## Description

This book is intended for a one-semester course in the analysis of linear electric circuits. The goal of this text is to ensure that the reader has firmly mastered those skills that are necessary for analyzing the majority of electric circuits encountered in later courses of an electrical engineering curriculum as well as other disciplines in engineering. This book

• Covers the basic concepts of voltage and current as well as the fundamental laws (KVL and KCL) governing those quantities. The node-voltage and mesh-current techniques are explained.

• Explains a generalized method of solving electric circuits by representing the given circuit in the form of linear graph.

• Discusses additional techniques such as superposition, Thevenin, and Norton theorem for solving the electric circuits.

• The concepts of resonance in series and parallel RLC circuits is discussed in detail.

Analysis of the time-domain (transient) response of circuits as a result of switching is treated in the classical fashion using differential equations followed by a number of solved problems.

## Table of Content

**Chapter 1 Basic Concepts**

1.1 Introduction

1.2 Basic Two-Terminal Circuit Elements

1.2.1 Linear Time-Invariant Resistor

1.2.2 Linear Time-Invariant Capacitor

1.2.3 Linear Time-Invariant Inductor

1.3 Energy Concepts in Two-Terminal Elements

1.3.1 Energy Dissipated in a Resistor

1.3.2 Energy Stored in a Capacitor

1.3.3 Energy Stored in an Inductor

1.4 Ideal Voltage Source

1.5 Ideal Current Source

1.6 Kirchhoff’s Laws

1.6.1 Kirchhoff’s Current Law (KCL)

1.6.2 Kirchhoff’s Voltage Law (KVL)

1.7 Series and Parallel Connections

1.7.1 Series Combination

1.7.2 Parallel Combination

1.8 Linearly Independent KCL and KVL Equations

1.8.1 Independent KCL Equations

1.8.2 Independent KVL Equations

1.9 Methods of Analysis

1.9.1 Nodal Analysis

1.9.2 Solution of Circuits having Super Node

1.9.3 Loop Analysis

1.9.4 Mesh Equations by Inspection

1.9.5 Solution of Circuit shaving Super Mesh

1.10 Circuit Reduction using Star-Delta Transformation

**Chapter 2 Network Topology**

2.1 Graph of a Network

2.1.1 Tree

2.1.2 Loop

2.2 Fundamental Loop

2.3 Cut set

2.4 Fundamental Cut set

2.5 Matrices of Graphs

2.5.1 Incidence Matrix

2.6 Fundamental Cut set Matrix

2.7 Fundamental Circuit Matrix (Tie-set Matrix)

2.8 Inter-Relationships among the Matrices

2.9 Solution of Networks

2.10 Loop Analysis

2.10.1 Procedure

2.11 Cut set Analysis

2.11.1 Procedure

2.12 Duality

2.12.1 Graphical Construction in Finding the Dual of a Network

**Chapter 3 Network Theorems**

3.1 Superposition Theorem

3.2 Reciprocity Theorem

3.3 Thevenin’s Theorem

3.4 Norton’s Theorem

3.5 Maximum Power Transfer Theorem

3.6 Millman’s Theorem

**Chapter 4 Resonant Circuits**

4.1 Introduction

4.2 Series Resonance

4.3 Parallel Resonance

4.4 Frequency Response of Series Resonance Circuit

4.5 Series Resonance by Inductance Variation

4.6 Series Resonance by Capacitance Variation

4.7 Parallel Resonance

**Chapter 5 Transient Behaviour and Initial Conditions in Circuits**

5.1 Transient Analysis for D.C. Excitation

5.1.1 Representation of Initial Conditions

5.1.2 Behavior of Capacitor Voltages and Inductor Currents

5.1.3 First Order Circuits

5.1.4 RL Transient

5.1.5 RC Transient

5.2 Initial Conditions in Elements

5.3 Importance of Initial Conditions

5.3.1 Second Order Circuits

5.4 Transient Analysis for A.C. Excitation

5.4.1 RL Sinusoidal Transient

5.4.2 RC Sinusoidal Transient

5.4.3 RLC Sinusoidal Transient

**Chapter 6 Laplace Transforms and Applications**

6.1 Introduction

6.2 Definition of Laplace Transform

6.3 Properties of Laplace Transform

6.4 Signal Wave forms

6.5 Step Function

6.5.1 Unit Step Function

6.5.2 Shifted Unit Step Function

6.5.3 Various Unit Step Function

6.5.4 Laplace Transform of Unit Step Function

6.5.5 Laplace Transform of Shifted Unit Step Function

6.6 Ramp Function

6.6.1 Unit Ramp Function

6.6.2 A hifted Unit Ramp Function

6.6.3 Laplace Transform of a Unit Ramp Function

6.6.4 Laplace Transform of a Shifted Unit Ramp Occurring at t = a

6.7 Pulse Wave form

6.8 Impulse Function

6.8.1 Unit Impulse Function

6.8.2 Laplace Transform of a Unit Impulse Function

6.9 Laplace Transform of a Periodic Function

6.9.1 Laplace Transform of Train of Unit Impulses

6.10 Time Displacement Theorem or Shifting Theorem

6.11 Complex Translation Theorem

6.12 Scaling Theorem

6.13 Initial Value Theorem

6.14 Final Value Theorem

6.15 Convolution Integral

6.15.1 Convolution Theorem

6.16 Analysis of Circuits using Laplace Transform Technique

6.16.1 Step Input Response of an RL Series Circuit

6.16.2 Step Input Response of an RC Series Circuit

6.16.3 Step Input Response of RLC Series Circuit

6.16.4 Pulse Response of Series RL Circuit

6.16.5 Pulse Response of RC Series Circuit

6.17 AC Transients

6.17.1 RL Series Circuit Transient Response to Sinusoidal Input

6.17.2 RC Series Circuit Transient Response to Sinusoidal Input

6.17.3 RLC Series Circuit Transient Response to Sinusoidal Input

6.18 Application of Laplace Transforms to Circuit Analysis

6.18.1 Capacitive Element

6.18.2 Inductive Element

6.18.3 Impedance and Admittance

6.19 Mesh Analysis

6.20 Nodal Analysis

6.21 Equivalent Sources

6.21.1 Voltage Source Conversion

6.21.2 Current Source Conversion

**Chapter 7 Two-port Networks**

7.1 Z Parameters

7.2 Y Parameters (Short-circuit Admittance Parameters)

7.3 ABCD Parameters

7.4 Hybrid Parameters (h Parameters)

7.5 Relationships among Different Two Port Parameters

7.5.1 Express the Z Parameters in Terms of the Transmission Parameters

7.6 Interconnection of Two-ports

7.6.1 Series Connection

7.6.2 Parallel Connection

7.6.3 Series Parallel Connection

## About The Author

**Dr. E. G. Shivakumar** is Associate Professor, Electrical Engineering Department, University Visvesvaraya College of Engineering, Bangalore University, Bengaluru. He received the B.E. degree (1982) from UVCE, Bangalore University and M.Tech. (Electrical) degree (1984) from the I.I.T.M at Chennai and the Ph.D. degree (2002) from the I.I.Sc, Bengaluru. From 1984-89 he worked in H. M. T. R & D as Design Engineer. From 1989-92 he worked in S.K.F. Bearings as Maintenance Engineer. From 1992-95 he worked as Senior Lecturer in DSCE, Bengaluru. Since 1995 he has been with UVCE teaching both undergraduate and Post Graduate students. He has published 25 research papers in

International conferences and journals. He is a member of the Institution of Engineers (India) and Life member of I.S.T.E.

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