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TRANSIENT ANALYSISOF ELECTRIC
POWER CIRCUITS HANDBOOK
Transient Analysis of Electric
Power Circuits Handbook
by
ARIEH L. SHENKMAN
Holon Academic Institute of Technology,
Holon, Israel
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 0-387-28797-3 (HB)
ISBN-13 978-0-387-28797-3 (HB)
ISBN-10 0-387-28799-X ( e-book)
ISBN-13 978-0-387-28799-7 (e-book)
Published by Springer,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
www.springeronline.com
Printed on acid-free paper
All Rights Reserved
© 2005 Springer
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
Printed in the Netherlands.
T his book is dedicated to my dearest wife Iris
and wonderful children
Daniel, Elana and Joella
CONTENTS
FOREWORD
xiii
PREFACE
xv
CHAPTER 1
Classical approach to transient analysis
1
1.1. Introduction
1
1.2. Appearance of transients in electrical circuits
2
ff
1.3.1. Exponential solution of a simple di
ff
erential equations describing electrical circuits
4
ff
erential equation 7
1.4. Natural and forced responses
11
1.5. Characteristic equation and its determination
14
1.6. Roots of the characteristic equation and di
ff
erent kinds of transient
responses
21
1.6.1. First order characteristic equation
21
1.6.2. Second order characteristic equation
22
1.7. Independent and dependent initial conditions
26
1.7.1. Two switching laws (rules)
26
(a) First switching law (rule)
26
(b) Second switching law (rule)
27
1.7.2. Methods of finding independent initial conditions
29
1.7.3. Methods of finding dependent initial conditions
31
1.7.4. Generalized initial conditions
35
(a) Circuits containing capacitances
35
(b) Circuits containing inductances
39
1.8. Methods of finding integration constants
44
CHAPTER 2
Transient response of basic circuits
49
2.1. Introduction
49
2.2. The five steps of solving problems in transient analysis
49
1.3. Di
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