Linear Circuit Transfer Functions E-Book

Christophe P. Basso

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 474

Veröffentlichungsjahr: 2016

Beschreibung

Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner.

Starting with simple examples, the author explains step-by-step how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speed-up analysis and predict the frequency response of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra.

Key features:

• Emphasizes analysis through employing time constant-based methods discussed in other text books but not widely used or explained.
• Develops current techniques on transfer functions, to fast analytical techniques leading to low-entropy transfer functions immediately exploitable for analysis purposes.
• Covers calculation techniques pertinent to different fields, electrical, electronics, signal processing etc.
• Describes how a technique is applied and demonstrates this through real design examples.
• All Mathcad® files used in examples and problems are freely available for download.

An ideal reference for electronics or electrical engineering professionals as well as BSEE and MSEE students, this book will help teach them how to: become skilled in the art of determining transfer function by using less algebra and obtaining results in a more effectual way; gain insight into a circuit’s operation by understanding how time constants rule dynamic responses; apply Fast Analytical Techniques to simple and complicated circuits, passive or active and be more efficient at solving problems.

Leseprobe

Contents

Cover

Title Page

Copyright

About the Author

Preface

Acknowledgement

Chapter 1: Electrical Analysis – Terminology and Theorems

1.1 Transfer Functions, an Informal Approach

1.2 The Few Tools and Theorems You Did Not Forget . . .

1.3 What Should I Retain from this Chapter?

References

1.4 Appendix 1A – Finding Output Impedance/Resistance

1.5 Appendix 1B – Problems

Answers

Chapter 2: Transfer Functions

2.1 Linear Systems

2.2 Time Constants

2.3 Transfer Functions

2.4 First Step Towards a Generalized 1st-order Transfer Function

2.5 What Should I Retain from this Chapter?

References

2.6 Appendix 2A – Problems

Answers

Chapter 3: Superposition and the Extra Element Theorem

3.1 The Superposition Theorem

3.2 The Extra Element Theorem

3.3 A Generalized Transfer Function for 1st-order Systems

3.4 Further Reading

3.5 What Should I Retain from this Chapter?

References

3.6 Appendix 3A – Problems

Answers

References

Chapter 4: Second-order Transfer Functions

4.1 Applying the Extra Element Theorem Twice

4.2 A Generalized Transfer Function for 2nd-Order Systems

4.3 What Should I Retain from this Chapter ?

References

4.4 Appendix 4A – Problems

Answers

References

Chapter 5: Nth-order Transfer Functions

5.1 From the 2EET to the NEET

5.2 Five High-order Transfer Functions Examples

5.3 What Should I Retain from this Chapter ?

References

5.4 Appendix 5A – Problems

Answers

References

Conclusion

Glossary of Terms

Index

End User License Agreement

List of Illustrations

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Guide

Cover

Table of Contents

Begin Reading

Chapter 1

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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 officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

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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

About the Author

Christophe Basso is a Technical Fellow at ON Semiconductor in Toulouse, France, where he leads an application team dedicated to developing new offline PWM controller's specifications. He has originated numerous integrated circuits among which the NCP120X series has set new standards for low standby power converters.

Further to his 2008 book Switch-Mode Power Supplies: SPICE Simulations and Practical Designs, published by McGraw-Hill, he released a new title in 2012 with Artech House, Designing Control Loops for Linear and Switching Power Supplies: a Tutorial Guide. He holds 17 patents on power conversion and often publishes papers in conferences and trade magazines including How2Power and PET.

Christophe has over 20 years of power supply industry experience. Prior to joining ON Semiconductor in 1999, Christophe was an application engineer at Motorola Semiconductor in Toulouse. Before 1997, he worked at the European Synchrotron Radiation Facility in Grenoble, France, for 10 years. He holds a BSEE equivalent from the Montpellier University (France) and a MSEE from the Institut National Polytechnique of Toulouse (France). He is an IEEE Senior member.

When he is not writing, Christophe enjoys snowshoeing in the Pyrenees.

Preface

First as a student and later as an engineer, I have always been involved in the calculation of transfer functions. When designing power electronics circuits and switch mode power supplies, I had to apply my analytical skills on passive filters. I also had to linearize active networks when I needed the control-to-output dynamic response of my converter. Methods to determine transfer functions abounded and there are numerous textbooks on the subject. I started in college with mesh-node analysis, and at some point ended up using state variables. If all paths led to the correct result, I often struggled rearranging equations to make them fit a friendly format. Matrices were useful for immediate numerical results but, when trying to extract a meaningful symbolic transfer function, I was often stuck with an intractable result. What matters with a transfer function formula is that you can immediately distinguish poles, zeros and gains without having to rework the expression. This is the idea behind the term low-entropy, a concept forged by Dr. Middlebrook.

Simulation gives you an idea where poles and zeros hide by interpreting the phase and magnitude plots with minimum-phase functions. However, inferring which terms really affect a pole or a zero position from a Bode plot is a different story. Fortunately, if the transfer function is written the right way, then you can immediately identify which elements contribute to the roots and assess how they impact the dynamic response. As some of these parasitics vary in production or drift with temperature, you have to counteract their effects so that reliability is preserved during the circuit's life. The typical example is when you are asked to assess the impact of a parasitic term variation on a product you have designed: if a new capacitor or a less expensive inductor is selected by the buyers, will production be affected? Is there a chance that stability will be jeopardized in some operating conditions? Implementing the classical analysis method will surely deliver a result describing the considered circuit, but extracting the information you need from the final expression is unlikely to happen if the equations you have are disorganized or in a high-entropy form.

This is where Fast Analytical Circuit Techniques (FACTs) come into play. The acronym was formed by Dr. Vatché Vorpérian, who formalized the technique you are about to discover here. Before him, Dr. Middlebrook published numerous papers and lectured on his Extra-Element Theorem (EET), later generalized to the N extra-element theorem by one of his alumni. Since Hendrik Bode in the 40's, authors have come up with techniques aiming to simplify linear circuit analysis through various approaches. All of them were geared towards determining the transfer function at a pace quicker than what traditional methods could provide. Unfortunately, while traveling and visiting customers world-wide, I have found that, despite all the available documentation, FACTs were rarely adopted by engineers or students. When describing examples in my seminars and showing the method at work in small-signal analysis, I could sense interest from the audience through questions and comments. However, during the discussions I had later on with some of the engineers or students, they confessed that they tried to acquire the skill but gave up because of the intimidating mathematical formalism and the complexity of the examples. If one needs to be rigorous when tackling electrical analysis, perhaps a different approach and pace could make people feel at ease when learning the method. This is what I strived to do with this new book, modestly shedding a different light on the subject by progressing with simple-to-understand examples and clear explanations. As a student, I too struggled to apply these fast analytical circuits techniques to real-world problems; as such, I identified the obstacles and worked around them with success. Thus, the seeds for this book were sown.

This book consists of five chapters. The first chapter is a general introduction to the technique, explaining what transfer functions are and how time constants characterize a circuit. The second chapter digs into transfer function definitions and polynomial forms, introducing the low-Q approximation, and how to organize 2nd and 3rd-order denominators or numerators. The third chapter uses the superposition theorem to gently introduce the extra-element theorem. Numerous examples are given to illustrate its usage in different 1st-order configurations. The fourth chapter deals with the 2-extra element theorem, generalized and applied to 2nd-order networks. Numerous examples illustrated with Mathcad® and SPICE punctuate the explanations. Finally, the fifth chapter tackles 3rd- and 4th-order circuits, all illustrated with examples. Each chapter ends with 10 fully documented problems. There is no secret; mastering a technique requires patience and practice, and I encourage you to test what you have learned after each chapter through these problems.

I have adopted the same casual writing style already used in my previous books, as readers' comments show that the way I present things better explains complex matters. Please let me know if my approach still applies here and if you enjoy reading this new book. As usual, feel free to send me your comments or any typos you may find at [email protected]. I will maintain an errata list in my personal webpage as I did for the previous books (http://cbasso.pagesperso-orange.fr/Spice.htm). Thank you, and have fun determining transfer functions!

Christophe BassoMay 2015

Acknowledgement

A book like this one could not have been written and published without the help of many contributing friends. My warmest thanks and love first go to my sweet wife Anne who endured my ups and downs when determining some of the book transfer functions: equations time is over and we can now enjoy the long and warm evenings of summer to come!

I was fortunate to share my work with my ON Semiconductor colleagues and friends who played a crucial role in reviewing my pages and challenging the method. Stéphanie Cannenterre reviewed and practiced numerous book exercises. She now masters the method: well done! Dr. José Capilla raced with me several times to determine a transfer function with his Driving Point Impedance method and I recognize his skills in doing so. Special thanks go to my friend Joël Turchi with whom I spent endless hours debating the method or discussing the validity of an equation. Merci Joël for your kindness and invaluable support for this book!

Two people did also accompany me from the beginning of the writing process. Mon ami Canadien Alain Laprade from ON Semiconductor in East Greenwich who developed an addicted relationship to the FACTs and kindly reviewed all my work. Monsieur Feucht from Innovatia did also a tremendous work in correcting my pages but also kindly polished my English. I am not exactly a novelist and cannot hide my French origins Dennis!

I want to warmly thank the following reviewers for their kind help in reading my pages during the 2015 summer: Frank Wiedmann (Rhode & Schwarz), Thierry Bordignon, Doug Osterhout (both are with ON Semiconductor), Tomas Gubek – děkuji! (FEI), Didier Balocco (Fairchild), Jochen Verbrugghe, Bart Moeneclaey (both are with Ghent University), Bruno Allard (INSA Lyon), Vatché Vorpérian (JPL), Luc Lasne (Bordeaux University) and Garrett Neaves (Freescale Semiconductor).

Last but not least, I would like to thank Peter Mitchell at Wiley & Sons UK for giving me the opportunity to publish my work.