Analog and digital filter design
Ed ANALOG AND DIGITAL FILTER DESIGN Second Edition Other titles in the EDN Series for Design Engineers Electromagnetics Explained: A Handbook for Wireless, RE EMC, and High-speed Electronics by Ron Schmitt, 0-7506-7403-2, Hardcover, 359 pgs., $34.99 Practical RF Handbook, Third Edition by Ian Hickman 0-7506-5639-8, Paperback, 304 pgs., $39.99 Poti'er Supply Cookbook, Second Edition by Marty Brown 0-7506-7329-X, Paperback, 336 pgs., $39.99 Radio Frequency Transistors, Norman Dye and Helge Granberg 0-7506-7281-1, Paperback, 320 pgs., $49.99 Troubleshooting Analog Circuits by Robert A. Pease 0-7506-9499-8, Paperback, 21 7 pgs., $34.99 The Art and Science of Analog Circuit Design, edited by Jim Williams 0-7506-7062-2, Paperback, 416 pgs., $34.99 Introducing the EmM BOOKSTORE The mM Bookstore offers you: + Hundreds of great technical books by engineers for engineers + Monthly drawings for FREE books + Specials offers & discount pricing + FREE sample chapters Visit the Em Bookstore at www.ednmag/bookstore.com ANALOG AND DIGITAL FILTER DESIGN Second Edition STEVE WINDER @ Newnes An ~mprmnl of Butterworth-Hemernonn Amsterdam Boston London New York Oxford Paris Son Diego San Francisco Singapore Sydney Tokyo Newnes is an imprint of Elsevier Science. Copyright 0 2002, Elsevier Science (USA). 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. Recognizing the importance of preserving what has been written, Elsevier Science prints its books on acid-frec 63 paper whenever possible. 6~ Elsevier Scicnce supports the efforts of American Forests and the Globdl RcLcaf program in its %f& campaign for the betterment of trees, forests, and our environment. Library of Congress Cataloging-in-Publication Data Winder, Steve. Analog and digital filter design / Steve Winder 2nd ed. Rev. ed. of: Filter design. c1997. Includes bibliographical references. ISBN 0-7506-7547-0 (pbk. : alk.paper) 1. Electric filters-Design and construction. I. Winder, Steve. Filter design. 11. Title. p. cm. TK7872.F5 W568 2002 621.38 15’3244~21 2002071430 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library The publisher offers special discounts on bulk orders of this book. For information, please contact: Manager of Special Sales Elsevier Science 225 Wildwood Avenue Woburn, MA 01801-2041 Tel: 781-904-2500 Fax: 781-904-2620 For information on all Newnes publications available, contact our World Wide Web home page at: http://www.newnespress.com 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America CONTENTS Preface 13 CHAPTER 1 Introduction Fundamentals Why Use Filters? What Are Signals? Decibels The Transfer Function Filter Terminology Frequency Response Phase Response Analog Filters The Path to Analog Filter Design Digital Filters Signal Processing for the Digital World The "Brick Wall" Filter Digital Filter Types The Path to Digital Filter Design Exercises CHAPTER 2 Time and Frequency Response Filter Requirements The Time Domain Analog Filter Normalization Normalized Lowpass Responses Bessel Response Bessel Normalized Lowpass Filter Component Values Butterworth Response Butterworth Normalized Lowpass Component Values Normalized Component Values for RL >> RS or RL << RS Normalized Component Values for Source and Load Impedances within a Factor of Ten 19 19 19 19 21 21 22 23 24 25 29 31 31 34 38 39 39 41 41 44 46 47 47 49 54 55 56 57 6 Analog and Digital Filter Design Chebyshev Response Normalized Component Values Equal Load Normalized Component Value Tables Normalized Element Values for Filters with RS = 0 or RS = - Inverse Chebyshev Response Component Values Normalized for 1 Rads Stopband Normalized 3dB Cutoff Frequencies and Passive Component Cauer Response Passive Cauer Filters Normalized Cauer Component Values The Cutoff Frequency References Exercises Values 58 63 65 67 69 71 75 78 78 80 81 81 82 CHAPTER 3 Poles and Zeroes 83 Frequency and Time Domain Relationship The S-Plane Frequency Response and the S-Plane Impulse Response and the S-Plane The Laplace Transform-Converting between Time and Frequency Domains First-Order Filters Pole and Zero Locations Butterworth Poles Bessel Poles Chebyshev Pole Locations Inverse Chebyshev Pole and Zero Locations Inverse Chebyshev Zero Locations Cauer Pole and Zero Locations Cauer Pole Zero Plot References Exercises 84 84 85 88 90 90 94 94 96 98 1 09 1 09 117 121 122 122 CHAPTER 4 Analog Lowpass Filters 125 Passive Filters Formulae for Passive Lowpass Filter Denormalization Denormalizing Passive Filters with Resonant Elements Mains Filter Design Active Lowpass Filters First-Order Filter Section 125 127 128 129 132 132 Contents Sullen and Key Lowpass Filter Denormalizing Sullen and Key Filter Designs State Variable Lowpass Filters Cauer and Inverse Chebyshev Active Filters Denormalizing State Variable or Biquad Designs Frequency Dependent Negative Resistance (FDNR) Filters Denormalization of FDNR Filters References Exercises CHAPTER 5 Highpass Filters Passive Filters Formulae for Passive Highpass Filter Denormalization Highpass Filters with Transmission Zeroes Active Highpass Filters First-Order Filter Section Sullen and Key Highpass Filter Using Lowpass Pole to Find Component Values Using Highpass Poles to Find Component Values Operational Amplifier Requirements Denormalizing Sullen and Key or First-Order Designs State Variable Highpass Filters Cauer and Inverse Chebyshev Active Filters Denormalizing State Variable or Biquad Designs Gyrator Filters Reference Exercises CHAPTER 6 Bandpass Filters Lowpass to Bandpass Transformation Passive Filters Formula for Passive Bandpass Filter Denormalization Passive Cauer and Inverse Chebyshev Bandpass Filters Active Bandpass Filters Bandpass Poles and Zeroes Bandpass Filter Midband Gain Multiple Feedback Bandpass Filter Denormalizing MFBP Active Filter Designs Dual Amplifier Bandpass (DABP) Filter Denormalizing DABP Active Filter Designs State Variable Bandpass Filters 7 133 135 136 137 138 1 40 144 146 146 147 147 150 152 1 54 156 157 158 158 159 159 161 162 166 167 171 172 173 173 174 178 180 182 182 185 187 188 190 191 192 [...]...8 Analog and Digital Filter Design Denormalization of State Variable Design Cauer and Inverse Chebyshev Active Filters Denormalizing Biquad Designs Reference Exercises CHAPTER Bandstop Filters 7 Passive Filters Formula for Passive Bandstop Filter Denormalization Passive Cauer and Inverse Chebyshev Bandstop Filters Active Bandstop Filters Bandstop Poles and Zeroes The Twin Tee Bandstop Filter Denormalization... Notch Filter Bandstop Using Multiple Feedback Bandpass Section Denormalization of Bandstop Design Using M B Section FP Bandstop Using Dual Amplifier Bandpass (DABP) Section Denormalization of Bandstop Design Using DABP Section State Variable Bandstop Filters Denormalization of Bandstop State Variable Filter Section Cauer and Inverse Chebyshev Active Filters Denormalization of Bandstop Biquad Filter. .. 304 305 10 Analog and Digital Filter Design CHAPTER Transmission Lines and Printed Circuit 12 Boards as Filters Transmission Lines as Filters Open-circuit Line Short-circuit Line Use of Misterminated Lines Printed Circuits as Filters Bandpass Filters References Exercises CHAPTER Filters for Phase-locked loops 13 Loop Filters Higher-Order Loops Analog versus Digital Phase-Locked Loop Practical Digital. .. passed; DC is blocked (d) Bandstop filters stop a band of frequencies between the lower and upper cutoff points They are the opposite of bandpass filters and allow two frequency bands to pass One band that is passed goes from DC to the lower cutoff frequency The other band passed covers all frequencies above the upper cutoff point 24 Analog and Digital Filter Design The designer must determine the... the filter design, even though it is not physically part of the filter The practicalities of measuring the source voltage are described in Chapter 10 When 26 Analog and Digital Filter Design the filter is designed for zero source impedance, the filter' s input voltage and the source voltage are identical, so the voltage at the filter input is measured Analog filters can be passive or active Passive filters... lowpass filter responses Pole and zero locations are important in active filter design With only knowledge of the normalized lowpass pole and zero locations for a certain transfer function, an active filter can be designed Pole and zero locations can be scaled or converted for highpass bandpass, or bandstop designs Chapters 4 to 7 describes how to design active or passive lowpass highpass bandpass, and bandstop... 400 12 Analog and Digital Filter Design Denormalization Lowpass Filter Design Highpass Frequency Scaling Bandpass Frequency Scaling Bandstop Frequency Scaling IIR Filter Stability Reference Appendix Design Equations Bessel Transfer Function Butterworth Filter Attenuation Butterworth Transfer Function Butterworth Phase Nonstandard Butterworth Passband Normalized Component Values for Butterworth Filter. .. is about analog and digital filter design The analog sections include both passive and active filter designs, a subject that has fascinated me for several years Included in the analog section are filter designs specifically aimed at radio frequency engineers, such as impedance matching networks and quadrature phase all-pass networks The digital sections include infinite impulse response (IIR) and finite... software on a personal computer As is the case in all filter design books, not every possible design topology is included However, I have included useful material that is hard to find in other filter design books such as Inverse Chebyshev filters and filter noise bandwidth I have researched many filter design books and papers in search of simple design methods to reduce the amount of mathematics required... the highpass model Bandpass and bandstop filters are more complex but can still be derived from a normalized lowpass model As an illustration, I will consider a bandpass filter and describe how to find out whether the filter specification is demanding, and hence I will be able to determine the filter order required to achieve it First, I need to find out the bandwidth of the passband Second, I need . Passive Bandpass Filter Denormalization Passive Cauer and Inverse Chebyshev Bandpass Filters Active Bandpass Filters Bandpass Poles and Zeroes Bandpass Filter. Analog Filter Design Digital Filters Signal Processing for the Digital World The "Brick Wall" Filter Digital Filter Types The Path to Digital