Network Analysis and Synthesis

987 Pages·11.896 MB·English

by  S P Ghosh, A K Chakraborty

About the Authors
S P Ghosh obtained his BE (Hons) in Electrical Engineering from National Insti-
tute of Technology, Durgapur, and received a Master of Electrical Engineering
degree from Jadavpur University with specialization in High Voltage Engineer-
ing. He joined College of Engineering and Management, Kolaghat, as a lecturer
in 2002. Presently, he is working as an Assistant Professor in the department of
Electrical Engineering at College of Engineering and Management, Kolaghat.
He has published several papers in national and international conferences. He is
also pursuing his PhD at Bengal Engineering and Science University, Shibpur.
His areas of interest include Power Systems, Electrical Machines, and Artificial
Neural Networks.
A K Chakraborty received his BEE (Hons) from Jadavpur University, MTech
in Power System Engineering from IIT Kharagpur and PhD (Engineering)
from Jadavpur University. He joined College of Engineering and Management,
Kolaghat, in 1998 as Assistant Professor and was elevated to the rank of Profes-
sor in the Electrical Engineering Department. He served as HOD from 2002 to
2005 in the same department. Presently, he is working as Professor and Head of
the Department of Electrical Engineering. He also worked as a Lecturer in NIT
Silchar for five years. He served industries, namely, CESC Ltd. and Tinplate Com-
pany of India Ltd (a Tata Enterprise) for over fourteen years before joining this
institute. He is a Fellow of Institute of Engineers (India), Chartered Engineer,
Member IET (UK) and Life Member of ISTE. He has published several technical
papers in national and international conferences and also in reputed journals. He has guided several MTech
and PhD scholars. His research interests are in the field of Power System Protection, Economic Operation of
Power Systems, Deregulated Power System, and HVDC.
S P Ghosh
Assistant Professor
Department of Electrical Engineering
College of Engineering and Management
Kolaghat, West Bengal
A K Chakraborty
Professor and Head
Department of Electrical Engineering
College of Engineering and Management
Kolaghat, West Bengal
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To my family
My Wife, Lipika
Daughter, Adrita
S P Ghosh
To my family
Wife, Indira
Daughters, Amrita and Ananya
A K Chakraborty

Contents
Foreword xv
Preface xvii
1. Introduction to Different Types of Systems 1–22
Introduction 1
1.1 Concepts of Signals and Systems 1
1.2 Different Types of Signals 2
1.3 Different Types of Systems 6
1.4 Interconnection of Systems 10
Solved Problems 11
Summary 17
Short-Answer Questions 18
Exercises 20
Questions 20
Multiple-Choice Questions 20
Answers 22
2 Introduction to Circuit-Theory Concepts 23–102
Introduction 23
2.1 Some Basic Terminologies of Electric Circuits 23
2.2 Different Notations 26
2.3 Basic Circuit Elements 27
2.4 Passive Circuit Elements 28
2.5 Types of Electrical Energy Sources 39
2.6 Fundamental Laws 41
2.7 Source Transformation 43
2.8 Network Analysis Techniques 48
2.9 Duality 50
2.10 Star-Delta Conversion Technique 52
Solved Problems 55
Summary 79
Short-Answer Questions 81
Exercises 89
Questions 92
Multiple-Choice Questions 92
Answers 102
3 Network Topology (Graph Theory) 103–154
Introduction 103
3.1 Graph of a Network 103
3.2 Terminology 104
3.3 Concept of a Tree 105
viii
Contents
3.4 Incidence Matrix [A] 107
a
3.5 Tie-Set Matrix and Loop Currents 110
3.6 Cut-Set Matrix and Node-Pair Potential 112
3.7 Formulation of Network Equilibrium Equations 115
3.8 Generalized Equations in Matrix Forms for Circuits having Sources 116
Solved Problems 118
Summary 147
Short-Answer Questions 147
Exercises 150
Questions 151
Multiple-Choice Questions 152
Answers 154
4 Network Theorems 155–230
Introduction 155
4.1 Network Theorems 155
4.2 Substitution Theorem 156
4.3 Superposition Theorem 156
4.4 Reciprocity Theorem 159
4.5 Thevenin’s Theorem 160
4.6 Norton’s Theorem 161
4.7 Maximum Power Transfer Theorem 166
4.8 Tellegen’s Theorem 170
4.9 Millman’s Theorem 172
4.10 Compensation Theorem 175
Solved Problems 177
Summary 217
Short-Answer Questions 218
Exercises 220
Questions 224
Multiple-Choice Questions 225
Answers 230
5 Laplace Transform and Its Applications 231–326
Introduction 231
5.1 Advantages of Laplace-Transform Method 231
5.2 Definition of Laplace Transform 232
5.3 Concept of Complex Frequency 232
5.4 Basic Theorems of Laplace Transform 233
5.5 Region of Convergence (ROC) 237
5.6 Laplace Transform of some Basic Functions 238
5.7 Laplace Transform Table 242
5.8 Other Important Laplace Transforms 243
5.9 Laplace Transform of Periodic Functions 244
5.10 Inverse Laplace Transform 244
5.11 Applications of Laplace Transform 248
5.12 Transient Analysis of Electric Circuits using Laplace Transform 250
5.13 Response with Pulse Input Voltage 268
5.14 Steps for Circuit Analysis using Laplace Transform Method 271
5.15 Concept of Convolution Theorem 271
ix
Contents
Solved Problems 273
Summary 303
Short-Answer Questions 304
Exercises 309
Questions 312
Multiple-Choice Questions 313
Answers 325
6 Two-Port Network 327–412
Introduction 327
6.1 Relationships of Two-Port Variables 327
6.2 Conditions for Reciprocity and Symmetry 334
6.3 Interrelationships between Two-Port Parameters 338
6.4 Interconnection of Two-Port Networks 339
6.5 Two-Port Network Functions 344
6.6 Transfer Functions of Terminated Two-Port Networks 345
6.7 Application of Network Parameters to the Analysis of Typical Two-Port Networks 348
6.8 Some Special Two-Port Networks 351
6.9 Image Parameters of a Two-Port Network 354
Solved Problems 359
Summary 398
Short-Answer Questions 398
Exercises 402
Questions 405
Multiple-Choice Questions 406
Answers 412
7 Fourier Series and Fourier Transform 413–472
Part I: Fourier Series 413
Introduction 413
7.1 Definition of Fourier Series 414
7.2 Dirichlet’s Conditions 414
7.3 Convergence of Fourier Series 414
7.4 Fourier Analysis 415
7.5 Waveform Symmetry 419
7.6 Truncating Fourier Series 422
7.7 Steady-State Response of Network to Periodic Signals 424
7.8 Steps for Application of Fourier Series to Circuit Analysis 424
7.9 Power Spectrum 425
Part II: Fourier Transform 425
Introduction 425
7.10 Definition of Fourier Transform 425
7.11 Convergence of Fourier Transform 426
7.12 Fourier Transform of Some Functions 427
7.13 Properties of Fourier Transforms 429
7.14 Energy Density and Parseval’s Theorem 432
7.15 Comparison between Fourier Transform and Laplace Transform 433
7.16 Steps for Application of Fourier Transform to Circuit Analysis 434
Solved Problems 434
x
Contents
Summary 460
Short-Answer Questions 460
Exercises 467
Questions 469
Multiple-Choice Questions 470
Answers 472
8 Sinusoidal Steady State Analysis 473–542
Introduction 473
8.1 Advantages of using Alternating Currents in Electrical Engineering 473
8.2 Basics of Sinusoids 474
8.3 Terminologies 474
8.4 Some Values of Alternating Quantities 476
8.5 Complex Number Systems 479
8.6 Phasor Representation 480
8.7 The j Operator 484
8.8 Phasor Diagrams 484
8.9 Circuit Response to Sinusoids 484
8.10 Kirchhoff’s Laws in Phasor Domain 485
8.11 Voltage and Current Phasors in Single-Element Circuits 485
8.12 Phasor Analysis of R-L Series Circuit 488
8.13 Phasor Analysis of RC Series Circuit 490
8.14 Phasor Analysis of RLC Series Circuit 492
8.15 Steps for Sinusoidal Steady-State Analysis (Phasor Approach to Circuit Analysis) 494
8.16 Concept of Reactance, Impedance, Susceptance and Admittance as Phasors 494
8.17 AC Power Analysis 496
8.18 Power Calculations in Different Electrical Elements 498
8.19 Sinusoidal Steady-State Response of Parallel AC Circuits 503
8.20 Sinusoidal Steady-State Response of Series–Parallel AC Circuits 507
Solved Problems 507
Summary 527
Short-Answer Questions 528
Questions 534
Exercises 535
Multiple-Choice Questions 537
Answers 542
9 Magnetically Coupled Circuits 543–590
Introduction 543
9.1 Self-Inductance 543
9.2 Coupled Inductor 544
9.3 Mutual Inductance 544
9.4 Mutual Inductance between Two Coupled Inductors 545
9.5 Dot Convention 546
9.6 Determination of Coefficient of Coupling from Energy Calculations in Coupled Circuits 548
9.7 Inductive Coupling 549
9.8 Linear Transformer 551

(conductively Equivalent Circuit of a Magnetically Coupled Circuit) 552
9.10 Ideal Transformer 553