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# GATE Electronics & Communication Vol-3- Network Analysis

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PUBLISHED FOR GATE 2018

 Edition 8th Authors R K Kanodia & Ashish Murolia Publisher NODIA Pages 962 Binding Paper Back Language English

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SALIENT FEATURES

• Brief Theory

• Problem Solving Methodology

• Fundamental Concepts & Formulae Review

• Vast Question book with Full Solutions

• Multiple Choice Questions, Memory Based Questions and Numerical Types Questions

• Full width coverage of GATE Syllabus

• Well explained and error free solutions

CHAPTER 1 BASIC CONCEPTS

1.1 INTRODUCTION TO CIRCUIT ANALYSIS

1.2 BASIC ELECTRIC QUANTITIES OR NETWORK VARIABLES

1.2.1 Charge

1.2.2 Current

1.2.3 Voltage

1.2.4 Power

1.2.5 Energy

1.3 CIRCUIT ELEMENTS

1.3.1 Active and Passive Elements

1.3.2 Bilateral and Unilateral Elements

1.3.3 Linear and Non-linear Elements

1.3.4 Lumped and Distributed Elements

1.4 SOURCES

1.4.1 Independent Sources

1.4.2 Dependent Sources

EXERCISE 1.1

EXERCISE 1.2

SOLUTIONS 1.1

SOLUTIONS 1.2

CHAPTER 2 BASIC LAWS

2.1 INTRODUCTION

2.2 OHMâ€™S LAW AND RESISTANCE

2.3 BRANCHES, NODES AND LOOPS

2.4 KIRCHHOFFâ€™S LAW

2.4.1 Kirchhoffâ€™s Current Law

2.4.2 Kirchoffâ€™s Voltage Law

2.5 SERIES RESISTANCES AND VOLTAGE DIVISION

2.6 PARALLEL RESISTANCES AND CURRENT DIVISION

2.7 SOURCES IN SERIES OR PARALLEL

2.7.1 Series Connection of Voltage Sources

2.7.2 Parallel Connection of Identical Voltage Sources

2.7.3 Parallel Connection of Current Sources

2.7.4 Series Connection of Identical Current Sources

2.7.5 Series - Parallel Connection of Voltage and Current Sources

2.8 ANALYSIS OF SIMPLE RESISTIVE CIRCUIT WITH A SINGLE SOURCE

2.9 ANALYSIS OF SIMPLE RESISTIVE CIRCUIT WITH A DEPENDENT SOURCE

2.10 DELTA- TO- WYE(Î”-Y ) TRANSFORMATION

2.10.1 Wye To Delta Conversion

2.10.2 Delta To Wye Conversion

2.11 NON-IDEAL SOURCES

EXERCISE 2.1

EXERCISE 2.2

SOLUTIONS 2.1

SOLUTIONS 2.2

CHAPTER 3 GRAPH THEORY

3.1 INTRODUCTION

3.2 NETWORK GRAPH

3.2.1 Directed and Undirected Graph

3.2.2 Planar and Non-planar Graphs

3.2.3 Subgraph

3.2.4 Connected Graphs

3.2.5 Degree of Vertex

3.3 TREE AND CO-TREE

3.4 INCIDENCE MATRIX

3.4.1 Properties of Incidence Matrix

3.4.2 Incidence Matrix and KCL

3.5 TIE-SET

3.5.1 Tie-Set Matrix

3.5.2 Tie-Set Matrix and KVL

3.5.3 Tie-Set Matrix and Branch Currents

3.6 CUT-SET

3.6.1 Fundamental Cut - Set

3.6.2 Fundamental Cut-set Matrix

3.6.3 Fundamental Cut-set Matrix and KCL

3.6.4 Tree Branch Voltages and Fundamental Cut-set Voltages

EXERCISE 3.1

EXERCISE 3.2

SOLUTIONS 3.1

SOLUTIONS 3.2

CHAPTER 4 NODAL AND LOOP ANALYSIS

4.1 INTRODUCTION

4.2 NODAL ANALYSIS

4.3 MESH ANALYSIS

4.4 COMPARISON BETWEEN NODAL ANALYSIS AND MESH ANALYSIS

EXERCISE 4.1

EXERCISE 4.2

SOLUTIONS 4.1

SOLUTIONS 4.2

CHAPTER 5 CIRCUIT THEOREMS

5.1 INTRODUCTION

5.2 LINEARITY

5.3 SUPERPOSITION

5.4 SOURCE TRANSFORMATION

5.4.1 Source Transformation For Dependent Source

5.5 THEVENINâ€™S THEOREM

5.5.1 Theveninâ€™s Voltage

5.5.2 Theveninâ€™s Resistance

5.5.3 Circuit Analysis Using Thevenin Equivalent

5.6 NORTONâ€™S THEOREM

5.6.1 Nortonâ€™s Current

5.6.2 Nortonâ€™s Resistance

5.6.3 Circuit Analysis Using Nortonâ€™s Equivalent

5.7 TRANSFORMATION BETWEEN THEVENIN & NORTONâ€™S EQUIVALENT CIRCUITS

5.8 MAXIMUM POWER TRANSFER THEOREM

5.9 RECIPROCITY THEOREM

5.9.1 Circuit With a Voltage Source

5.9.2 Circuit With a Current Source

5.10 SUBSTITUTION THEOREM

5.11 MILLMANâ€™S THEOREM

5.12 TELLEGENâ€™S THEOREM

EXERCISE 5.1

EXERCISE 5.2

SOLUTIONS 5.1

SOLUTIONS 5.2

CHAPTER 6 INDUCTOR AND CAPACITOR

6.1 CAPACITOR

6.1.1 Voltage-Current Relationship of a Capacitor

6.1.2 Energy Stored In a Capacitor

6.1.3 Some Properties of an Ideal Capacitor

6.2 SERIES AND PARALLEL CAPACITORS

6.2.1 Capacitors in Series

6.2.2 Capacitors in Parallel

6.3 INDUCTOR

6.3.1 Voltage-Current Relationship of an Inductor

6.3.2 Energy Stored in an Inductor

6.3.3 Some Properties of an Ideal Inductor

6.4 SERIES AND PARALLEL INDUCTORS

6.4.1 Inductors in Series

6.4.2 Inductors in Parallel

6.5 DUALITY

EXERCISE 6.1

EXERCISE 6.2

SOLUTIONS 6.1

SOLUTIONS 6.2

CHAPTER 7 FIRST ORDER RL AND RC CIRCUITS

7.1 INTRODUCTION

7.2 SOURCE FREE OR ZERO-INPUT RESPONSE

7.2.1 Source-Free RC Circuit

7.2.2 Source-Free RL circuit

7.3 THE UNIT STEP FUNCTION

7.4 DC OR STEP RESPONSE OF FIRST ORDER CIRCUIT

7.5 STEP RESPONSE OF AN RC CIRCUIT

7.5.1 Complete Response

7.5.2 Complete Response in terms of Initial and Final Conditions

7.6 STEP RESPONSE OF AN RL CIRCUIT

7.6.1 Complete Response

7.6.2 Complete Response in terms of Initial and Final Conditions

7.7 STEP BY STEP APPROACH TO SOLVE RL AND RC CIRCUITS

7.7.1 Solution Using Capacitor Voltage or Inductor Current

7.7.2 General Method

7.8 STABILITY OF FIRST ORDER CIRCUITS

EXERCISE 7.1

EXERCISE 7.2

SOLUTIONS 7.1

SOLUTIONS 7.2

CHAPTER 8 SECOND ORDER CIRCUITS

8.1 INTRODUCTION

8.2 SOURCE-FREE SERIES RLC CIRCUIT

8.3 SOURCE-FREE PARALLEL RLC CIRCUIT

8.4 STEP BY STEP APPROACH OF SOLVING SECOND ORDER CIRCUITS

8.5 STEP RESPONSE OF SERIES RLC CIRCUIT

8.6 STEP RESPONSE OF PARALLEL RLC CIRCUIT

8.7 THE LOSSLESS LC CIRCUIT

EXERCISE 8.1

EXERCISE 8.2

SOLUTIONS 8.1

SOLUTIONS 8.2

CHAPTER 9 SINUSOIDAL STEADY STATE ANALYSIS

9.1 INTRODUCTION

9.2 CHARACTERISTICS OF SINUSOID

9.3 PHASORS

9.4 PHASOR RELATIONSHIP FOR CIRCUIT ELEMENTS

9.4.1 Resistor

9.4.2 Inductor

9.4.3 Capacitor

9.6 KIRCHHOFFâ€™S LAWS IN THE PHASOR DOMAIN

9.6.1 Kirchhoffâ€™s Voltage Law(KVL)

9.6.2 Kirchhoffâ€™s Current Law(KCL)

9.7 IMPEDANCE COMBINATIONS

9.7.1 Impedances in Series and Voltage Division

9.7.2 Impedances in Parallel and Current Division

9.7.3 Delta-to-Wye Transformation

9.8 CIRCUIT ANALYSIS IN PHASOR DOMAIN

9.8.1 Nodal Analysis

9.8.2 Mesh Analysis

9.8.3 Superposition Theorem

9.8.4 Source Transformation

9.8.5 Thevenin and Norton Equivalent Circuits

9.9 PHASOR DIAGRAMS

EXERCISE 9.1

EXERCISE 9.2

SOLUTIONS 9.1

SOLUTIONS 9.2

CHAPTER 10 AC POWER ANALYSIS

10.1 INTRODUCTION

10.2 INSTANTANEOUS POWER

10.3 AVERAGE POWER

10.4 EFFECTIVE OR RMS VALUE OF A PERIODIC WAVEFORM

10.5 COMPLEX POWER

10.5.1 Alternative Forms For Complex Power

10.6 POWER FACTOR

10.7 MAXIMUM AVERAGE POWER TRANSFER THEOREM

10.7.1 Maximum Average Power Transfer, when Z is Restricted

10.8 AC POWER CONSERVATION

10.9 POWER FACTOR CORRECTION

EXERCISE 10.1

EXERCISE 10.2

SOLUTIONS 10.1

SOLUTIONS 10.2

CHAPTER 11 THREE PHASE CIRCUITS

11.1 INTRODUCTION

11.2 BALANCED THREE PHASE VOLTAGE SOURCES

11.2.1 Y-connected Three-Phase Voltage Source

11.2.2 Î”-connected Three-Phase Voltage Source

11.4 ANALYSIS OF BALANCED THREE-PHASE CIRCUITS

11.4.1 Balanced Y -Y Connection

11.4.2 Balanced Y -Î” Connection

11.4.3 Balanced Î”-Î” Connection

11.4.4 Balanced Î”-Y connection

11.5 POWER IN A BALANCED THREE-PHASE SYSTEM

11.6 TWO-WATTMETER POWER MEASUREMENT

EXERCISE 11.1

EXERCISE 11.2

SOLUTIONS 11.1

SOLUTIONS 11.2

CHAPTER 12 MAGNETICALLY COUPLED CIRCUITS

12.1 INTRODUCTION

12.2 MUTUAL INDUCTANCE

12.3 DOT CONVENTION

12.4 ANALYSIS OF CIRCUITS HAVING COUPLED INDUCTORS

12.5 SERIES CONNECTION OF COUPLED COILS

12.5.2 Series Opposing Connection

12.6 PARALLEL CONNECTION OF COUPLED COILS

12.7 ENERGY STORED IN A COUPLED CIRCUIT

12.7.1 Coefficient of Coupling

12.8 THE LINEAR TRANSFORMER

12.8.1 T -equivalent of a Linear Transformer

12.8.2 Ï€ -equivalent of a Linear Transformer

12.9 THE IDEAL TRANSFORMER

12.9.1 Reflected Impedance

EXERCISE 12.1

EXERCISE 12.2

SOLUTIONS 12.1

SOLUTIONS 12.2

CHAPTER 13 FREQUENCY RESPONSE

13.1 INTRODUCTION

13.2 TRANSFER FUNCTIONS

13.2.1 Poles and Zeros

13.3 RESONANT CIRCUIT

13.3.1 Series Resonance

13.3.2 Parallel Resonance

13.4 PASSIVE FILTERS

13.4.1 Low Pass Filter

13.4.2 High Pass Filter

13.4.3 Band Pass Filter

13.4.4 Band Stop Filter

13.5 EQUIVALENT SERIES AND PARALLEL COMBINATION

13.6 SCALING

13.6.1 Magnitude Scaling

13.6.2 Frequency Scaling

13.6.3 Magnitude and Frequency Scaling

EXERCISE 13.1

EXERCISE 13.2

SOLUTIONS 13.1

SOLUTIONS 13.2

CHAPTER 14 CIRCUIT ANALYSIS USING LAPLACE TRANSFORM

14.1 INTRODUCTION

14.2 DEFINITION OF THE LAPLACE TRANSFORM

14.2.1 Laplace Transform of Some Basic Signals

14.2.2 Existence of Laplace Transform

14.2.3 Poles and Zeros of Rational Laplace Transforms

14.3 THE INVERSE LAPLACE TRANSFORM

14.3.1 Inverse Laplace Transform Using Partial Fraction Method

14.4 PROPERTIES OF THE LAPLACE TRANSFORM

14.4.1 Initial Value and Final Value Theorem

14.5 CIRCUIT ELEMENTS IN THE S -DOMAIN

14.5.1 Resistor in the s-domain

14.5.2 Inductor in the s-domain

14.5.3 Capacitor in the s-domain

14.6 CIRCUIT ANALYSIS IN THE s-DOMAIN

14.7 THE TRANSFER FUNCTION

14.7.1 Transfer Function and Steady State Response

EXERCISE 14.1

EXERCISE 14.2

SOLUTIONS 14.1

SOLUTIONS 14.2

CHAPTER 15 TWO PORT NETWORK

15.1 INTRODUCTION

15.2 IMPEDANCE PARAMETERS

15.2.1 Some Equivalent Networks

15.2.2 Input Impedance of a Terminated Two-port Network in Terms of Impedance Parameters

15.2.3 Thevenin Equivalent Across Output Port in Terms of Impedance Parameters

15.3.1 Some Equivalent Networks

15.3.2 Input Admittance of a Terminated Two-port Networks in Terms of Admittance Parameters

15.4 HYBRID PARAMETERS

15.4.1 Equivalent Network

15.4.2 Input Impedance of a Terminated Two-port Networks in Terms of Hybrid Parameters

15.4.3 Inverse Hybrid Parameters

15.5 TRANSMISSION PARAMETERS

15.5.1 Input Impedance of a Terminated Two-port Networks in Terms of ABCD Parameters

15.6 SYMMETRICAL AND RECIPROCAL NETWORK

15.7 RELATIONSHIP BETWEEN TWO-PORT PARAMETERS

15.8 INTERCONNECTION OF TWO-PORT NETWORKS

15.8.1 Series Connection

15.8.2 Parallel Connection