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1715-ElecFilter_FM.qxd 06/09/06 17:02 Page i 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter ELECTRONIC FILTER DESIGN HANDBOOK Arthur B. Williams Fred J.Taylor Fourth Edition McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page ii 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 0 1 9 8 7 6 ISBN 0-07-147171-5 The sponsoring editor for this book was Wendy Rinaldi, the editing supervisor was Jody McKenzie, and the production supervisor was Jean Bodeaux. It was set in Times Roman by International Typesetting and Composition. The art director for the cover was Handel Low. Printed and bound by RR Donnelley. McGraw-Hill books are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please write to the Director of Special Sales, McGraw-Hill Professional, Two Penn Plaza, New York, NY 10121-2298. Or contact your local bookstore. Information contained in this work has been obtained by The McGraw- Hill Companies, Inc. (“McGraw-Hill”) from sources believed to be reli- able. However, neither McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and nei- ther McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought.

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page iii 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter From Arthur B. Williams To my Family Ellen, Howard, Bonnie, Robin, Mitchell and grandchildren Leviah and Ilona From Dr. Fred J. Taylor To my grandchildren Schuyler, Bennett, and Graysen and their devoted grandmother Lori

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page iv 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter ABOUT THE AUTHORS Arthur Williams is the Chief Scientist at Telebyte Inc., a developer and manufacturer of broadband test equipment and data communication products. Previously, he was Senior Staff Engineer and Manager of Engineering for Tellabs Inc. Author of five books and holder of eleven patents, Mr. Williams has served as a consultant to the industry and is currently the Chairman of the IEEE Circuits and Systems (CAS) chapter on Long Island. Fred J. Taylor is co-founder and Chairman of the Board of the Athena Group, a DSP semi- conductor silicon intellectual property company and education technology innovator. He is also professor of electrical and computer engineering, and computer and information science engineering at the University of Florida. Author of ten textbooks and holder of three patents, Dr. Taylor serves as a consultant to Fortune 500 companies and government agencies. iv

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page v 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter CONTENTS Preface xiii Chapter 1. Introduction to Modern Network Theory 1.1. Modern Network Theory / 1 The Pole-Zero Concept / 1 Synthesis of Filters from Polynomials / 2 Active vs. Passive Filters / 7 Bibliography / 8 Chapter 2. Selecting the Response Characteristic 1 9 2.1. Frequency-Response Normalization / 9 Frequency and Impedance Scaling / 9 Low-Pass Normalization / 12 High-Pass Normalization / 14 Bandpass Normalization / 16 Band-Reject Normalization / 24 2.2. Transient Response / 29 The Effect of Nonuniform Time Delay / 29 Step Response of Networks / 32 Impulse Response / 34 Estimating Transient Characteristics / 34 2.3. Butterworth Maximally Flat Amplitude / 42 2.4. Chebyshev Response / 47 2.5. Bessel Maximally Flat Delay / 52 2.6. Linear Phase with Equiripple Error 2.7. Transitional Filters / 64 2.8. Synchronously Tuned Filters / 70 2.9. Elliptic-Function Filters / 79 / 64 Using the Filter Solutions (Book Version) Software for Design of Elliptic Function Low- Pass Filters / 86 Using the ELI 1.0 Program for the Design of Odd-Order Elliptic-Function Low-Pass Filters up to the 31st Order / 87 2.10. Maximally Flat Delay with Chebyshev Stopband / 88 Bibliography / 88 Chapter 3. Low-Pass Filter Design 89 3.1. LC Low-Pass Filters / 89 All-Pole Filters / 89 v

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page vi 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter vi CONTENTS Elliptic-Function Filters / 90 Duality and Reciprocity / 93 Designing for Unequal Terminations / 93 Effects of Dissipation / 97 Using Predistorted Designs / 99 3.2. Active Low-Pass Filters / 103 All-Pole Filters / 103 VCVS Uniform Capacitor Structure / 113 The Low-Sensitivity Second-Order Section / 114 Elliptic-Function VCVS Filters / 116 State-Variable Low-Pass Filters / 120 Generalized Impedance Converters / 128 Bibliography / 135 Chapter 4. High-Pass Filter Design 4.1. LC High-Pass Filters / 137 The Low-Pass to High-Pass Transformation / 137 The T-to-Pi Capacitance Conversion / 142 4.2. Active High-Pass Filters / 143 The Low-Pass to High-Pass Transformation / 143 All-Pole High-Pass Filters / 144 Elliptic-Function High-Pass Filters / 145 State-Variable High-Pass Filters / 151 High-Pass Filters Using the GIC / 159 Active Elliptic-Function High-Pass Filters Using the GIC / 161 Bibliography / 164 Chapter 5. Bandpass Filters 5.1. LC Bandpass Filters / 165 Wideband Filters / 165 Narrowband Filters / 167 Narrowband Coupled Resonators / 183 Predistorted Bandpass Filters / 189 Elliptic-Function Bandpass Filers / 192 5.2. Active Bandpass Filters / 199 Wideband Filters / 199 137 165 The Bandpass Transformation of Low-Pass Poles and Zeros / 202 Sensitivity in Active Bandpass Circuits / 207 All-Pole Bandpass Configurations / 207 Elliptic-Function Bandpass Filters / 224 State-Variable (Biquad) Circuit / 230 Bibliography / 237 Chapter 6. Band-Reject Filters 239 6.1. LC Band-Reject Filters / 239 The Band-Reject Circuit Transformation / 239 All-Pole Band-Reject Filters / 240 Elliptic-Function Band-Reject Filters / 245 Null Networks / 252 6.2. Active Band-Reject Filters / 257 Wideband Active Band-Reject Filters / 257

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page vii 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter vii 279 CONTENTS Band-Reject Transformation of Low-Pass Poles / 261 Narrowband Active Band-Reject Filters / 265 Active Null Networks / 271 Bibliography / 277 Chapter 7. Networks for the Time Domain 7.1. All-Pass Transfer Functions / 279 First-Order All-Pass Transfer Functions / 279 Second-Order All-Pass Transfer Functions / 281 7.2. Delay Equalizer Sections / 283 LC All-Pass Structures / 283 Active All-Pass Structures / 287 7.3. Design of Delay Lines / 292 The Low-Pass to All-Pass Transformation / 292 LC Delay Lines / 293 Active Delay Lines / 297 7.4. Delay Equalization of Filters / 299 First-Order Equalizers / 300 Second-Order Equalizers / 303 7.5. Wideband 90° Phase-Shift Networks / 307 7.6. Adjustable Delay and Amplitude Equalizers / 313 LC Delay Equalizers / 314 LC Delay and Amplitude Equalizers / 316 Active Delay and Amplitude Equalizers / 319 Bibliography / 323 Chapter 8. Refinements in LC Filter Design and the Use of Resistive Networks 325 8.1. Introduction / 325 8.2. Tapped Inductors / 325 8.3. Circuit Transformations / 327 Norton’s Capacitance Transformer Narrowband Approximations / 330 / 328 8.4. Designing with Parasitic Capacitance / 333 8.5. Amplitude Equalization for Inadequate Q / 336 8.6. Coil-Saving Elliptic-Function Bandpass Filters / 340 8.7. Filter Tuning Methods / 343 8.8. Measurement Methods / 345 Insertion Loss and Frequency Response / 345 Input Impedance of Filter Networks / 346 Time-Domain Characteristics / 347 Measuring the Q of inductors / 351 8.9. Designing for Unequal Impedances / 351 Impedance Matching / 351 Exponentially Tapered Impedance Scaling / 351 Minimum Loss Resistive Pad for Impedance Matching / 352 8.10. Symmetrical Attenuators / 355 Bridged T Attenuator 8.11. Power Splitters / 357 / 356 Resistive Power Splitters / 357 A Magic-T Splitter / 357 Bibliography / 360

1715-ElecFilter_FM.qxd 06/09/06 17:02 Page viii 6x9 Handbook / Electronic Filter Design / Williams & Taylor /147171-5 / Front Matter viii CONTENTS Chapter 9. Design and Selection of Inductors for LC Filters 361 9.1. Basic Principles of Magnetic-Circuit Design / 361 Units of Measurement / 361 Saturation and DC Polarization / 362 Inductor Losses / 363 Effect of an Air Gap / 363 The Design of Coil Windings / 364 9.2. MPP Toroidal Coils / 367 Characteristics of Cores / 367 Winding Methods for Q Optimization / 371 Designing MPP Toroids from Q Curves / 372 9.3. Ferrite Pot Cores / 376 The Pot Core Structure / 376 Electrical Properties of Ferrite Pot Cores / 377 Winding of Bobbins / 380 RM Cores / 382 9.4. High-Frequency Coil Design / 383 Powdered-Iron Toroids / 383 Winding Methods / 384 Air-Core Inductors / 387 Surface Mount RF Inductors / 387 Bibliography / 392 Chapter 10. Component Selection for LC and Active Filters 393 10.1. Capacitor Selection / 393 Properties of Dielectrics / 393 Capacitor Construction / 394 Selecting Capacitors for Filter Applications / 398 10.2. Resistors / 403 Fixed Resistors / 403 Variable Resistors / 408 Resistor Johnson (Thermal) Noise / 409 10.3. Operational Amplifiers / 410 A Review of Basic Operational-Amplifier Theory / 410 An Analysis of Non-Ideal Amplifiers / 413 Practical Amplifier Considerations / 415 Operational Amplifier Selection / 417 A Survey of Popular Amplifier Types / 419 10.4. General Manufacturing Considerations / 422 Bibliography / 423 Chapter 11. Normalized Filter Design Tables Chapter 12. Introduction to Digital Filters 12.1. Introduction to Signal Processing / 497 12.2. Introduction to Digital Signal Processing (DSP) 12.3. The Relation to Analog Filters / 498 / 497 Digital Advantages / 498 Analog Advantages / 499 12.4. Signal Representation / 500 425 497

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