Analog and Digital Filter Design, Essays (university) of Digital & Analog Electronics

Download Analog and Digital Filter Design and more Essays (university) Digital & Analog Electronics in PDF only on Docsity!

E d

ANALOGAND 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.

Practical RF Handbook, Third Edition by Ian Hickman

0-7506-5639-8, Paperback, 304 pgs., $39.

Poti'er Supply Cookbook, Second Edition by Marty Brown

0-7506-7329-X, Paperback, 336 pgs., $39.

Radio Frequency Transistors, Norman Dye and Helge Granberg

0-7506-7281-1, Paperback, 320 pgs., $49.

Troubleshooting Analog Circuits by Robert A. Pease

0-7506-9499-8, Paperback, 21 7 pgs., $34.

The Art and Science of Analog Circuit Design, edited by Jim Williams

0-7506-7062-2, Paperback, 416 pgs., $34.

Introducing the EmM BOOKSTORE

The m M 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 E mBookstore at

www.ednmag/bookstore.com

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

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- Tel: 781-904- Fax: 781-904-

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

24 25 29 31 31 34 38 39 39

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

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

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 UAF Integrated Circuit Filter MAX Integrated Circuit Filter MAX Integrated Circuit Filter MAX270lMAX Switched Capacitor Filters Switched Capacitor Filter IC LT1066- Microprocessor Programmable ICs MAX260IMAX261/MAX Pin Programmable ICs MAX263/MAX264/MAX267/MAX Other Switched Capacitor Filters An Application of Switched Capacitor Filters Resistor Value Calculations Synthesizer Filtering Reference

CHAPTER 15 Introduction to Digital Filters

Analog-to-DigitalConversion Under-Sampling Over-Sampling

35 1

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 Implementationof 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 16 Digital 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 b y 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-SamplingRate-Changer References

CHAPTER 17 IIR Filter Design

Bilinear Transformation Pre-Warping

PREFACE

This book 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 impulse response (FIR) filter design, which are now quite com-

monly used with digital signal processors. Infinite impulse response filters are

based on analog filter designs.

Detailed circuit theory and mathematical derivations are not included, because

this book is intended to be an aid in practical filter design by engineers. The

circuit theory and mathematical material that is included is of an introductory

nature only. Those who are more academically minded will find much of the

information useful as an introduction. A more in-depth study of filter theory

can be found in academic books referred to in the bibliography. Equations and

supplementary material are included in the Appendix.

Designing filters requires the use of mathematics. Fortunately, it is possible to

successfully design filters with very little theoretical and mathematical knowl-

edge. In fact, for passive analog filter design the mathematics can be limited to

simple multiplication and division by the use of look-up tables. The design of

active analog filters is slightly more ditlicult, requiring both arithmetic and

algebra combined with look-up tables. The equations behind many of the look-

up tables are included in the Appendix.

Digital FIR filters perform their function by first passing a digitized signal

through a series of discrete delay elements and then multiplying the output of

each delay element by a number (or coefficient). The values produced from all

the multiplication functions at each clock period are then added together to give

an output. Hence digital filter designs do not produce component values.

Instead, they produce a series of numbers (coefficients) that are used by the mul-

tiplication functions. There are no design tables; the series of coefficients is pro-

duced by an algebraic equation, so the designer must be familiar with arithmetic

and algebra in order to produce these coefficients.

1 4

Analog and Digital Filter Design

The principles behind digital filters are based on the relationship between the

time and frequency domains. Although digital filters can be designed without

knowledge of this relationship, a basic awareness makes the process far more

understandable. The relationship between the time and frequency domains can

be grasped by performing a practical test: apply a range of signals to both the

input of an oscilloscope and the input of a spectrum analyzer, and then compare

the instrument displays. More formally, Fourier and Laplace transforms are

used to convert between the time and frequency domains. A brief introduction

to these is given in chapter 3. Whole books are devoted to the Fourier and

Laplace transforms; references are given in the Bibliography.

All the designs described in this book have been either built by myself or sim-

ulated using circuit analysis 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.

Chapters have been arranged in what I think is a logical order. A summary of

the chapters in this book follows.

Chapter 1 gives examples of filter applications, to explain why filter design is

such an important topic. A description of the limitations for a number of filter

types is given; this will help the designer to decide whether to use an active,

passive, or digital filter. Basic filter terminology and an overview of the design

process are also discussed.

Chapter 2 describes the frequency response characteristics of filters, both ideal

and practical. Ideally, filters should not attenuate wanted signals but give infi-

nite attenuation to unwanted signals. This response is known as a brick wall

filter: it does not exist, but approximations to it are possible. The four basic

responses are described (Le.. flat or rippled passband and smooth or rippled

stopband) and show how standard Bessel, Butterworth, Chebyshev, Cauer, and

Inverse Chebyshev approximations have one of these responses. Graphs describe

the shape of each frequency response.

A very important topic of this chapter is the use of normalized lowpass filters

with a 1 rad/s cutoff frequency. Normalized lowpass filters can be used as a basis

for any filter design. For example, a normalized lowpass filter can be scaled to

design a lowpass filter with any cutoff frequency. Also, with only slightly more

difficulty, the normalized design can be translated into highpass, bandpass, and

bandstop designs. Tables of component values for some normalized approxi-

mations are given. Formulae for deriving these tables are also provided, where

applicable.

1 6

Analog and Digital Filter Design

are also described (amplifier parameters can have a significant effect), as are

measurement techniques.

Chapter 1 1 describes current software availability, including integrated

circuit-specific software. The actual filter design process can be considerably

automated. Indeed, I have written a program with Number One Systems Ltd.

called FILTECH, which designs and simulates filter circuits. I outline how

FILTECH operates at a systems level. There are also other programs on the

market. Some of these only design active filters; they are offered free because

they enable users to design filters using certain manufacturers’ integrated

circuits.

Executable PC programs, capable of designing useful filters, are supplied at

www.bh.com/companions/0750675470. This chapter basically serves as a user

guide. describing their operation. These programs are far simpler than

FILTECH and give a netlist compatible with SPICE-like analysis programs.

Chapter 12 describes how transmission lines can be used to filter signals.

Quarter-wave lines of either short or open circuit termination can be used to

pass or stop certain frequencies. One application of this is to allow a radio

carrier signal into a receiver from an antenna while preventing internal radio

signals from radiating back to the antenna.

Printed circuit board (PCB) filters are also described. Tracks on a PCB can be

transmission lines when the signal frequency is high. The width of a track on a

printed circuit board defines its impedance; sections of wider or narrower track

become inductive or capacitive. Concatenation of narrow and wide track sec-

tions can therefore form an LC (inductor capacitor) filter.

Phase-locked loop filters are usually quite simple, but poor design can cause

instability of the loop. Many people avoid designing phase-locked loops for this

reason. Chapter 13 provides some examples that may help remove some of this

fear.

Chapter 14 provides an introduction to switched capacitor filters. Commercial

filter ICs (integrated circuits) are described and plots of some practical exam-

ples are given. Problems with this type of filter are described, as are some of the

benefits such as being able to make the filter cutoff programmable or adjustable.

Chapter 15 outlines the process of digital filtering. In this chapter I cover the

data sampling operation (under-sampling, over-sampling, interpolation, and

decimation) and the advantages or problems of each. A brief outline of digital

filtering techniques provides some understanding of digital signal processing.

Digital signal processors (DSPs) are described, along with the mathematical

methods by which they handle data during signal processing.

17

Preface

Chapters 16 and 17 cover digital filtering in a little more depth. Chapter 16

covers Finite Impulse Response (FIR) filters and Chapter 17 covers Infinite

Impulse Response (IIR) filters. Equations needed to find multiplier coefficients

are included with worked examples.