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Rabin Raut and M. N. S. Swamy Modern Analog Filter Analysis and Design

Related Titles Shenoi, B. A. Introduction to Digital Signal Processing and Filter Design 2005 ISBN: 978-0-471-46482-2 Madsen, C. K., Zhao, J. H. Optical Filter Design and Analysis A Signal Processing Approach 1999 ISBN: 978-0-471-18373-0

Rabin Raut and M. N. S. Swamy Modern Analog Filter Analysis and Design A Practical Approach

The Authors Dr. Rabin Raut Concordia University Electrical and Computer Engineering Montreal, Canada rabinr@ece.concordia.ca Dr. M. N. S. Swamy Concordia University Electrical and Computer Engineering Montreal, Canada swamy@ece.concordia.ca Cover Spieszdesign, Neu-Ulm, Germany All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at .  2010 WILEY-VCH Verlag & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Cover Design Adam Design, Weinheim Typesetting Laserwords Private Ltd., Chennai, India Printing and Binding Fabulous Printers Pte Ltd, Singapore Printed in Singapore Printed on acid-free paper ISBN: 978-3-527-40766-8

V A student acquires a quarter of knowledge from the teacher, a quarter from self study, a quarter from class mates, and the ﬁnal quarter in course of time. From Neeti Sara To Our parents, teachers, and our wives Sucheta & Leela and Late Prof. B. B. Bhattacharyya (Ph.D. supervisor of R. Raut and First Ph.D. student of M. N. S Swamy) Modern Analog Filter Analysis and Design: A Practical Approach. Rabin Raut and M. N. S. Swamy Copyright  2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40766-8

VII 28 9 9 A Review of Network Analysis Techniques 7 Transformed Impedances 7 Nodal Analysis Loop (Mesh) Analysis Network Functions 11 One-Port and Two-Port Networks 12 One-Port Networks 12 Two-Port Networks 13 Admittance Matrix Parameters 13 Impedance Matrix Parameters 14 Chain Parameters (Transmission Parameters) 14 Interrelationships 15 Three-Terminal Two-Port Network 16 Equivalent Networks 16 Some Commonly Used Nonreciprocal Two-Ports Indeﬁnite Admittance Matrix 18 Network Functions of a Multiterminal Network 20 Analysis of Constrained Networks 24 Active Building Blocks for Implementing Analog Filters Operational Ampliﬁer 28 Operational Transconductance Ampliﬁer 30 Current Conveyor 31 Practice Problems 33 16 2 2.1 2.2 2.3 2.4 2.5 2.5.1 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.2.4 2.5.2.5 2.5.2.6 2.5.2.7 2.6 2.6.1 2.7 2.8 2.8.1 2.8.2 2.8.3 3 3.1 3.2 3.3 Contents Preface XV Abbreviations XIX 1 Introduction 1 Network Theorems and Approximation of Filter Functions 41 Impedance Scaling 41 Impedance Transformation 42 Dual and Inverse Networks 44 Modern Analog Filter Analysis and Design: A Practical Approach. Rabin Raut and M. N. S. Swamy Copyright  2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40766-8

VIII Contents 3.3.1 3.3.2 3.4 3.5 3.6 3.7 3.8 3.9 3.9.1 3.9.1.1 3.9.2 3.9.2.1 3.9.3 3.9.4 3.10 3.10.1 3.10.2 3.10.3 3.11 3.11.1 3.11.2 3.11.3 3.11.4 3.12 4 4.1 4.2 4.3 4.4 5 5.1 5.2 5.3 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.5 5.6 5.6.1 45 69 44 Dual and Inverse One-Port Networks Dual Two-Port Networks Reversed Networks 47 Transposed Network 48 Applications to Terminated Networks 50 Frequency Scaling 52 Types of Filters 52 Magnitude Approximation 54 Maximally Flat Magnitude (MFM) Approximation 55 MFM Filter Transfer Function 56 Chebyshev (CHEB) Magnitude Approximation 60 CHEB Filter Transfer Function 63 Elliptic (ELLIP) Magnitude Approximation 65 Inverse-Chebyshev (ICHEB) Magnitude Approximation 68 Frequency Transformations LP to HP Transformation 69 LP to BP Transformation 71 LP to BR Transformation 73 Phase Approximation 73 Phase Characteristics of a Transfer Function 74 The Case of Ideal Transmission 74 Constant Delay (Linear Phase) Approximation 75 Graphical Method to Determine the BT Filter Function 76 Delay Equalizers 77 Practice Problems 78 Basics of Passive Filter Design 83 Singly Terminated Networks 83 Some Properties of Reactance Functions 85 Singly Terminated Ladder Filters Doubly Terminated LC Ladder Realization 92 Practice Problems 100 88 Second-Order Active-RC Filters 103 Some Basic Building Blocks using an OA 104 Standard Biquadratic Filters or Biquads 104 Realization of Single-Ampliﬁer Biquadratic Filters 109 Positive Gain SAB Filters (Sallen and Key Structures) 111 Low-Pass SAB Filter 111 RC:CR Transformation 113 High-Pass Filter 115 Band-Pass Filter 115 Inﬁnite-Gain Multiple Feedback SAB Filters 115 Inﬁnite-Gain Multiple Voltage Ampliﬁer Biquad Filters 117 KHN State-Variable Filter 119

Contents IX 5.6.2 5.6.3 5.7 5.7.1 5.7.2 5.7.3 5.7.4 5.8 5.8.1 5.8.1.1 5.8.1.2 5.8.1.3 5.8.2 5.9 124 126 Tow–Thomas Biquad 121 Fleischer–Tow Universal Biquad Structure 123 Sensitivity Basic Deﬁnition and Related Expressions 124 Comparative Results for ωp and Qp Sensitivities A Low-Sensitivity Multi-OA Biquad with Small Spread in Element Values 126 Sensitivity Analysis Using Network Simulation Tools 129 Effect of Frequency-Dependent Gain of the OA on the Filter Performance 130 Cases of Inverting, Noninverting, and Integrating Ampliﬁers Using an OA with Frequency-Dependent Gain 130 Inverting Ampliﬁer 130 Noninverting Ampliﬁer 131 Inverting Integrating Ampliﬁer 132 Case of Tow–Thomas Biquad Realized with OA Having Frequency-Dependent Gain 132 Second-Order Filter Realization Using Operational Transconductance Ampliﬁer (OTA) Realization of a Filter Using OTAs 138 An OTA-C Band-Pass Filter 138 A General Biquadratic Filter Structure 139 Technological Implementation Considerations 140 Resistances in IC Technology 141 135 5.9.1 5.9.2 5.9.3 5.10 5.10.1 5.10.1.1 Diffused Resistor 141 Pinched Resistor 142 5.10.1.2 Epitaxial and Ion-Implanted Resistors 142 5.10.1.3 Active Resistors 5.10.1.4 Capacitors in IC Technology 5.10.2 5.10.2.1 Junction Capacitors 145 5.10.2.2 MOS Capacitors 145 Polysilicon Capacitor 5.10.2.3 5.10.3 Inductors 146 5.10.4 Active Building Blocks 147 5.10.4.1 Operational Ampliﬁer (OA) 5.10.4.2 Operational Transconductance Ampliﬁer (OTA) 5.10.4.3 5.10.4.4 Transconductance Ampliﬁers (TCAs) Current Conveyor (CC) Practice Problems 152 143 144 150 146 147 151 148 6 6.1 6.2 6.2.1 Switched-Capacitor Filters 161 Switched C and R Equivalence Discrete-Time and Frequency Domain Characterization 163 SC Integrators: s ↔ z Transformations 164 162

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