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Analog and digital filter design
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Ed
ANALOG AND DIGITAL
FILTER DESIGN
Second Edition
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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
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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
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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 7 Bandstop Filters
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 of Twin Tee Notch Filter
Bandstop Using Multiple Feedback Bandpass Section
Denormalization of Bandstop Design Using MFBP Section
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 Section
References
Exercises
CHAPTER 8 impedance Matching Networks
Power Splitters and Diplexer Filters
Power Splitters and Combiners
Designing a Diplexer
Impedance Matching Networks
Series and Parallel Circuit Relationships
Matching Using L, T, and PI Networks
Component Values for L Networks
Component Values for PI and T Networks
Bandpass Matching into a Single Reactance Load
Simple Networks and VSWR
VSWR of L Matching Network (Type A)
VSWR of L Matching Network (Type B)
VSWR of T Matching Networks
VSWR of PI Matching Networks
Exercises
193
194
196
197
197
199
200
204
205
209
209
213
21 4
21 4
216
216
21 7
218
219
21 9
22 1
22 1
22 1
223
226
228
23 1
232
233
234
236
237
238
238
239
240
240
24 1
Contents 9
CHAPTER 9 Phase-Shift Networks (All-Pass Filters)
Phase Equalizing All-Pass Filters
Introduction to the Problem
Detailed Analysis
The Solution: All-Pass Networks
Passive First-Order Equalizers
Passive Second-Order Equalizers
Active First-Order Equalizers
Active Second-Order Equalizers
Equalization of Butterworth and Chebyshev Filters
Group Delay of Butterworth Filters
Equalization of Chebyshev Filters
Chebyshev Group Delay
Quadrature Networks and Single Sideband Generation
References
Exercises
CHAPTER 10 Selecting Components for Analog Filters
Capacitors
Inductors
Resistors
The Printed Circuit Board (PCB)
Surface-Mount PCBs
Assembly and Test
Operational Amplifiers
Measurements on Filters
Reference
Exercises
CHAPTER 11 Filter Design Software
Filter Design Programs
Supplied Software
Active-F
Filter2
Ellipse
Diplexer
Match2A
References
243
243
243
244
246
247
249
253
254
255
256
263
263
273
283
284
285
285
289
29 1
292
293
294
295
296
297
297
299
299
299
300
30 1
302
303
304
305
1 0 Analog and Digital Filter Design
CHAPTER 12 Transmission Lines and Printed Circuit
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 13 Filters for Phase-locked loops
Loop Filters
Higher-Order Loops
Analog versus Digital Phase-Locked Loop
Practical Digital Phase-Locked Loop
Phase Noise
Capture and Lock Range
Reference
Chapter 14 Filter Integrated Circuits
Continuous Time Filters
Integrated Circuit Filter UAF42
Integrated Circuit Filter MAX274
Integrated Circuit Filter MAX275
Integrated Circuit Filter MAX270lMAX271
Switched Capacitor Filters
Switched Capacitor Filter IC LT1066-1
Microprocessor Programmable ICs MAX260IMAX261 /MAX262
Pin Programmable ICs MAX263/MAX264/MAX267/MAX268
Other Switched Capacitor Filters
An Application of Switched Capacitor Filters
Resistor Value Calculations
Synthesizer Filtering
Reference
CHAPTER 15 Introduction to Digital Filters
Analog-to-Digital Conversion
Under-Sampling
Over-Sampling
307
308
309
310
310
317
319
320
320
32 1
324
326
329
329
332
332
334
335
335
336
337
338
339
339
34 1
342
343
344
344
347
350
35 1
353
353
354
355
Contents 1 1
Decimation
Interpolation
Digital Filtering
Digital Lowpass Filters
Truncation (Applied to FIR Filters)
Transforming the Lowpass Response
Bandpass FIR Filter
Highpass FIR Filter
Bandstop FIR Filter
DSP Implementation of an FIR Filter
Introduction to the Infinite Response Filter
DSP Mathematics
Binary and Hexadecimal
Two's Complement
Adding Two's Complement Numbers
Subtracting Two's Complement Numbers
Multiplication
Division
Signal Handling
So, Why Use a Digital Filter?
Reference
Exercises
CHAPTER 16Digital FIR Filter Design
Frequency versus Time-Domain Responses
Denormalized Lowpass Response Coefficients
Denormalized Highpass Response Coefficients
Denormalized Bandpass Response Coefficients
Denormalized Bandstop Response Coefficients
Fourier Method of FIR Filter Design
Window Types
Summary of Fixed FIR Windows
Number of Taps Needed by Fixed Window Functions
FIR Filter Design Using the Remez Exchange Algorithm
Number of Taps Needed by Variable Window Functions
Windows
FIR Filter Coefficient Calculation
A Data-Sampling Rate-Changer
References
CHAPTER 17 IIR Filter Design
355
356
356
357
36 1
362
363
363
363
364
365
366
367
367
369
370
370
373
373
375
375
375
377
380
380
38 1
38 1
382
384
384
385
390
390
392
392
393
394
394
395
Bilinear Transformation
Pre-Warping
397
400
1 2 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 with
Normalized Component Values for Butterworth Filter:
Chebyshev Filter Response
Equations to Find Chebyshev Element Values
RL >> RS or RL << RS
Source and Load Impedances within a Factor of Ten
Chebyshev with Zero or Infinite Impedance Load
Chebyshev Filter with Source and Load Impedances
Load Impedance for Even-Order Chebyshev Filters
Inverse Chebyshev Filter Equations
within a Factor of Ten
Elliptic or Cauer Filter Equations
Noise Bandwidth
Butterworth Noise Bandwidth
Chebyshev Noise Bandwidth
Pole and Zero Location Equations
Butterworth Pole Locations
Chebyshev Pole Locations
Inverse Chebyshev Pole and Zero Locations
Inverse Chebyshev Zeroes
Cauer Pole and Zero Locations
Scaling Pole and Zero Locations
Finding FIR Filter Zero Coefficient Using L'Hopital's Rule
Digital Filter Equations
Appendix References
Bibliography
Answers
Index
400
40 1
403
405
406
407
408
409
409
412
41 2
41 3
414
41 5
41 5
41 6
41 7
41 7
41 8
419
419
42 1
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426
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427
429
43 1
432
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435
436
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439
447