Network

Theory
Analysis and Synthesis


Network Theory
Analysis and Synthesis

Smarajit Ghosh
Professor
Department of Electrical and Instrumentation Engineering
Thapar University
Patiala

Delhi-110 092
2015
NETWORK THEORY: Analysis and Synthesis
Smarajit Ghosh

© 2005 by Prentice-Hall of India Private Limited, New Delhi. All rights reserved. No part of this
book may be reproduced in any form, by mimeograph or any other means, without permission
in writing from the publisher.

ISBN-978-81-203-2638-5

The export rights of this book are vested solely with the publisher.

Ninth Printing   August, 2015

Published by Asoke K. Ghosh, Prentice-Hall of India Private Limited, M-97, Connaught Circus,
New Delhi-110001 and Printed by Mohan Makhijani at Rekha Printers Private Limited,
New Delhi-110020.
 CONTENTS

Preface xv
Acknowledgements xvii
1. Fundamentals of Circuits 1–39
1.1 Charge 1
1.2 Drift Velocity 1
1.3 Current 2
1.4 Current density 2
1.5 Voltage 3
1.6 Energy 3
1.7 Power 3
1.8 Basic Circuit 4
1.9 SI Base Units 4
1.10 Multiples and Submultiples of Units 5
1.11 Some Derived Units 5
1.12 Ohm’s Law 5
1.13 Resistance and Resistivity 6
1.14 Conductance and Conductivity 7
1.15 Open Circuit and Short Circuit 8
1.16 Variation of Resistance with Temperature 8
1.17 Variation of Resistivity with Temperature 8
1.18 Conductors, Insulators, Semiconductors, Superconductors 9
1.19 Series Combination of Resistors 9
1.20 Parallel Combination of Resistors 10
1.21 Division of Current in Parallel Resistors 11
1.22 Voltage Division 13
1.23 Inductors 13
1.24 Capacitors 14
1.25 Energy Stored in an Inductor 15
1.26 Energy Stored in a Capacitor 15
1.27 Energy Sources 16
1.28 Source Transformation 18
1.29 Generation of Alternating Voltage 19
1.30 Expression of the Alternating Voltage and Current 20
1.30.1 Representation of E.M.F. Equations 22
1.31 Mean or Average Value of Alternating Current 22
iii
iv Contents

1.32 Root Mean Square (RMS) Value of Alternating Current 23

1.33 Form Factor 26
1.34 Peak/Amplitude/Crest Factor 26
1.35 Signal Waveforms 27
1.35.1 Sinusoidal Signal 27
1.35.2 Exponential Function 27
1.35.3 Unit-Step Function 28
1.35.4 Ramp Function 28
1.35.5 Impulse Function 28
1.35.6 Periodic Function 28
1.36 Additional Solved Examples 29
Exercises 38

2. Kirchhoff’s Laws 40–58

2.1 Basic Definitions 40
2.2 Kirchhoff’s Laws 41
2.3 Solving Simultaneous Equations Using Determinants 42
2.4 Nodal Analysis 44
2.5 Maxwell’s Loop Current Method 46
2.6 Star–Delta Transformation 47
2.7 Duality 50
2.8 Additional Solved Examples 50
Exercises 57

3. DC Network Theorems 59–93

3.1 Superposition Theorem 59
3.2 Thévenin’s Theorem 60
3.3 Norton’s Theorem 62
3.4 Maximum Power Transfer Theorem 64
3.5 Reciprocity Theorem 66
3.6 Millman’s Theorem 66
3.7 Substitution Theorem 67
3.8 Compensation Theorem 68
3.9 Tellegen’s Theorem 69
3.10 Additional Solved Examples 69
3.11 Circuits Containing Dependent Sources—Numerical Problems 86
Exercises 92

4. DC Transients 94–111
4.1 RL Circuit 94
4.1.1 Growth of Current 94
4.1.2 Decay of Current 96
4.2 RC Circuit 97
4.2.1 Charging a Capacitor 97
4.2.2 Discharging a Capacitor 99
 Contents v

4.3 Transient Response of RLC Circuits 101

4.4 Additional Solved Examples 104
Exercises 110

5. Single-Phase AC Circuits 112–138

5.1 Pure Resistive Circuit 112
5.2 Pure Inductive Circuit 113
5.3 Pure Capacitive Circuit 113
5.4 Series RL Circuit 114
5.5 Series RC Circuit 116
5.6 Series RLC Circuit 118
5.7 Parallel RL Circuit 120
5.8 Parallel RC Circuit 121
5.9 Parallel RLC Circuit 121
5.10 Power Relations in AC Circuits 122
5.11 Power in Pure Resistive Circuits 122
5.12 Power in Pure Inductive Circuits 123
5.13 Power in Pure Capacitive Circuits 124
5.14 Power in a General Series Circuit 125
5.15 Reactive Power 126
5.16 Power Triangle 126
5.17 Complex Power 127
5.18 Additional Solved Examples 127
Exercises 137

6. Resonance 139–158
6.1 SeriesResonance 139
6.1.1 Quality Factor 140
6.1.2 Sharpness of Resonance 140
6.1.3 Fractional Detuning Factor (d ) 142
6.1.4 Expression of Z in Terms of Fractional Detuning Factor d and
Quality Factor Q 142
6.1.5 Expression for Half-Power Frequencies in RLC Series
Resonant Circuits 143
6.1.6 Selectivity 144
6.1.7 Frequency at which VC is Maximum 144
6.1.8 Frequency at which VL is Maximum 145
6.1.9 Variation of Z and I with Frequency 146
6.2 Parallel Resonance 146
6.2.1 Relationship among Z, d, Q 148
6.2.2 Resonance between Parallel RL and RC Circuits 150
6.2.3 Parallel RLC Circuit 152
6.3 Additional Solved Examples 152
Exercises 157
vi Contents

7. Three-Phase Systems 159–184

7.1 Advantages of the Three-Phase System 160
7.2 Numbering of Phases 161
7.3 Interconnection of Three-Phases 161
7.3.1 Star and Delta Connections 161
7.4 Voltages, Currents, and Power in Star Connection 162
7.5 Voltages, Currents and Power in Delta Connection 164
7.6 Star-Connected Load 166
7.7 Measurement of Power in Three-Phase Systems 168
7.8 Two Wattmeter Method 169
7.9 Unbalanced Load 171
7.10 Calculation of Neutral Shift 172
7.11 Balanced Delta-Connected Load 172
7.12 Additional Solved Examples 173
Exercises 183

8. Fourier Series and Fourier Transform 185–227

8.1 Fourier Series 185
8.2 Dirichlet Conditions 186
8.3 Orthogonal Functions 186
8.4 Determination of Fourier Coefficients 187
8.5 Wave Symmetry 191
8.5.1 Even or Mirror Symmetry 191
8.5.2 Odd or Rotation Symmetry 192
8.5.3 Half-Wave Symmetry 193
8.5.4 Quarter-Wave Symmetry 194
8.6 Exponential Form of Fourier Series 196
8.7 Fourier Transform 199
8.8 Fourier Transform of Some Functions 201
8.8.1 Fourier Transform of Gate Function 201
8.8.2 Fourier Transform of Impulse Function 202
8.8.3 Fourier Transform of Shifted Impulse Function 203
8.8.4 Fourier Transform of One-Sided Exponential Function 203
8.8.5 Fourier Transform of Two-Sided Exponential Function 204
8.8.6 Fourier Transform of sgn(t)e–a(t) 205
8.8.7 Fourier Transform of Signum Function 206
8.8.8 Fourier Transform of f(t) = 1 206
8.8.9 Fourier Transform of u(t) 207
8.9 Fourier Transformation Theorems 208
8.9.1 Linearity 208
8.9.2 Time Scaling 208
8.9.3 Time Differentiation 209
8.9.4 Time Shifting Property 210
8.9.5 Translation in the Frequency Domain 210
 Contents vii

8.9.6 Modulation Theorem 210

8.9.7 Symmetry or Duality Property 211
8.9.8 Time Convolution Property 211
8.9.9 Frequency Convolution 211
8.9.10 Frequency Differentiation 211
8.9.11 Time Integration 211
8.10 Parseval’s Theorem 211
8.11 Additional Solved Examples 212
Exercises 227

9. Laplace Transform 228–256

9.1 Laplace Transform 228
9.2 Inverse Laplace Transformation 229
9.3 Basic Properties of Laplace Transforms 229
9.4 Laplace Transform of a Derivative [df(t)/dt] 232
9.5 Laplace Transform of an Integral Ú f(t) dt 233
9.6 Laplace Transform of Some Common Time Functions 233
9.6.1 Unit-Step Function 233
9.6.2 Impulse Function 234
9.6.3 Exponential Function eat 234
9.6.4 Sinusoidal Function 234
9.6.5 Cosine Function 235
9.6.6 Ramp Function 235
9.6.7 Parabolic Function 236
9.6.8 Hyperbolic Sinusoidal Functions 236
9.6.9 Damped Sinusoidal Functions 237
9.6.10 Damped Hyperbolic Sinusoidal Functions 237
n
9.6.11 Laplace Transform of t 238
9.6.12 Laplace Transforms of Some Useful Functions 238
9.7 Initial-Value Theorem 238
9.8 Final-Value Theorem 240
9.9 Partial Fraction Expansion 244
9.10 Relation between Step Response and Impulse Response 247
Exercises 256

10. Application of Laplace Transform 257–286

10.1 Resistance Element 257
10.2 Inductance Element 257
10.3 Capacitance Element 258
10.4 Step Response of RL Circuit 259
10.5 Step Response of RC Circuit 260
10.6 Step Response of RLC Circuit 260
10.7 Impulse Response of Series RL Circuit 262
10.8 Impulse Response of Series RC Circuit 263
viii Contents

10.9 Pulse Response 263

10.10 Pulse Response of Series RC Circuit 264
Exercises 285

11. Analysis of Special Signal Waveforms 287–300

11.1 Basic Types of Special Signals 287
11.1.1 Shifted Unit-Step Function 287
11.1.2 Ramp Function 288
11.1.3 Impulse Function 289
11.1.4 Unit-Doublet Function 290
11.2 Laplace Transformation of Some Special Signal Waveforms 290
11.2.1 Shifted Unit-Step Function 290
11.2.2 Impulse Function 290
11.2.3 Unit-Doublet Function 291
11.2.4 Ramp Function 291
Exercises 299

12. Application of Kirchhoff’s Laws and Network Theorems to

AC Circuits 301–324
12.1 Mesh Analysis 301
12.2 Nodal Analysis 302
12.3 Thévenin’s and Norton’s Theorems 304
12.4 Superposition Theorem 311
12.5 Maximum Power Transfer Theorem 314
12.6 Millman’s Theorem 316
12.7 Reciprocity Theorem 317
12.8 Additional Solved Examples 318
Exercises 323

13. Coupled Circuits 325–345

13.1 Self-Inductance 325
13.2 Mutual Coupling 327
13.3 Magnetic Coupling 327
13.4 Mutual Inductance 328
13.5 Coefficient of Coupling 328
13.6 Dot Convention 331
13.7 Inductive Coupling in Series 331
13.8 Inductive Coupling in Parallel 334
13.9 Tuned Coupled Circuits 336
13.9.1 Single-Tuned Coupled Coils 336
13.9.2 Double-Tuned Coupled Coils 339
13.10 Additional Solved Examples 341
Exercises 344
 Contents ix

14. Two-Port Networks 346–403

14.1 Network Configurations 346
14.2 z-Parameters 349
14.3 y-Parameters 351
14.4 h-Parameters 352
14.5 ABCD-Parameters 353
14.6 Equivalent Circuit Using z-Parameters 355
14.7 Equivalent Circuit Using y-Parameters 356
14.8 Equivalent Circuit Using h-Parameters 356
14.9 Condition for Reciprocity and Symmetry of Two-Port Networks in
Different Parameters Representations 357
14.9.1 Reciprocity and Symmetry in z-Parameter Representation 357
14.9.2 Reciprocity and Symmetry in y-Parameter Represention 358
14.9.3 Reciprocity and Symmetry in h-Parameter Representation 359
14.9.4 Reciprocity and Symmetry in ABCD-Parameter Representation 360
14.10 Interrelationships between Parameters of Two-Port Network 361
14.10.1 z-Parameters in Terms of y-Parameters 361
14.10.2 z-Parameters in Terms of h-Parameters 362
14.10.3 z-Parameters in Terms of ABCD-Parameters 363
14.10.4 y-Parameters in Terms of z-Parameters 364
14.10.5 y-Parameters in Terms of h-Parameters 365
14.10.6 y-Parameters in Terms of ABCD-Parameters 365
14.10.7 h-Parameters in Terms of z-Parameters 366
14.10.8 h-Parameters in Terms of y-Parameters 367
14.10.9 h-Parameters in Terms of ABCD-Parameters 367
14.10.10 ABCD-Parameters in Terms of z-Parameters 368
14.10.11 ABCD-Parameters in Terms of y-Parameters 369
14.10.12 ABCD-Parameters in Terms of h-Parameters 370
14.11 Interconnection of Two-Port Networks 371
14.11.1 Cascade Connection 371
14.11.2 Series Connection 372
14.11.3 Parallel Connection 373
14.11.4 Series-Parallel Connection of Two-Port Networks 374
14.12 Analysis of Typical Two-Port Networks 374
14.12.1 T-Network 375
14.12.2 p-Network 376
14.12.3 Lattice Network 378
14.13 Open-Circuit and Short-Circuit Impedances and the ABCD-Parameters 379
14.14 Input and Output Impedances of Terminated Two-Port Networks 381
14.14.1 Input Impedance in Terms of z-Parameters 382
14.14.2 Input Impedance in Terms of y-Parameters 382
14.14.3 Input Impedance in Terms of ABCD-Parameters 383
14.14.4 Input Impedance in Terms of h-Parameters 384
14.14.5 Output Impedance in Terms of z-Parameters 384
 Network Theory Analysis and Synthesis

Publisher : PHI Learning ISBN : 9788120326385 Author : Smarajit Ghosh

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