Linear Circuit Transfer Functions(2016).pdf

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Contents

About the Author

Preface

Acknowledgement

1 Electrical Analysis – Terminology and Theorems

2 Transfer Functions

3 Superposition and the Extra Element Theorem

4 Second-order Transfer Functions

5 Nth-order Transfer Functions

Conclusion

Glossary of Terms

Index

LINEAR CIRCUIT TRANSFER FUNCTIONS

LINEAR CIRCUIT TRANSFER FUNCTIONS AN INTRODUCTION TO FAST ANALYTICAL TECHNIQUES Christophe P. Basso ON Semiconductor, Toulouse, France

This edition ﬁrst published 2016  2016 John Wiley & Sons, Ltd Registered ofﬁce John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial ofﬁces, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identiﬁed as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. 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, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Names: Basso, Christophe P., author. Title: Linear circuit transfer functions : an introduction to fast analytical techniques / Christophe Basso. Description: Chichester, West Sussex ; Hoboken, NJ : Wiley, 2016. | Includes index. Identiﬁers: LCCN 2015047967 | ISBN 9781119236375 (cloth) | ISBN 9781119236351 (epub) Subjects: LCSH: Transfer functions. | Electric circuits, Linear. Classiﬁcation: LCC TA347.T7 B37 2016 | DDC 621.3815–dc23 LC record available at http://lccn.loc.gov/2015047967 A catalogue record for this book is available from the British Library. ISBN: 9781119236375 Set in 9.5/11.5 pt TimesLTStd-Roman by Thomson Digital, Noida, India 1 2016

Contents About the Author Preface Acknowledgement 1 1.1 1.2 Input and Output Ports Electrical Analysis – Terminology and Theorems Transfer Functions, an Informal Approach 1.1.1 1.1.2 Different Types of Transfer Function The Few Tools and Theorems You Did Not Forget . . . 1.2.1 1.2.2 1.2.3 1.2.4 Norton’s Theorem at Work The Voltage Divider The Current Divider Thévenin’s Theorem at Work 1.3 What Should I Retain from this Chapter? 1.4 Appendix 1A – Finding Output Impedance/Resistance 1.5 Appendix 1B – Problems Answers 2 2.1 2.2 2.3 2.4 A Linear Time-invariant System The Need for Linearization Transfer Functions Linear Systems 2.1.1 2.1.2 Time Constants 2.2.1 Transfer Functions 2.3.1 Low-entropy Expressions 2.3.2 Higher Order Expressions 2.3.3 2.3.4 2.3.5 2.3.6 How to Determine the Order of the System? 2.3.7 First Step Towards a Generalized 1st-order Transfer Function Solving 1st-order Circuits with Ease, Three Examples 2.4.1 Second-order Polynomial Forms Low-Q Approximation for a 2nd-order Polynomial Approximation for a 3rd-order Polynomial Time Constant Involving an Inductor Zeros in the Network ix xi xiii 1 1 3 6 11 11 12 14 19 25 26 37 39 41 41 43 43 44 47 49 54 59 60 62 68 69 76 78 82

vi Contents 2.4.2 Obtaining the Zero with the Null Double Injection 2.4.3 Checking Zeros Obtained in Null Double Injection with SPICE 2.4.4 Network Excitation 2.5 What Should I Retain from this Chapter? References 2.6 Appendix 2A – Problems Answers 3 3.1 3.2 A Two-input/Two-output System Superposition and the Extra Element Theorem The Superposition Theorem 3.1.1 The Extra Element Theorem 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 The EET at Work on Simple Circuits The EET at Work – Example 2 The EET at Work – Example 3 The EET at Work – Example 4 The EET at Work – Example 5 The EET at Work – Example 6 Inverted Pole and Zero Notation 3.3 A Generalized Transfer Function for 1st-order Systems 3.3.1 Generalized Transfer Function – Example 1 3.3.2 Generalized Transfer Function – Example 2 3.3.3 Generalized Transfer Function – Example 3 3.3.4 Generalized Transfer Function – Example 4 3.3.5 Generalized Transfer Function – Example 5 Further Reading 3.4 3.5 What Should I Retain from this Chapter? References 3.6 Appendix 3A – Problems Answers References Second-order Transfer Functions 4 4.1 Applying the Extra Element Theorem Twice Low-entropy 2nd-order Expressions 4.1.1 4.1.2 Determining the Zero Positions 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 Rearranging and Plotting Expressions Example 1 – A Low-Pass Filter Example 2 – A Two-capacitor Filter Example 3 – A Two-capacitor Band-stop Filter Example 4 – An LC Notch Filter 4.2 A Generalized Transfer Function for 2nd-Order Systems Inferring the Presence of Zeros in the Circuit 4.2.1 4.2.2 Generalized 2nd–order Transfer Function – Example 1 4.2.3 Generalized 2nd–order Transfer Function – Example 2 4.2.4 Generalized 2nd–order Transfer Function – Example 3 4.2.5 Generalized 2nd–order Transfer Function – Example 4 89 94 95 100 101 102 105 116 116 120 126 130 132 137 138 140 146 150 153 156 159 163 170 174 180 180 182 183 185 218 219 219 227 231 233 235 241 245 248 255 256 257 262 266 273

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