Network analysis and practice

354 Pages·1987·13.48 MB·English

by  A K Walton

It is the aim of this book to take undergraduates in science
and engineering to an acceptable level of competence in net-
work analysis. The author assumes no previous knowledge of
the subject.
The book starts from basic physical ideas and progresses
through essential network laws and theorems to Fourier and
Laplace transform methods of analysing transient and steady-
state problems. Traditional transient and alternating-current
theory is covered prior to introducing transform methods, since
the author believes that the gain in physical insight from such
an approach is invaluable. Throughout, the relevance of the
analysis to practical electric and electronic circuits is stressed.
This book will be of value to students in universities and
polytechnics in physics and electrical and electronics engi-
neering departments.

Network analysis
and practice
A. K. WALTON
Department of Physics, Sheffield University
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© Cambridge University Press 1987
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 1987
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Walton, A. K. (Alan Keith), 1933-
Network analysis and practice.
Includes index.
1. Electric network analysis. I. Title.
TK454.2.W32 1987 621.319'2 87-4255
ISBN-13 978-0-521-26459-4 hardback
ISBN-10 0-521-26459-6 hardback
ISBN-13 978-0-521-31903-4 paperback
ISBN-10 0-521-31903-X paperback
Transferred to digital printing 2006
CONTENTS
Preface ix
Electric charge, field and potential
1.1 Electric charge 1
1.2 The inverse square law 2
1.3 Force, electric field and potential 6
Electric current, resistance and electromotive force
2.1 Electrical conduction, electric current and current
density 11
2.2 Ohm's law and electrical resistance 14
2.3 Resistors and nonlinear circuit elements 18
2.4 Electromotive force 21
2.5 Internal resistance, sources and matching 25
Direct-current networks
3.1 Kirchhoffs laws 30
3.2 Resistors in series and parallel 33
3.3 Generality of analysis by KirchhofFs laws 36
3.4 Mesh current analysis 37
3.5 Node-pair potential analysis 39
3.6 The superposition and reciprocity theorems 41
3.7 The Thevenin and Norton theorems 45
3.8 Measurement of direct current, potential difference
and resistance 54
3.9 The Wheatstone bridge 59
3.10 Load-line analysis 62
vi Contents
4 Capacitance, inductance and electrical transients
4.1 Capacitance and capacitors 65
4.2 Inductance and inductors 71
4.3 Transient responses of C-R and L-R circuits to a
step e.m.f. 80
4.4 Basic four-terminal C-R networks 84
4.5 Transient response of an L-C-R circuit to a step
e.m.f. 89
5 Introduction to the steady-state responses of networks to
sinusoidal sources
5.1 Sinusoidal sources and definitions 97
5.2 Responses of purely resistive, purely capacitive and
purely inductive circuits to sinusoidal e.m.f.s 100
5.3 Sinusoidal response through differential equation
solution 102
5.4 Steady-state sinusoidal response from phasor
diagram 105
5.5 Steady-state sinusoidal response through complex
representation 107
5.6 Series resonant circuit 110
5.7 Parallel resonant circuits 114
5.8 Power dissipation associated with sinusoidal current 119
5.9 Sinusoidal sources in nonlinear circuits 124
6 Transformers in networks
6.1 Mutual inductance 127
6.2 Transformers 131
6.3 Reflected impedance and matching by transformers 135
6.4 Critical coupling of resonant circuits 139
7 Alternating-current instruments and bridges
7.1 Alternating-current meters 144
7.2 Measurement of impedance by a.c. meters 148
7.3 Measurement of impedance by the Wheatstone
form of a.c. bridge 151
7.4 A.c. bridges for determining inductance 155
7.5 The Schering bridge for determining capacitance 157
7.6 The Heydweiller bridge for determining mutual
inductance 158
Contents vii
7.7 A.c. bridges for determining the frequency of a
source 160
7.8 Transformer ratio-arm bridges 161
8 Attenuators and single-section filters
8.1 Attenuators 167
8.2 Simple single-section filters 173
8.3 Wien, bridged-T and twin-T rejection filters 179
8.4 Phase-shift networks 186
9 Multiple-section filters and transmission lines
9.1 Ladder filters 189
9.2 Constant-*; filters 193
9.3 m-Derived filters 202
9.4 Asymmetric sections 209
9.5 Transmission lines 212
10 Signal analysis of nonlinear and active networks
10.1 Two-terminal nonlinear networks 220
10.2 Four-terminal nonlinear networks 223
10.3 Small-signal equivalent circuits and analysis 230
10.4 Feedback 235
10.5 Operational amplifiers 240
10.6 Nyquist's criterion and oscillators 244
10.7 Amplifier instability and Bode diagrams 249
11 Fourier and Laplace transform techniques
11.1 Fourier analysis of periodic nonsinusoidal signals 252
11.2 Fourier analysis of pulses 256
11.3 The Laplace transform 259
11.4 Commonly required Laplace transforms 261
11.5 Inverse Laplace transforms 265
11.6 Network analysis by Laplace transformation 269
11.7 Pole-zero plots in the complex s-plane 275
12 Filter synthesis
12.1 Introduction 278
12.2 Butterworth filters 279
12.3 Chebyshev filters 282
12.4 Synthesis of high-pass filters 285
12.5 Band filter synthesis 286
viii Contents
Mathematical background appendices
1 Harmonic functions 289
2 Exponential functions 291
3 Phasors and complex representation 293
4 Linear differential equations with constant coefficients 296
Problems 302
Answers 313
Solutions 318
Index 331
PREFACE
Where to begin constitutes a difficulty in expounding most subjects. For
completeness' sake, the present treatment of the analysis of electrical
networks begins by establishing from first principles those basic electrical
concepts such as current, potential and electromotive force in terms of
which analysis is executed. In covering these basic concepts in the first two
chapters it is, of course, recognised that some students will already be
thoroughly conversant with them, some will merely need to 'brush up' on
them and others will prefer to acquire them through studying more-detailed
physical texts.
Network analysis begins in earnest in chapter 3 where network laws and
theorems, such as Kirchhoff's laws and Thevenin's theorem, are introduced
in the easy context of direct-current networks. Following descriptions of the
physical nature of capacitance and inductance, traditional methods of
deducing transient and sinusoidal steady-state responses are developed.
These encompass the solution of linear differential equations and the
application of phasor and complex algebraic methods. Consideration of the
powerful Fourier and Laplace transform techniques is delayed until
towards the end of the book, by which stage it is hoped that any reader will
have acquired considerable mathematical and physical insight regarding
the signal responses of circuits. Overall, the intention is that the book will
take a student from 'scratch' to a level of competence in network analysis
that is broadly commensurate with a graduate in Electrical or Electronic
Engineering, or one in Physics if specialising somewhat in electrical aspects.
A concerted attempt has been made throughout the text to relate the
analysis to as great a variety of practical circuits and situations as possible.
The reader is strongly recommended to put theory to the test by building
real circuits, observing their response and discovering whether there is
accordance with design expectation. Fortunately, the construction and
x Preface
testing of practical circuits can be quick and quite inexpensive. As a further
aid to assessing whether the contents have been grasped, a collection of
over 50 relatively straightforward problems has been incorporated
together with worked solutions to many and answers to all of them.
Assistance with preparation of the manuscript in the Physics
Department at Sheffield is gratefully acknowledged. During a difficult
staffing period several individuals have been involved, but thanks are
especially due to Mrs S. Stapleton, Mrs E. Lycett and Mrs J. Hedge for most
of the typing and to Mrs K. J. Batty for all the line-drawings.
Physics Department, University of Sheffield, 1986 A. K. WALTON