T. The 100 Mbps

Balanced element Element shield Overall shielding

TP = twisted pair U = unshielded F = foil shielded F = foil shielded S = braid shielded SF = braid and foil shielded

Figure 14-3. ISO/IEC 11801 cable naming convention.

Table 14-16 gives the equivalent TIA and ISO classifications for structured cabling. Table 14-16. TIA and ISO Equivalent Classifications Frequency TIA ISO bandwidth Components Cabling Components Cabling 1–100 MHz

Cat 5e

Class D

1–250 MHz

Cat 6

Class E

1–500 MHz

Cat 6a

Class EA

1–600 MHz

n/s

Cat 7

Class F

1–1000 MHz

n/s

Cat 7A

Class FA

Transmission Techniques: Wire and Cable

Category 2. Defined as the IBM Type 3 cabling system. IBM Type 3 components were designed as a higher grade 100 : UTP system capable of operating 1 Mb/s Token Ring, 5250, and 3270 applications over shortened distances. This category is not part of the EIA/TIA 568 standard. Category 3. Characterized to 16 MHz and supports applications up to 10 Mbps. Cat 3 conductors are 24 AWG. Applications range from voice to 10Base-T. Category 4. Characterized to 20 MHz and supports applications up to 16 Mb/s. Cat 4 conductors are 24 AWG. Applications range from voice to 16 Mbps Token Ring. This category is no longer part of the EIA/TIA 568 standard. Category 5. Characterized to 100 MHz and supports applications up to 100 Mbps. Cat 5 conductors are 24 AWG. Applications range from voice to 100Base-T. This category is no longer part of the EIA/TIA 568 standard. Category 5e. Characterized to 100 MHz and supports applications up to 1000 Mbps/1 Gbps. Cat 5e conductors are 24 AWG. Applications range from voice to 1000Base-T. Cat 5e is specified under the TIA standard ANSI/TIA/EIA-568-B.2. Class D is specified under ISO standard ISO/IEC 11801, 2nd Ed. Category 6. Characterized to 250 MHz, in some versions bandwidth is extended to 600 MHz, and supports 1000 Mbps/1 Gbps and future applications and is backward compatible with Cat 5 cabling systems. Cat 6 conductors are 23 AWG. This gives improvements in power handling, insertion loss, and high-frequency attenuation. Fig. 14-4 shows the improvements of Cat 6 over Cat 5e. Cat 6 is specified under the TIA standard ANSI/TIA/EIA-568-B.2-1. Class E is specified under ISO standard ISO/IEC 11801, 2nd Ed. Cat 6 is available most commonly in the United States as UTP. Category 6 F/UTP. Cat 6 F/UTP (foiled unshielded twisted pair) or ScTP (screened twisted pair) consists of four twisted pairs enclosed in a foil shield with a conductive material on one side. A drain wire runs adjacent to the conductive side of the shield, Fig. 14-5. When appropriately connected, the shield reduces ANEXT, RFI, and EMI. Cat 6 FTP can only be designed to 250 MHz per TIA/EIA 568B.2-1.

2.5 Normalized value

Category 1. Meets the minimum requirements for analog voice or plain old telephone service (POTS). This category is not part of the EIA/TIA 568 standard.

413

Cat 5

2.0

Cat 6 1.5 1.0 0.5 0.0

Bandwidth

Loss

Figure 14-4. Normalized comparison of Cat 5e and Cat 6. Drain wire Cable jacket

Foil shield Source: BICSI

Figure 14-5. Cat 6 F/UTP.

Category 6a. Cat 6a (Augmented Category 6) is characterized to 500 MHz, and in special versions to 625 MHz, has lower insertion loss, and has more immunity to noise. Cat 6a is often larger than the other cables. 10GBase-T transmission uses digital signal processing (DSP) to cancel out some of the internal noise created by NEXT and FEXT between pairs. Cat 6a is specified under the TIA standard ANSI/TIA/EIA 568-B.2-10. Class E A is specified under ISO standard ISO/IEC 11801, 2nd Ed. Amendment 1. Cat 6a is available as UTP or FTP. Category 7 S/STP. Cat 7 S/STP (foil shielded twistedpair) cable is sometimes called PiMF (pairs in metal foil). Shielded-twisted pair 10GBase-T cable dramatically reduces alien crosstalk. Shielding reduces electromagnetic interference (EMI) and radio-frequency interference (RFI). This is particularly important as the airways are getting more congested. The shield reduces signal leakage and makes it harder to tap by an outside source. Shield termination at 14.16 Class F will be specified under ISO standard ISO/IEC 11801, 2nd Ed. Class FA will be specified under ISO standard ISO/IEC 11801, 2nd Ed. Amendment 1. 14.9.3.6.4 Comparisons Table 14-17 compares network data rates for Cat 3 through Cat 6a and Table 14-18 compares various characteristics of Cat 5e, 6, and 6a. Fig. 14-6 compares the

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media distance-bandwidth product of Cat 5e and Cat 6a with 802.11 (a, b, g, n) wireless media, often called Wi-Fi. Table 14-17. Network Data Rates, Supporting Cable Types, and Distance Minimum Performance

Token Ring

Ethernet

Maximum Distance

Cat 3

4 Mb/s

10 Mbps

100 m /328 ft

Cat 4

16 Mb/s

–

100 m /328 ft

Fig. 14-7 shows various problems that can be found in UTP cabling. Fig. 14-8 gives the maximum distances for UTP cabling as specified by ANSI/TIA. Open pair

Shorted between pairs Px

Reversed pair

Cat 5

–

Cat 5e Cat 6

–

Cat 6a

100 Mbps

100 m /328 ft

1000 Mbps

100 m /328 ft

10 Gbps

55 m /180 ft

10 Gbps

100 m /328 ft

Table 14-18. Characteristics of Cat 5e, Cat 6, and Cat 6a Cabling Type Relative Price (%)

Cat 5e

Cat 6

100

Cat 6a

135–150

165–180

Available Bandwidth

100 MHz 250 MHz

500 MHz

Data rate Capability

1.2 Gbps

2.4 Gbps

10 Gbps

Noise Reduction

1.0

0.5

0.3

Broadband Video Channels 6 MHz/channel

Broadband Video Channels rebroadcast existing channels

60+

No. of Cables in Pathway 24 inches × 4 inches

1400

1000

700

100,000

Mbits/s

10,000 1000 100 10 1 Cat 5e

802.11b 802.11n Cat 6 802.11g Transmission media

Figure 14-6. Comparison of media distance to bandwidth

New cable designs can affect size and pathway load so consult the manufacturer. Note that cable density is continually changing with newer, smaller cable designs. Numbers in Table 14-18 should be considered worst case. Designers and installers of larger systems should get specific dimensional information from the manufacturer.

Shorted pair Px

Miswired pairs Px Py

Split pairs 1 2 3 4

Figure 14-7. Paired wiring faults. Courtesy Belden.

Four (4) pair 100 : ±15% UTP Cat 5e cabling is the recommended minimum requirement for residential and light commercial installations because it provides excellent flexibility. Pair counts are four pair for desktop and twenty five pair for backbone cabling. The maximum length of cable is 295 ft (90 m) with another 33 ft (10 m) for patch cords. Unshielded twisted pairs (UTP) and shielded twisted pairs (STP) are used for structured cabling. Unshielded twisted pairs (UTP) are the most common today. These cables look like the POTS cable, however, their construction makes them usable in noisy areas and at high frequencies because of the short, even twisting of the two wires in each pair. The twist must be even and tight so complete noise cancellation occurs along the entire length of the cable. To best keep the twist tight and even, better cable has the two wires bonded together so they will not separate when bent or flexed. Patch cable is flexible so twist and impedance are not as well controlled. The color codes for the pairs are given in Table 14-19. Cable diameter varies for the different types of cable. TIA recommends that two Cat 6 cables but only one Cat 6a cable can be put in a ¾ inch (21 mm) conduit at 40% fill. The diameter and the stiffness of the cables determine their bend radius and therefore the bend radius of conduits and trays, Table 14-20 Fig. 14-9 shows the construction of UTP and screened UTP cable. 14.9.3.6.5 Critical Parameters Critical parameters for UTP cable are: NEXT, PS-NEXT, FEXT, ELFEXT, PS-ELFEXT, RL, ANEXT. NEXT. NEXT, or near-end crosstalk, is the unwanted signal coupling from the near end of one sending pair to a receiving pair.

Transmission Techniques: Wire and Cable

800 m Equipment room (ER) ER main cross 500 m/1650 ft intermediate connect crossconnect Jumper/ patch cords: 20 m/65 ft

TeleInformation 300 m/1000 ft communicatons 90 m/300 ft outlet closet

Jumper/patch cords: 6 m/20 ft

Backbone cabling

415

3 m/10 ft

Work area

Horizontal cabling

Figure 14-8. Maximum distances between areas for UTP cable.

Table 14-19. Color Code for UTP Cable Pair No.

1st Conductor Base/Band

2nd Conductor

White/Blue

Blue

White/Orange

Orange

White/Green

Green

White/Brown

Brown

Table 14-20. Diameter and Bend Radius for 10GbE Cabling Cable

Diameter

Bend Radius

Category 6

0.22 inch (5.72 mm)

1.00 inch (4 × OD)

Category 6a

0.35 inch (9 mm)

1.42 inch (4 × OD)

Category 6 FTP

0.28 inch (7.24 mm)

2.28 inch (8 × OD)

Category 7 STP

0.33 inch (8.38 mm)

2.64 inch (8 × OD)

Cable diameters are nominal values.

UTP

S/UTP

Conductor Pair Pair shield Insulation Sheath

Conductor Pair Insulation Shield Pair shield Sheath

STP

S/STP

Figure 14-9. UTP and S/UTP cable design.

PS-NEXT. PS-NEXT, or power-sum near-end crosstalk, is the crosstalk between all of the sending pairs to a receiving pair. With four-pair cable, this is more important than NEXT. FEXT. FEXT, or far-end crosstalk, is the measure of the unwanted signal from the transmitter at the near end coupling into a pair at the far end.

EL-FEXT. EL-FEXT, or equal level far-end crosstalk, is the measure of the unwanted signal from the transmitter end to a neighboring pair at the far end relative to the received signal at the far end. The equation is EL – FEXT = FEXT – Attenuation

(14-3)

Power sum equal-level far-end crosstalk is the computation of the unwanted signal coupling from multiple transmitters at the near end into a pair measured at the far end relative to the received signal level measured on the same pair. Return Loss (RL). RL is a measure of the reflected energy from a transmitted signal and is expressed in dB, the higher the value, the better. The reflections are caused by impedance mismatch caused by connectors, improper installation such as stretching the cable or too sharp a bend radius, improper manufacturing, or improper load. Broadcasters are very familiar with return loss, calling it by a different name, SWR (standing wave ratio) or VSWR (voltage standing wave ratio). In fact, return loss measurements can easily be converted into VSWR values, or vice versa. Return loss can be found with the equation (14-4) RL = 20 log Difference ---------------------------Sum where, Difference is the difference (absolute value) between the desired impedance and the actual measured impedance, Sum is the desired impedance and the actual measured impedance added together. • The desired impedance for all UTP data cables (Cat 5, 5e, 6, 6a) is 100 : • The desired impedance for all passive video, HD, HD-SDI or 1080p/60 components is 75 : • The desired impedance for all digital audio twisted pairs is 110 :

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• The desired impedance for all digital audio on coaxial cable is 75 : . With 1000Base-T systems, the pairs simultaneously transmit and receive. As the transmitter sends data, it is also listening for data being sent from the opposite end of the same pair. Any reflected signal from the sending end that reflects back to the sending end mixes with the sending signal from the far end, reducing intelligibility. With 10Base-T or 100Base-T data networks, one pair transmits while another receives, so reflections (RL, return loss) are not a major consideration and were not required to be measured. Now, with pairs simultaneously transmitting and receiving, called duplex mode, RL is a critical measurement for data applications. Delay Skew. Since every pair (and every cable) takes a specific amount of time to deliver a signal from one end to the other, there is a delay. Where four pairs must deliver data to be recombined, the delay in each pair should, ideally, be the same. However, to reduce crosstalk, the individual pairs in any Category cable have different twist rates. This reduces the pair-to-pair crosstalk but affects the delivery time of the separate parts. This is called delay skew. While delay skew affects the recombining of data, in 1000Base-T systems, for instance, the same delay skew creates a problem when these UTP data cables are used to transmit component video or similar signals, since the three colors do not arrive at the receiving end at the same time, creating a thin bright line on the edge of dark images. Some active baluns have skew correction built in, see Section 14.12.5. ANEXT. ANEXT, or alien crosstalk, is coupling of signals between cables. This type of crosstalk cannot be cancelled by DSP at the switch level. Alien crosstalk can be reduced by overall shielding of the pairs, or by inserting a nonconducting element inside that cable to push away the cables around it. 14.9.3.6.6 Terminating Connectors All structured cabling use the same connector, an RJ-45. In LANs (local area networks) there are two possible pin-outs, 568A and 568B. The difference is pair 2 and pair 3 are reversed. Both work equally well as long as they are not intermixed. The termination is shown in Fig. 14-10. In the past decade, the B wiring scheme has become the most common. However, if you are adding to or extending and existing network, you must determine

2 1

3 4

1234 5 678

T568A

T568B

Figure 14-10. Termination layout for EIA/TIA 568-B.2 cable.

which wiring scheme was used and continue with that scheme. A mixed network is among the most common causes of network failure. It is very important that the pairs be kept twisted as close to the connector as possible. For 100Base-T (100 MHz, 100 Mbps) applications, a maximum of ½ inch should be untwisted to reduce crosstalk and noise pickup. In fact, with Cat 6 (250 MHz) or Cat 6a (500 MHz) it is safe to say that any untwisting of the pairs will affect performance. Therefore there are many connectors, patch panels, and punch-down blocks that minimize the untwisting of the pairs.

14.9.3.6.7 Baluns Baluns (Balanced-Unbalanced) networks are a method of connecting devices of different impedance and different formats. Baluns have been commonly used to convert unbalanced coax, to balanced twinlead for television antennas, or to match coaxial data formats (coaxial Ethernet) to balanced line systems (10Base-T, 100Base-T etc.). Other balun designs can allow unbalanced sources, such as video or consumer audio, for instance, to be carried on balanced lines, such as UTP Cat 5e, 6, etc. Since there are four pairs in a common data cable, this can carry four channels. Since category cables are rarely tested below 1 MHz, the audio performance was originally suspect. Crosstalk at audio frequencies in UTP has been measured and is consistently better than 90 dB even on marginal Cat 5. On Cat 6, the crosstalk at audio frequencies is below the noise floor of most network analyzers. Baluns are commonly available to handle such signals as analog and digital audio, composite video, S-video, RGB or other component video (VGA, Y/R-Y/B-Y,Y/Cr/Cb), broadband RF/CATV, and even DVI and HDMI. The limitations to such applications

Transmission Techniques: Wire and Cable

14.9.3.6.8 Adaptors Users and installers should be aware there are adaptors, often that fit in wall plates, where keystone data jacks are intended to be snapped in place. These adaptors often connect consumer audio and video (RCA connectors) to 110 blocks or other twisted pair connection points. However, there is no unbalanced-to-balanced device in these, so the noise rejection inherent in twisted pairs when run as a balanced line is not provided. These adaptors simply unbalance the twisted pair and offer dramatically short effective distances. Further, baluns can change the source impedance and extend distance. Adaptors with no transformers or similar components cannot extend distance and often reduce the effective distance. These devices should be avoided unless they contain an actual balun. 14.9.3.6.9 Power Over Ethernet (PoE) PoE supplies power to various Ethernet services as VoIP (Voice over Internet Protocol) telephones, wireless LAN access points, Blu-tooth access points, and Web cameras. Many audio and video applications will soon use this elegant powering system. IEEE 802.3af-2003 is the IEEE standard for PoE. IEEE 802.3af specifies a maximum power level of 15.4 W at the power sourcing equipment (PSE) and a maximum of 12.95 W of power over two pairs to a powered device (PD) at the end of a 100 m (330 ft) cable. The PSE can provide power by one of two configurations: 1. 2.

Alternative A, sometimes called phantom powering, supplies the power over pairs 2 and 3. Alternative B supplies power over pairs 1 and 4, as shown in Fig. 14-11.

Power sourcing equipment (PSE) 4 5

48 Vdc

4 5 Spare pair

− RX

1 Signal pair

Signal pair

7 8

DC/DC converter

Powered device (PD)

7 8 Spare pair

A. Power supplied via data pairs Power sourcing equipment (PSE) 48 Vdc

Powered device (PD) 4 5

4 5 Spare pair

− RX

1 2

1 Signal pair

Signal pair

DC/DC converter

are the bandwidth specified on the cable and the performance of the cable (attenuation, return loss, crosstalk, etc.) at those higher frequencies. Passive baluns can also change the source impedance in audio devices. This dramatically extends the effective distance of such signals from only a few feet to many hundreds of feet. Consult the balun manufacturer for the actual output impedance of their designs. Some baluns can include active amplification, equalizations, or skew (delivery timing) compensation. While more expensive, these active baluns can dramatically increase the effective distance of even marginal cable.

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7 8

7 8 Spare pair B. Power supplied by spare pairs

Figure 14-11. Two methods of supplying power via the Ethernet. Courtesy of Panduit Int’l Corp.

The voltage supplied is nominally 48 Vdc with a minimum of 44 Vdc, a maximum of 57 Vdc, and the maximum current per pair is 350 mAdc, or 175 mAdc per conductor. For a single solid 24 AWG wire, common to many category cable designs, of 100 m length (328 ft) this would be a resistance of 8.4 : . Each conductor would dissipate 0.257 W or 1.028 W per cable (0.257 W × 4 conductors). This causes a temperature rise in the cable and conduit which must be taken into consideration when installing PoE.

14.9.3.6.10 Power Over Ethernet Plus (PoE Plus) PoE Plus is defined in IEEE 802.3at and is capable of delivering up to 30 W. Work is being done to approach 60 W or even greater. This requires the voltage supply to be 50 to 57 Vdc. Assuming a requirement of 42 W of power at the endpoint at 50 Vdc, the total current would be 0.84 A, or 0.21 A per pair, or 0.105 A (105 mA) per conductor, or a voltage drop of only 0.88 V in one 24 AWG wire.

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14.10 Coaxial Cable Coaxial cable is a design in which one conductor is accurately centered inside another with both conductors carrying the desired signal currents (source to load and return), as shown in Fig. 14-12. Coaxial cable is so called because if you draw a line through the center of a cross-sectional view, you will dissect all parts of the cable. All parts are on the same axis, or coaxial.

mission of high-frequency signals. At high frequencies, above 100 kHz, coax has a dramatically better performance than twisted pairs. However, coax lacks the ability to reject noise that twisted pairs can do when configured as balanced lines. Coaxial cable was first installed in 1931 to carry multiple telephone signals between cities.

14.10.2 Coaxial Cable Construction

Figure 14-12. Construction of a coaxial cable.

14.10.1 History of Coaxial Cable It has been argued that the first submarine telegraph cable (1858) was coaxial, Fig. 14-13. While this did have multiple layers, the outer layer was not part of the signal-carrying portion. It was a protective layer.

Figure 14-13. First submarine cable.

Modern coaxial cable was invented on May 23, 1929 by Lloyd Espenscheid and Herman Affel of Bell Laboratories. Often called coax, it is often used for the trans-

The insulation between the center conductor and the shield of a coaxial cable affects the impedance and the durability of the cable. The best insulation to use between the center conductor and the shield would be a vacuum. The second best insulation would be dry air, the third, nitrogen. The latter two are familiar insulators in hard-line transmission line commonly used to feed high-power antenna in broadcasting. A vacuum is not used, even though it has the lowest dielectric constant of “1,” because there would be no conduction of heat from the center conductor to the outer conductor and such a transmission line would soon fail. Air and nitrogen are commonly used under pressure in such transmission lines. Air is occasionally used in smaller, flexible cables. Polyethylene (PE) was common as the core material in coaxial cables during WW II. Shortly after the war, polyethylene was declassified and most early cable d e s i g n s f e a t u r e d t h i s p l a s t i c . To d a y m o s t high-frequency coaxial cables have a chemically formed foam insulation or a nitrogen gas injected foam. The ideal foam is high-density hard cell foam, which approaches the density of solid plastic but has a high percentage of nitrogen gas. Current state-of-the-art polyethylene foam velocity is 86% (dielectric constant: 1.35) although most digital video cables are 82–84% velocity of propagation. High-density foam of this velocity resists conductor migration when the cable is bent, keeping impedance variations to a minimum. This high velocity improves the high-frequency response of the cable. A problem with soft foam is it easily deforms, which changes the distance between the center conductor and the shield, changing the cable impedance. This can be caused by bending the cable too sharply, or running over it, or pulling it too hard, or any other possibility. To reduce this problem, a hard cell foam is used. Some cable that is rated as having a very high velocity of propagation might use very soft foam. A simple test can be performed where the user squeezes the foam dielec-

Transmission Techniques: Wire and Cable tric of various cables. It will be immediately apparent that some cables have a density (crush resistance) double that of other designs. Soft foam can lead to conductor migration over time which will change timing, impedance, return loss, and bit errors over distance. Coaxial cable is used quite extensively with various types of test equipment. When such cable is replaced, the capacitance per foot, which is determined by the dielectric constant of the insulator, must be taken into consideration, particularly for oscilloscope probes. 14.10.2.1 CCTV Cable CCTV (closed circuit television) cable has a 75 : characteristic impedance. CCTV is a baseband signal comprised of low-frequency vertical and horizontal sync pulse information and high-frequency video information. Since the signal is broadband, only cable with a center conductor of solid copper should be used. If the cable is constantly in motion as in pan and tilt operation, a stranded center conductor should be used as a solid conductor will work-harden and break. There are also robotic coaxes designed to flex millions of times before failure for intense flexing applications. Shielding for CCTV cable should have a copper or tinned-copper braid of at least 80% coverage, for low-frequency noise rejection. If an aluminum foil shield is used in conjunction with a braid, either tinned copper or aluminum only may be used for the shield. A bare copper braid will result in a galvanic reaction.

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Effect). Television frequencies in the United States, for instance, start with Channel 2 (54 MHz) which is definitely in the area of skin effect. So these cables can use center conductors that have a layer of copper over a steel wire, since only the copper layer will be working. If one uses a copper-clad steel conductor for applications below 50 MHz, the conductor has a dc resistance from four to seven times that of a solid copper conductor. If a copper-clad cable is used on a baseband video signal, for instance, the sync pulses may be attenuated too much. If such a cable is used to carry audio, almost the entire audio signal will be running down the steel wire. CATV/broadband cable should have a foil shield for good high-frequency noise rejection. CATV cable should also have a braid shield to give the connector something to grab onto, 40% to 60% aluminum braid being the most common. Multiple layer shields are also available such as tri-shielded (foil-braid-foil) and quad shields (foil-braid-foil-braid). Assumptions that quad shields give the best shield effectiveness are erroneous, there being single foil/braid and tri-shield configurations that are measurably superior. Refer to Section 14.8.6 on shield effectiveness. Modern CATV/broadband cable will use a foamed polyethylene or foamed FEP dielectric, and preferably one with gas injected foam. This will reduce the losses in the cable. The jacket material is determined by the environment that the cable will be working in (see Sections 14.4, 14.5, 14.6).

14.10.3 Coaxial Cable Installation Considerations 14.10.2.1.1 CCTV Distances For common CCTV 75 : cables, their rule-of-thumb transmission distances are shown in Table 14-21. These distances can be extended by the use of in-line booster amplifiers.

14.10.3.1 Indoor Installation

Table 14-21. Transmission Distances for CCTV Cable

RG-59

1000 ft

RG-6

1500 ft

RG-11

3000 ft

Indoor environments are the most common for coaxial cable installations. A few tips on installing coaxial cable are as follows:

14.10.2.2 CATV Broadband Cable For higher-frequency applications, such as carrying radio frequencies or television channels, only the skin of the conductor is working (see Section 14.2.8, Skin

First and foremost, follow all NEC requirements when installing coaxial cables. Distribute the pulling tension evenly over the cable and do not exceed the minimum bend radius of ten times the diameter. Exceeding the maximum pulling tension or the minimum bend radius of a cable can cause permanent damage both mechanically and electrically to the cable. When pulling cable through conduit, clean and deburr the conduit completely and use proper lubricants in long runs.

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14.10.3.2 Outdoor Installation

14.10.4.3 Twist-On Connectors

Outdoor installations require special installation techniques that will enable the cable to withstand harsh environments. When using cable in an aerial application, lash the cable to a steel messenger, or buy cable with a built-in steel messenger. This will help support the cable and reduce the stress on the cable during wind, snow, and ice storms. When direct burying a cable, lay the cable without tension so it will not be stressed when earth is packed around it. When burying in rocky soil, fill the trench with sand. Lay the cable and then place pressure-treated wood or metal plates over the cable. This will prevent damage to the cable from rocky soil settling; in cold climate areas, bury the cable below the frost line. Buy direct burial cable designed to be buried.

Twist-on connectors are the quickest way of terminating a coaxial cable; however, they do have some drawbacks. When terminating the cable with this type of connector, the center conductor is scored by the center pin on the connector, thus too much twisting can cause damage to the center conductor. It is not recommended for pan and tilt installations as the constant movement of the cable may work the connector loose. Because there is no mechanical or electrical crimp or solder connection, this connector is not as reliable as the other methods.

14.10.4 Coaxial Cable Termination Techniques 14.10.4.1 Soldering Soldering offers several advantages as it can be used on solid or stranded conductors and it creates both a solid mechanical and electrical connection. The disadvantage is that it takes more time to terminate than other methods and cold solder joints can cause problems if the connector is not soldered to the cable properly. The use of lead-based solder might also be a consideration if RoHS (reduction of hazardous substances) requirements are part of the installation. Soldering is not recommended for high-frequency applications, such as HD-SDI or 1080p/60 as the variations in dimensions will show up as variations in impedance and contribute to return loss (see Section 14.10.5).

14.10.4.2 Crimping Crimping is probably the most popular method of terminating BNC and F connectors on coax cable. Like the solder method, it can be used on solid or stranded conductors and provides a good mechanical and electrical connection. This method is the most popular because there is no need for soldering so installation time is reduced. It is very important to use the proper size connector for a tight fit on the cable. Always use the proper tool. Never use pliers as they are not designed to place the pressure of the crimp evenly around the connector. Pliers will crush the cable and can degrade the electrical properties of the cable.

14.10.4.4 Compression Connectors There are connectors, often a one-piece connector, that fit over the stripped cable and fasten by having two parts squeeze or compress together. This is a very simple and reliable way of connecting cable. However, the very high-frequency performance (beyond 500 MHz) has yet to be proven and so these connectors are not recommended for professional digital applications. A compression connector that is measured with a return loss of 20 dB at 2 GHz would be acceptable for professional broadcast HD applications.

14.10.5 Return Loss At high frequencies, where cable and connectors are a significant percentage of a wavelength, the impedance variation of cable and components can be a significant source of signal loss. When the signal sees something other than 75 : , a portion of the signal is reflected back to the source. Table 14-22 shows the wavelength and quarter wavelength at various frequencies. One can see that this was a minor problem with analog video (quarter wave 59 ft) since the distances are so long. However, with HD-SDI and higher signals, the quarter wave can be 1 inch or less, meaning that everything in the line is critical: cable connectors, patch panels, patch cords, adaptors, bulkhead/feedthrough connectors, etc. Table 14-22. Wavelength and Quarter Wavelength of Various Signals at Various Frequencies Signal

Clock Third Wavelength Quarter Frequency Harmonic Wavelength

Analog video analog (4.2 MHz)

analog

234 ft

59 ft

Transmission Techniques: Wire and Cable Table 14-22. Wavelength and Quarter Wavelength of Various Signals at Various Frequencies Signal

Clock Third Wavelength Quarter Frequency Harmonic Wavelength

SD-SDI

135 MHz

405 MHz

2.43 ft

7.3 inches

HD-SDI

750 MHz

2.25 GHz

5.3 inches

1.3 inches

1080p/60

1.5 GHz

4.5 GHz

2.6 inches

0.66 inches

In fact, Table 14-22 above is not entirely accurate. The distances should be multiplied by the velocity of propagation of the cable or other component, to get the actual length, so they are even shorter still. Since everything is critical at high frequencies, it is appropriate to ask the manufacturers of the cable, connectors, patch panels, and other passive components, how close to 75 : their products are. This can be established by asking for the return loss of each component. Table 14-23 will allow the user to roughly translate the answers given. Table 14-23. Return Loss versus % of Signal Received and Reflected Return Loss

% of Signal Received

% Reflected

50 dB

99.999%

0.001%

40 dB

99.99%

0.01%

30 dB

99.9%

0.1%

20 dB

99.0%

1.0%

10 dB

90.0%

10.0%

Most components intended for HD can pass 20 dB return loss. In fact, 20 dB return loss at 2 GHz is a good starting point for passive components intended for HD-SDI. Better components will pass 30 dB at 2 GHz. Better still (and rarer still) would be 30 dB at 3 GHz. There are currently no components that are consistently 40 dB return loss at any reasonable frequency. In Table 14-22, it can be seen that 1080p/60 signals need to b e te s te d to 4 .5 GH z. T hi s r equi r es expensi ve custom-built matching networks. As of this writing, only one company (Belden) has made such an investment. Note that the number of nines in the Signal Received column is the same as the first digit of the return loss (i.e., 30 dB = 3 nines = 99.9%). There are similar tests, such as SRL (structural return loss). This test only partially shows total reflection. Do not accept values measured in any way except return loss. The SMPTE maximum amount of reflection on a passive line (with all components measured and added together) is 15 dB

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or 96.84% received, 3.16% reflected. A line with an RL of 10 dB (10% reflected) will probably fail. 14.10.6 Video Triaxial Cable Video triaxial cable is used to interconnect video cameras to their related equipment. Triaxial cable contains a center conductor and two isolated shields, allowing it to support many functions on the one cable. The center conductor and outer shield carry the video signals plus intercoms, monitoring devices, and camera power. The center shield carries the video signal ground or common. Triax cable is usually of the RG-59 or RG-11 type. 14.10.7 S-Video S-video requires a duplex (dual) coaxial cable to allow separate transmission of the luminance (Y) and the chrominance (C). The luminance signal is black or white or any gray value while the chrominance signal contains color information. This transmission is sometimes referred to as Y-C. Separating signals provides greater picture detail and resolution and less noise interference. S-video is sometimes referred to as S-VHS™ (Super-Video Home System). While its intention was for improved consumer video quality, these cameras were also used for the lower end of the professional area, where they were used for news, documentaries, and other less-critical applications. 14.10.8 RGB RGB stands for red-green-blue, the primary colors in color television. It is often called component video since the signal is split up to its component colors. When these analog signals are carried separately much better image resolution can be achieved. RGB can be carried on multiple single video cables, or in bundles of cables made for this application. With separate cables, all the cables used must be precisely the same electrical length. This may or may not be the same as the physical length. Using a vectorscope, it is possibly to determine the electrical length and compare the RGB components. If the cables are made with poor quality control, the electrical length of the coaxes may be significantly different (i.e., one cable may have to be physically longer than the others to align the component signals). Cables made with very good quality control can simply be cut at the same physical length. Bundles of RGB cables should be specified by the amount of timing error, the difference in the delivery

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time on the component parts. For instance, all Belden bundled coax cables are guaranteed to be 5 ns (nanosecond) difference per 100 ft of cable. Other manufacturers should have a similar specification and/or guarantee. The de facto timing requirement for broadcast RGB is a maximum of 40 ns. Timing cables by hand with a vectorscope allows the installer to achieve timing errors of >1 ns. Bundled cables made for digital video can also be used for RGB analog, and similar signals (Y, R–Y, B–Y or Y, Pb, Pr or YUV or VGA, SVGA, XGA, etc.) although the timing requirements for VGA and that family of signals has not been established. These bundled coaxes come in other version besides just three coax RGB. Often the horizontal and vertical synchronizing signals (H and V) are carried with the green video signal on the green coax. For even greater control, these signals can be carried by a single coax (often called RGBS) or five coaxes, one for each signal (called RGBHV). These cables are becoming more common in the home, where they are often referred to as five-wire video. There are also four-pair UTP data cables made especially to run RGB and VGA signals. Some of these have timing tolerance (called delay skew in the UTP world) that is seriously superior to bundled coaxes. However, the video signals would have to be converted from 75 :to 100 : , and the baluns to do this, one for each end of the cable, would be added to the cost of the installation. Further, the impedance tolerance of coax, even poorly made coax, is dramatically superior to twisted pairs. Even bonded twisted pairs are, at best, ±7 : , where most coaxial cables are ±3 : , with precision cables being twice as good as that, or even better.

such as DVI (Section 14.9.4.1) and HDMI (Section 14.9.4.2). Table 14-24. Resolution of Various VGA and Family Formats Signal Type VGA

Resolution 640 × 480

SVGA

800 × 600

XGA

1024 × 768

WXGA

1280 × 720

SXGA

1280 × 1024

SXGA-HD

1600 × 1200

WSXGA

1680 × 1050

QXGA

2048 × 1536

QUSXG

3840 × 2400

14.11.1 Digital Signals and Digital Cable Control communications, or data communications, uses digital signals. Digital video signals require wide bandwidth cabling. Control communications and data communications use lower-performance cabling because they carry less information, requiring less bandwidth. High-speed data communications systems have significant overhead added to handle error correction so if data is lost, it can be re-sent. Digital video has some error correction capabilities, however, if all of the data bits required to make the system work are not received, picture quality is reduced or lost completely. Table 14-25 compares various digital formats.

14.10.9 VGA and Family

14.11.2 Coax and SDI

VGA stands for video graphics array. It is an analog format to connect progressive video source to displays, such as projectors and screens. VGA comes in a number of formats, based on resolution. These are shown in Table 14-24. There are many more variations in resolution and bandwidth than the ones shown in Table 14-24.

Most professional broadcast formats (SDI and HD-SDI) are in a serial format and use a single coaxial cable with BNC connectors. Emerging higher resolution formats, such as 1080p/60, are also BNC based. Some work with smaller connectors for dense applications, such as patch panels and routers, which use subminiature connectors such as LCC, DIN 1.0/2.3 or DIN 1.0/2.5. Proprietary miniature BNC connectors are also available.

14.11 Digital Video There are many formats for digital video, for both consumer, commercial and professional applications. This section concentrates on the professional applications, mainly SD-SDI (standard definition—serial digital interface) and HD-SDI (high-definition—serial digital interface.) There are sections on related consumer standards

14.11.3 Cables and SDI The most common form of SDI, component SDI, operates at data rates of 270 Mbps (clock 135 MHz). Cable loss specifications for standard SDI are specified in SMPTE 259M and ITUR BT.601. The maximum cable length is specified as 30 dB signal loss at one-half the

Transmission Techniques: Wire and Cable

423

Table 14-25. Comparing Coaxial Digital Formats Standard

Format Intended Use

Connector Style

Cable Type

Transmission Distance2

Sample Rate

Data Rate (Mbps)

Guiding Document

SDI

serial

broadcast

one BNC

coax1

300 m/1000 ft

27 MHz

270

SDTI

serial

data transport

one BNC

coax1

300 m/1000 ft

variable

270 or 360

SMPTE 305

SDTV

serial

broadcast

one BNC

coax1

300 m/1000 ft

27 MHz

3 to 8

ATSC; N53

HDTV

serial

broadcast

one BNC

coax1

122 m/400 ft

74.25 MHz

19.4

ATSC; A/53

HD-SDI

serial

broadcast

one BNC

coax1

122 m/400 ft

74.25 MHz

1500

SMPTE 292M

1080p/60

serial

Master format

one BNC

coax1

80 m/250 ft

148.5 MHz

3000

SMPTE 424M

1 2

SMPTE 259

Also implemented over fiber systems Transmission distances may vary widely depending on cabling and the specific equipment involved.

clock frequency and is acceptable because serial digital receivers have signal recovery processing. HD-SDI, whose cable loss is governed by SMPTE 292M, operates at a data rate of 1.5 Gbps (clock 750 MHz). The maximum cable length is specified at 20 dB signal loss at one-half the clock frequency. These are Manchester Coded signals and the bit rate is therefore double the clock rate. Emerging 1080p/60 applications are covered under SMPTE 424M. The data rate is 3 Gbps (clock 1.5 GHz).

14.11.4 Receiver Quality The quality of the receiver is important in the final performance of a serial digital system. The receiver has a greater ability to equalize and recover the signal with SDI signals. SMPTE 292M describes the minimum capabilities of a type A receiver and a type B receiver. SDI receivers are considered adaptive because of their ability to amplify, equalize, and filter the information. Rise time is significantly affected by distance, and all quality receivers can recover the signal from a run of HD-SDI RG-6 (such as Belden 1694A) for a minimum distance of 122 m (400 ft). The most important losses that affect serial digital are rise time/fall time degradation and signal jitter. Serial digital signals normally undergo reshaping and reclocking as they pass through major network hubs or matrix routers. Table 14-26 gives the specifications mandated in SMPTE 259M and SMPTE 292M in terms of rise/fall time performance and jitter. If the system provides this level of performance at the end of the cable run, the SDI receiver should be able to decode the signal. swept at 2.25 GHz. RL can be no greater than 15 dB at

14.11.5 Serial Digital Video Serial digital video (SDI) falls under standards by the Society of Motion Picture and Television Engineers (SMPTE) and ITU and falls under the following categories: SMPTE 259M D i g i t a l v i d e o t r a n s m i s s i o n s o f composite NTSC 143 Mb/s (Level A) and PAL 177 Mb/s (Level B). It also covers 525/625 component transmissions of 270 Mb/s (Level C) and 360 Mb/s (Level D). SMPTE 292M HDTV transmissions at 1.485 Gb/s SMPTE 344M Component widescreen transmission of 540 Mb/s ITU-R BT.601 International standard for PAL transmissions of 177 Mb/s These standards can work with standard analog video coax cables, however, the newer digital cables provide the more precise electrical characteristics required for high-frequency transmission. SDI cable utilizes a solid bare-copper center-conductor which improves impedance stability and reduced return loss (RL). Digital transmissions contain both low-frequency and high-frequency signals so it is imperative that a solid-copper center-conductor is used rather than a copper-clad steel center conductor. This allows the low frequencies to travel down the center of the conductor and the high frequencies to travel on the outside of the conductor due to the skin effect. Since digital video consists of both low and high frequencies, foil shields work best. All SDI cable should be sweep tested for return loss to the third harmonic of the fundamental frequency. For HD-SDI which is 1.485 Gb/s or has a 750 MHZ bandwidth, the cable is this frequency.

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Table 14-26. SMPTE Serial Digital Performance Specifications SMPTE 259 Parameter

SMPTE 292M

Level A

Level B

Level C

Level D

Level L

NTSC 4fsc Composite

PAL 4fsc Composite

525/625 Component

1920 × 1080 Interlaced

1280 × 720 Progressive

Data Rate in Mbps (clock)

143

177

270

360

1485

½ Clock Rate in MHz

71.5

88.5

135

180

742.5

Signal Amplitude (p-p)

800 mV

0 ±0.5

Rise/Fall Time Max. (ns)

1.50

1.5

0.27

Rise/Fall Time Min. (ns)

0.40

–

Rise/Fall Time Differential (ns)

0.5

0.10

dc Offset (volts)

% Overshoot Max.

Timing Jitter (ns)

1.40

1.13

0.74

0.56

0.67

Alignment Jitter (ns)

1.40

1.13

0.74

0.56

0.13

BNC 50 : connectors are often used to terminate digital video lines. This is probably acceptable if only one or two connectors are used. However, if more connectors are used, 75 : connectors are required to eliminate RL. Connectors should exhibit a stable 75 : impedance out to 2.25 GHz, the third harmonic of 750 MHz.

14.12 Radio Guide Designations From the late 1930s the U.S. Army and Navy began to classify different cables by their constructions. Since the intent of these high-frequency cables, both coaxes and twisted pairs, was to guide radio frequency signals, they carried the designation RG for radio guide. There is no correlation between the number assigned and any construction factor of the cable. Thus an RG-8 came after an RG-7 and before an RG-9, but could be completely different and unrelated designs. For all intents and purposes, the number simply represents the page number in a book of designs. The point was to get a specific cable design, with predictable performance, when ordered for military applications. As cable designs changed, with new materials and manufacturing techniques, variations on the original RG designs began to be manufactured. Some of these were specific targeted improvement, such as a special jacket on an existing design. These variations are noted by an additional letter on the designation. Thus RG-58C would be the third variant on the design of RG-58. The test procedure for many of these military cables is often long, complicated, and expensive. For the commercial user of these cables, this is a needless

expense. So many manufacturers began to make cables that were identical to the original RG specification except for testing. These were then designated utility grade and a slash plus the letter U is placed at the end. RG-58C/U is the utility version of RG-58C, identical in construction but not in testing. Often the word type is included in the RG designation. This indicates that the cable under consideration is based on one of the earlier military standards but differs from the original design in some significant way. At this point, all the designation is telling the installer is that the cable falls into a family of cables. It might indicate the size of the center conductor, the impedance, and some aspects of construction, with the key word being might. By the time the RG system approached RG-500, with blocks of numbers abandoned in earlier designs, the system became so unwieldy and unworkable that the military abandoned it in the 1970s and instituted MIL-C-17 (Army) and JAN C-17 (Navy) designations that continue to this day. RG-6, for instance, is found under MIL-C-17G.

14.13 Velocity of Propagation Velocity of propagation, abbreviated Vp , is the ratio of the speed of transmission through the cable versus the speed of light in free space, about 186,282 miles per second (mi/s) or 299,792,458 meters per second (m/s). For simplicity, this is usually rounded up to 300,000,000 meters per second (m/s). Velocity of propagation is a good indication of the quality of the cable. Solid polyethylene has a Vp of 66%. Chemically formed foam has a

Transmission Techniques: Wire and Cable Vp of 78%, and nitrogen gas injected foam has a Vp up to 86%, with current manufacturing techniques. Some hardline, which is mostly dry air or nitrogen dielectric, can exceed 95% velocity. Velocity of propagation is the velocity of the signal as it travels from one end of the line to the other end. It is caused because a transmission line, like all electrical circuits, possesses three inherent properties: resistance, inductance, and capacitance. All three of these properties will exist regardless of how the line is constructed. Lines cannot be constructed to eliminate these characteristics. Under the foregoing conditions, the velocity of the electrical pulses applied to the line is slowed down in its transmission. The elements of the line are distributed evenly and are not localized or present in a lumped quantity. The velocity of propagation (Vp ) in flexible cables will vary from 50% to a Vp of 86%, depending on the insulating composition used and the frequency. Vp is directly related to the dielectric constant (DC) of the insulation chosen. The equation for determining the velocity of propagation is 100 V p = -----------DC where, Vp is the velocity of propagation, DC is the dielectric constant.

(14-5)

Various dielectric constants (H are as follows: Material Vacuum Air Teflon Polyethylene Polypropylene PVC

Dielectric Constant 1.00 1.0167 2.1 2.25 2.3 3.0 to 6.5

14.14 Shielding From outdoor news gathering to studios and control rooms to sound reinforcement systems, the audio industry faces critical challenges from EM/RF interference (EMI and RFI). Shielding cable and twisting pairs insures signal integrity and provides confidence in audio and video transmissions, preventing downtime and maintaining sound and picture clarity. Cables can be shielded or unshielded, except for coaxial cable which is, by definition, a precise constructions of a shielded single conductor. There are a number of shield constructions available. Here are the most common. 14.14.1 Serve or Spiral Shields

Velocity can apply to any cable, coax or twisted pairs, although it is much more common to be expressed for cables intended for high-frequency applications. The velocity of propagation of coaxial cables is the ratio of the dielectric constant of a vacuum to the square root of the dielectric constant of the insulator, and is expressed in percent. VL 1 ------ = -----VS H or

425

(14-6)

V (14-7) V L = ------S H where, V L is the velocity of propagation in the transmission line, VS is the velocity of propagation in free space, H is the dielectric constant of the transmission line insulation.

Serve or spiral shield are the simplest of all wire-based shields. The wire is simply wound around the inner portions of the cable. Spiral shields can be either single or double spirals. They are more flexible than braided shields and are easier to terminate. Since spiral shields are, in essence, coils of wire, they can exhibit inductive effects which make them ineffective at higher frequencies. Therefore, spiral/serve shields are relegated to low frequencies and are rarely used for frequencies above analog audio. Serve or spiral shields tend to open up when the cable is bent or flexed. So shield effectiveness is less than ideal, especially at high frequencies. 14.14.2 Double Serve Shields Serve or spiral shields can be improved by adding a second layer. Most often, this is run at a 90° angle to the original spiral. This does improve coverage although the tendency to open up is not significantly improved and so this is still relegated to low-frequency or analog audio applications. This double serve or spiral construction is also called a Reussen shield (pronounced roy-sen).

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14.14.3 French BraidTM The French Braid shield by Belden is an ultraflexible double spiral shield consisting of two spirals of bare or tinned copper conductors tied together with one weave. The shield provides the long flex life of spiral shields and greater flexibility than braided shields. It also has about 50% less microphonic and triboelectric noise. Because the two layers are woven along one axis, they cannot open up as dual spiral/serve constructions can. So French Braid shields are effective up to high frequencies, and are used up to the Gigahertz range of frequencies. 14.14.4 Braid Braid shields provide superior structural integrity while maintaining good flexibility and flex life. These shields are ideal for minimizing low-frequency interference and have lower dc resistance than foil. Braid shields are effective at low frequencies, as well as RF ranges. Generally, the higher the braid coverage, the more effective the shield. The maximum coverage of a single braid shield is approximately 95%. The coverage of a dual braid shield can be as much as 98%. One hundred percent coverage with a braid is not physically possible. 14.14.5 Foil Foil shields can be made of bare metal, such as a bare copper shield layer, but more common is an aluminum-polyester foil. Foil shields can offer 100% coverage. Some cables feature a loose polyester-foil layer. Other designs can bond the foil to either the core of the cable or to the inside of the jacket of the cable. Each of these presents challenges and opportunities. The foil layer can either face out, or it can be reversed and face in. Since foil shields are too thin to be used as a connection point, a bare wire runs on the foil side of the shield. If the foil faces out, the drain wire must also be on the outside of the foil. If the foil layer faces in, then the drain wire must also be inside the foil, adjacent to the pair. Unbonded foil can be easily removed after cutting or stripping. Many broadcasters prefer unbonded foil layers in coaxial cable to help prevent thin slices of foil that can short out BNC connectors. If the foil is bonded to the core, the stripping process must be much more accurate to prevent creating a thin slice of core-and-foil. However, with F connectors, which are pushed onto the end of the coax, unbonded foil can bunch up and

prevent correct seating of these connectors. This explains why virtually all coaxes for broadband/CATV applications have the foil bonded to the core—so F connectors easily slip on. In shielded paired cables, such as analog or digital audio paired cables, the foil shield wraps around the pair. Once the jacket has been stripped off, the next step is to remove the foil shield. These cables are also available where the foil is bonded (glued) to the inside of the jacket. When the jacket is removed, the foil is also removed, dramatically speeding up the process. A shorting fold technique is often used to maintain metal-to-metal contact for improved high-frequency performance. Without the shorting fold, a slot is created through which signals can leak. A isolation fold also helps prevent the shield of one pair contacting the shield of an adjacent pair in a multipair construction. Such contact significantly increases crosstalk between these pairs. An improvement on the traditional shorting fold used by Belden employs the Z-Fold™, designed for use in multipair applications to reduce crosstalk, Fig. 14-14. The Z-Fold combines an isolation fold and a shorting fold. The shorting fold provides metal-to-metal contact while the isolation fold keeps shields from shorting to one another in multipair, individually shielded cables. Shorting fold Drain wire Isolation fold

Aluminum Insulated conductor

Insulating film

Figure 14-14. Z-Fold foil type shielded wire improves high frequency performance. Courtesy Belden.

Since the wavelength of high frequencies can eventually work through the holes in a braid, foil shields are most effective at those high frequencies. Essentially, foil shields represent a skin shield at high frequencies, where skin effect predominates. 14.14.6 Combination Shields Combination shields consist of more than one layer of shielding. They provide maximum shield efficiency

Transmission Techniques: Wire and Cable across the frequency spectrum. The combination foil-braid shield combines the advantages of 100% foil coverage and the strength and low dc resistance of a braid. Other combination shields available include various foil-braid-foil, braid-braid, and foil-spiral designs. 14.14.6.1 Foil + Serve Because of the inductive effects of serve/spiral shields, which relegate them to low-frequency applications, this combination is rarely seen. 14.14.6.2 Foil + Braid This is the most common combination shield. With a high-coverage braid (95%) this can be extremely effective over a wide range of frequencies, from 1 kHz to many GHz. This style is commonly seen on many cables, including precision video cable. 14.14.6.3 Foil + Braid + Foil Foil-braid-foil is often called a tri-shield. It is most commonly seen in cable television (CATV) broadband coaxial applications. The dual layers of foil are especially effective at high frequencies. However, the coverage of the braid shield in between is the key to shield effectiveness. If it is a reasonably high coverage (>80%) this style of braid will have excellent shield effectiveness. One other advantage of tri-shield coax cable is the ability to use standard dimension F connectors since the shield is essentially the same thickness as the common foil + braid shield of less expensive cables.

14.14.6.4 Foil + Braid + Foil + Braid Foil-braid-foil-braid is often called quad-shield or just quad (not to be confused with starquad microphone cable or old POTS quad hookup cable). Like trishield above, this is most common in cable television (CATV) broadband coaxial applications. Many believe this to be the ultimate in shield effectives. However, this is often untrue. If the two braids in this construction are high coverage braids (>80%) then, yes, this would be an exceptional cable. But most quad-shield cable uses two braids that are 40% and 60% coverage, respectively. With that construction, the tri-shield with an 80%+ braid is measurably superior. Further, quad-shield

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coaxial cables are considerably bigger in diameter and therefore require special connectors. Table 14-27 shows the shield effectiveness of different shield constructions at various frequencies. Note that all the braids measured are aluminum braids except for the last cable mentioned. That last cable is a digital precision video (such as Belden 1694A) and is many times the cost of any of the other cables listed. Table 14-27. Shield Effectiveness of Different Shield Constructions Shield Type (Aluminum Braid) 60% braid, bonded foil

5 10 MHz MHz

50 MHz

100 MHz

500 MHz 50

60% braid, tri-shield

0.8

60%/40% quad shield

0.8

0.2

0.3

77% braid, tri-shield

0.6

0.1

0.2

95% copper braid, foil

0.5

0.08

0.09

14.15 Shield Current Induced Noise There is significant evidence that constructions that feature bonded foil with an internal drain wire may affect the performance of the pairs, especially at high frequencies. Since an ideal balanced line is one where the two wires are electrically identical, having a drain wire in proximity would certainly seem to affect the symmetry of the pair. This would be especially critical where strong RF fields are around audio cables. Despite this evidence, there are very few cables made with appropriate symmetry. This may be based on lack of end-user demand, as manufacturers would be glad to redesign their cables should the demand arise. The drain wire could be easily substituted with a symmetrical low-coverage braid, for instance.

14.16 Grounds of Shields With any combination shield, the braid portion is the part that is making the connection. Even if we are shielding against high-frequency noise, in which case the foil is doing the actual work, the noise gets to ground by way of the braid which is much lower in resistance than the foil. Where the foil uses a drain wire, it is that drain wire that is the shield connection. Therefore, that drain wire must be bare so it can make contact with the foil. If the foil is floating, not glued or bonded to the core of the cable, then another plastic layer is used to carry the foil.

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The foil itself is much too thin and weak to even be applied in the factory by itself. The second plastic layer adds enough strength and flex-life (flexes until failure) to allow the foil to be used. The drain wire, therefore, must be in contact with the foil. In some cables, the foil faces out, so the drain wire must be on the outside of the foil, between the foil and the jacket. If the foil faces in, then the drain wire must be on the inside of the foil, adjacent to the pair (or other components) inside the cable. With an internal drain wire, there are a number of additional considerations. One is SCIN, shield current induced noise, mentioned earlier in Section 14.8.5.1. Another is the ability to make a multipair shielded cable where the shields are facing in and the plastic facing out. This allows the manufacturer to color code the pairs by coloring the plastic holding the foil. If you have a multipair cable, with individual foil shields, it is important that these foil shields do not touch. If the shields touch, then any signal or noise that is on one foil will be instantly shared by the other. You might as well put a foil shield in common around both pairs. Therefore, it is common to use foil shields facing in which will help prevent them from touching. These can then be color coded by using various colors of plastic with each foil to help identify each pair. However, simply coiling the foil around the pair still leaves the very edge of the foil exposed. In a multipair cable with many individual foils, where the cable is bent and flexed to be installed, it would be quite easy for the edge of one foil to touch the edge of another foil, thus compromising shield effectiveness. The solution for this is a Z-fold invented by Belden in 1960, shown in Fig. 14-14. This does not allow any foil edge to be exposed no matter how the cable is flexed.

the twisted pair. Instead of a small area of interference, such as where wires cross each other, a ground loop can use the entire length of the run to introduce noise. If one cannot afford the time or cost of a star ground system, there are still two options. The first option is to cut the ground at one end of the cable. This is called a telescopic ground. 14.16.2 Telescopic Grounds Where a cable has a ground point at each end, disconnecting one end produces a telescopic ground. Installers should be cautioned to disconnect only the destination (load) end of the cable, leaving the source end connected. For audio applications, the effect of telescopic grounds will eliminate a ground loop, but at a 50% reduction in shield effectiveness (one wire now connected instead of two). If one disconnects the source end, which in analog audio is the low-impedance end, and maintains the destination (load) connection, this will produce a very effective R-L-C filter at audio frequencies. At higher frequencies, such as data cables, even a source-only telescopic shield can have some serious problems. Fig. 14-15 shows the effect of a telescopic ground on a Cat 6 data cable. The left column shows the input impedance, the impedance presented to any RF traveling on the shield, at frequency Fk (bottom scale) in MHz. 10,000 9000 8000 7000

14.16.1 Ground Loops In many installations, the ground potential between one rack and another, or between one point in a building and another, may be different. If the building can be installed with a star ground, the ground potential will be identical throughout the building. Then the connection of any two points will have no potential difference. When two points are connected that do have a potential difference, this causes a ground loop. A ground loop is the flow of electricity down a ground wire from one point to another. Any RF or other interference on a rack or on an equipment chassis connected to ground will now flow down this ground wire, turning that foil or braid shield into an antenna and feeding that noise into

Zink

6000 5000 4000 3000 2000 1000 0 1

100

1000

fk Figure 14-15. Effect of a telescopic ground on a Cat 6 cable.

You will note that at every half-wavelength, the shield acts like an open circuit. Since most audio cables are foil shielded, and the foil is effective only at high

frequencies, this means that even a correctly terminated telescopic shield is less effective at RF frequencies.

14.17 UTP and Audio

1000 1244 1488 1732 1976 2173 2365 2558 2750 2942 3194 3472 3750 4043 4478 4913 5348 5783 6294 6882 7533 8125 8542 8958 9900 12,000 13,125 14,429 15,875 17,250 18,200 20,200 23,250 25,500 28,125 30,000 34,000 37,667 41,400 45,000 50,500

One other solution for ground loops is to have no ground connection. For the seasoned audio and video professional, this solution may require a leap of faith. In can clearly be seen that, with a cable that has no shield, no drain wire, and no ground wire, so no ground loop can develop. This is a common form of data cable called UTP, unshielded twisted pairs. With such a cable, having no shield means that you are totally dependent on the balanced line to reject noise. This is especially true, where you wish to use the four pairs in a Cat 5e, 6, or 6a cable to run four unrelated audio channels. Tests were performed on low-performance (stranded) Cat 5e patch cable (Belden 1752A) looking at crosstalk between the pairs. This test shows the average of all possible pair combinations, the worst possible case, and covered a bandwidth of 1 kHz to 50 kHz. The results are shown in Fig. 14-16.

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1000 1317 1634 1951 2212 2462 2712 2962 3306 3667 4043 4690 5174 5739 6412 7200 8042 8583 9300 11,333 13,125 14,857 16,833 18,000 20,600 24,400 27,667 30,667 35,400 40,200 45,000

Transmission Techniques: Wire and Cable

100

105

110

115

Frequency–Hz

Figure 14-17. NEXT crosstalk.

case is exactly 95 dB at just under 50 kHz. At 20 kHz and below, the numbers are even better than the previous graph, around 100 dB or better. There were attempts made to test a much better cable ( B e l d e n 1 8 7 2 A M e d ia Tw i s t) . T h is u n s h i e l d e d twisted-pair cable is now a Cat 6 bonded-pair design. After weeks of effort, it was determined that the pair-to-pair crosstalk could not be read on an Agilent 8714ES network analyzer. The crosstalk was somewhere below the noise floor of the test gear. The noise floor of that instrument is 110 dB. With a good cable, the crosstalk is somewhere below 110 dB. 14.17.1 So Why Shields?

100

105

110

115

Frequency–Hz

Figure 14-16. Crosstalk between Cat 5e patch cable.

You will note that the worst case is around 40 kHz where the crosstalk is slightly better than 95 dB. In the range of common audible frequencies (20 kHz) the pair-to-pair crosstalk approaches 100 dB. Since a noise floor of 90 dB is today considered wholly acceptable, a measurement of 95 dB or 100 dB is even better still. A number of data engineers questioned these numbers based on the fact that these measurements were FEXT, far-end crosstalk, where the signals are weakest in such a cable. So measurements were also taken of NEXT, near-end crosstalk, where the signals are strongest. Those measurements are shown in Fig. 14-17. The NEXT measurements are even better than the previous FEXT measurements. In this case, the worst

These experiments with unshielded cable beg the question, why have a shield? In fact, the answer is somewhat reversed. The pairs in data cables are dramatically improved over the historic audio pairs. The bandwidth alone, 500 MHz for Cat 6a, for instance, indicates that these are not the same old pairs but something different. In fact, what has happened is that the wire and cable (and data) industries have fixed the pairs. Before, with a poorly manufactured pair, a shield would help prevent signals from getting into, or leaking out of, a pair. The fact that either effect, ingress or egress, occurred indicated the poor balance, the poor performance of the pair. This does not mean shields are dead. There are data cables with overall shields (FTP), even individually shielded pairs (Cat 7) common in Europe. However, these are subject to the same problems as all shielded, grounded cables in terms of ground loops and wavelength effects as shown in Sections 14.8.6.5 and 14.8.6.6. The truth to the efficacy of unshielded twisted pairs running audio, video, data and many other signals is commonplace today. Many audio devices routinely use

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UTP for analog and digital connections. Where the source is not a balanced line, a device must change from balanced (UTP) to unbalanced (coax, for instance). Such a device matches Balanced-to-Unbalanced and is therefore called a balun. There is more on baluns in Section 14.9.3.6.7, Baluns.

14.18 AES/EBU Digital Audio Cable Digital audio technology has been around for many years, even decades, but until recently it has not been used much for audio. This has now changed and digital audio is overtaking analog audio. For this reason it is important that the cable used for digital signals meet the digital requirements. To set a standard, the Audio Engineering Society (AES) and the European Broadcast Union (EBU) have set standards for digital audio cable. The most common sampling rates and equivalent bandwidth are shows in Table 14-28. It is important that the line impedance be maintained to eliminate reflections that degrade the signal beyond recovery. Standard analog cable can be used for runs under 50 ft (15 m) but beyond that, reliability decreases. The impedance and capacitance of analog cable is 40 to 70 :"and 20 to 50 pF/ft. The impedance and capacitance for digital cable is 110 : and 13 pF/ft with a velocity of propagation of 78%. Proper impedance match and low capacitance are required so the square wave signal is not distorted, reflected, or attenuated. Broadcast cable is most often #24 (7 × 32) tinned copper wire with short overall twist lengths, low-loss foam insulation, and 100% aluminum polyester foil shield for permanent installations. Braided shields are also available for portable use. If required, #22 to #26 wire can be obtained. Digital audio cable also comes in multiple pairs with each pair individually shielded, and often jacketed, allowing each pair and its shield to be completely isolated from the others. One pair is capable of carrying two channels of digital audio. Cables are terminated with either XLR connectors or are punched down or soldered in patch panels. 14.18.1 AES/EBU Digital Coaxial Cable Digital audio requires a much wider bandwidth than analog. As the sampling rate doubles, the bandwidth also doubles, as shown in Table 14-28. Digital audio can be transmitted farther distances over coax than over twisted pairs. The coax should have a 75 : impedance, a solid copper center conductor, and

Table 14-28. Sampling Rate versus Bandwidth Sampling Rate kHz

Bandwidth MHz

Sampling Rate kHz

Bandwidth MHz

32.0

4.096

48.0

6.144

38.0

4.864

96.0

12.228

44.1

5.6448

192.0

24.576

have at least 90% shield coverage. When transmitting audio over an unbalanced coax line, the use of baluns may be required to change from balanced to unbalanced and back unless the device contains AES/EBU unbalanced coax inputs and outputs. The baluns change the impedance from 110 : balanced to 75 : unbalanced and back.

14.19 Triboelectric Noise Noise comes in a variety of types such as EMI (electromagnetic interference) and RFI (radio frequency interference). There are also other kinds of noise problems that concern cables. These are mechanically generated or mechanically induced noise, commonly called triboelectric noise. Triboelectric noise is generated by mechanical motion of a cable causing the wires inside the shield to rub against each other. Triboelectric noise is actually small electrical discharges created when conductors position changes relative to each other. This movement sets up tiny capacitive changes that eventually pop. Highly amplified audio can pick this up. Fillers, nonconductive elements placed around the conductors, help keep the conductor spacing constant while semiconductive materials, such as carbon-impregnated cloth or carbon-plastic layers, help dissipate charge buildup. Triboelectric noise is measured through low noise test equipment using three low noise standards: NBS, ISA-S, and MIL-C-17. Mechanically induced noise is a critical and frequent concern in the use of high-impedance cables such as guitar cords and unbalanced microphone cables that are constantly moving. The properties of special conductive tapes and insulations are often employed to help prevent mechanically induced noise. Cable without fillers can o ften prod uce trib oele ctric no ise. Thi s is why premise/data category cables are not suitable for flexing, moving audio applications. There are emerging flexible tactical data cables, especially those using bonded pairs, that might be considered for these applications.

Transmission Techniques: Wire and Cable 14.20 Conduit Fill To find the conduit size required for any cable, or group of cables, do the following: 1. 2. 3. 4. 5.

Square the OD (outside diameter) of each cable and total the results. To install only one cable: multiply that number by 0.5927. To install two cables: multiply by 1.0134. To install three or more cables: multiply the total by 0.7854. From step #2 or #3 or #4, select the conduit size with an area equal to or greater than the total area. Use the ID (inside diameter) of the conduit for this determination.

This is based on the NEC ratings of • single cable • two cables • three or more cables

53% fill 31% fill 40% fill

If the conduit run is 50 ft to 100 ft, reduce the number of cables by 15%. For each 90° bend, reduce the conduit length by 30 ft. Any run over 100 ft requires a pull box at some midpoint.

14.21 Long Line Audio Twisted Pairs As can be seen in Table 14-29, low frequency signals, such as audio, rarely go a quarter-wavelength and, therefore, the attributes of a transmission line, such as the determination of the impedance and the loading/matching of that line, are not considered. However, long twisted pairs are common for telephone and similar applications, and now apply for moderate data rate, such as DSL. A twisted-pair transmission line is loaded at stated intervals by connecting an inductance in series with the line. Two types of loading are in general usage—lumped and continuous. Loading a line increases the impedance of the line, thereby decreasing the series loss because of the conductor resistance. Although loading decreases the attenuation and distortion and permits a more uniform frequency characteristic, it increases the shunt losses caused by leakage. Loading also causes the line to have a cutoff frequency above which the loss becomes excessive. In a continuously loaded line, loading is obtained by wrapping the complete cable with a high-permeability magnetic tape or wire. The inductance is distributed

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evenly along the line, causing it to behave as a line with distributed constants. In the lumped loading method, toroidal wound coils are placed at equally spaced intervals along the line, as shown in Fig. 14-18. Each coil has an inductance on the order of 88 mH. The insulation between the line conductors and ground must be extremely good if the coils are to function properly.

Figure 14-18. Loading coil connected in a balanced transmission line.

Loading coils will increase the talking distance by 35 to 90 miles for the average telephone line. If a high-frequency cable is not properly terminated, some of the transmitted signal will be reflected back toward the transmitter, reducing the output.

14.22 Delay and Delay Skew The fact that every cable has a velocity of propagation, obviously means that it takes time for a signal to go down a cable. That time is called delay, normally measured in nanoseconds (Dn). Vp can easily be converted into delay. Since Vp is directly related to dielectric constant (DC ), they are all directly related as shown in Eq. 14-8 and determine the delay in nanoseconds- per-foot (ns/ft). 100 Dn = --------Vp =

(14-8)

While these equations will give you a reasonable approximate value, the actual equations should be Delay = 101.67164 ------------------------Vp

(14-9)

= 1.0167164 DC. Delay becomes a factor in broadcasting when multiple cables carry a single signal. This commonly occurs in RGB or other component video delivery systems. Delay also appears in high-data rate UTP, such

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a 1000Base-T (1GBase-T) and beyond where data is split between the four pairs and combined at the destination device. Where signals are split up and recombined, the different cables supplying the components will each have a measurable delay. The trick is for all the component cables to have the same delay to deliver their portions at the same time. The de facto maximum timing variation in delay for RGB analog is delivery of all components within 40 ns. Measuring and adjusting cable delivery is often called timing. By coincidence, the maximum delay difference in the data world is 45 ns, amazingly close. In the data world, this is called skew or delay skew, where delivery does not line up. In the RGB world, where separate coax cables are used, they have to be cut to the same electrical length. This is not necessarily the same physical length. Most often, the individual cables are compared by a Vectorscope, which can show the relationship between components, or a TDR (time domain reflectometer) that can establish the electrical length (delay) of any cable. Any difference in physical versus electrical length can be accounted for by the velocity of propagation of the individual coaxes, and therefore, the consistency of manufacture. If the manufacturing consistency is excellent, then the velocity of all coaxes would be the same, and the physical length would be the same as the electrical length. Where cables are purchased with different color jackets, to easily identify the components, they are obviously made at different times in the factory. It is then a real test of quality and consistency to see how close the electrical length matches the physical length. Where cables are bundled together, the installer then has a much more difficult time in reducing any timing errors. Certainly in UTP data cables, there is no way to adjust the length of any particular pair. In all these bundled cables, the installer must cut and connectorize. This becomes a consideration when four-pair UTP data cables (category cables) are used to deliver RGB, VGA, and other nondata component delivery systems. The distance possible on these cables is therefore based on the attenuation of the cables at the frequency of operation, and on the delay skew of the pairs. Therefore, the manufacturers measurement and guarantee (if any) of delay skew should be sought if nondata component delivery is the intended application.

14.23 Attenuation All cable has attenuation and the attenuation varies with frequency. Attenuation can be found with the equation

Rt A = 4.35 ----- + 2.78pf H Zo

(14-10)

where, A is the attenuation in dB/100 ft, Rt is the total dc line resistance in :/100 ft, H is the dielectric constant of the transmission line insulation, p is the power factor of the dielectric medium, f is the frequency, Zo is the impedance of the cable. Table 14-29 gives the attenuation for various 50 : : ,and 75 : cables. The difference in attenuation is due to either the dielectric of the cable or center-conductor diameter.

14.24 Characteristic Impedance The characteristic impedance of a cable is the measured impedance of a cable of infinite length. This impedance is an ac measurement, and cannot be measured with an ohmmeter. It is frequency-dependent, as can be seen in Fig. 14-19. This shows the impedance of a coaxial cable from 10 Hz to 100 MHz. At low frequencies, where resistance is a major factor, the impedance is changing from a high value (approximately 4000 : at 10 Hz) down to a lower impedance. This is due to skin effect (see Section 14.2.8), where the signal is moving from the whole conductor at low frequencies to just the skin at high frequencies. Therefore, when only the skin is carrying the signal, the resistance of the conductor is of no importance. This can be clearly seen in the equations for impedance, Eq. 14-13, for low frequencies, shows R, the resistance, as a major component. For high frequencies, Eq. 14-14, there is no R, no resistance, even in the equation. Once we enter that high-frequency area where resistance has no effect, around 100 kHz as shown in Fig. 14-19, we enter the area where the impedance will not change. This area is called the characteristic impedance of the cable. The characteristic impedance of an infinitely long cable does not change if the far end is open or shorted. Of course, it would be impossible to test this as it is impossible to short something at infinity. It is important to terminate coaxial cable with its rated impedance or a portion of the signal can reflect back to the input, reducing the efficiency of the transmission. Reflections can be caused by an improper load, using a wrong connector—i.e., using a 50 ȍ video BNC connector at

Transmission Techniques: Wire and Cable

433

Table 14-29. Coaxial Cable Signal Loss (Attenuation) in dB/100 ft Frequency

RG-174/ 8216

RG-58/ 8240

RG-8X/ 9258

RG-8/ 8237

RG-8/ RF-9913F

RG-59/ 8241

RG-6/ 9248

RG-11/ 9292

1 MHz

1.9

0.3

0.2

0.1

0.6

0.3

0.2

10 MHz

3.3

1.1

1.0

0.6

0.4

1.1

0.7

0.5

50 MHz

5.8

2.5

2.3

1.3

0.9

2.4

1.5

1.0