Electric Circuits and Networks : For GTU

Cover
Contents
Preface
Road Map to the Syllabus
Chapter 1: Circuit Variables and Circuit Elements
	Introduction
	1.1 Electromotive Force, Potential and Voltage
		1.1.1 Force Between Two Moving Point Charges and Retardation Effect
		1.1.2 Electric Potential and Voltage
		1.1.3 Electromotive Force and Terminal Voltage of a Steady Source
	1.2 a Voltage Source with a Resistance Connected at its Terminals
		1.2.1 Steady-State Charge Distribution in the System
		1.2.2 Drift Velocity and Current Density
		1.2.3 Current Intensity
		1.2.4 Conduction and Energy Transfer Process
		1.2.5 Two-terminal Resistance Element
		1.2.6 A Time-Varying Voltage Source with Resistance Across it
	1.3 Two-terminal Capacitance
	1.4 Two-terminal Inductance
		1.4.1 Induced Electromotive Force and its Location in a Circuit
		1.4.2 Relation Between Induced Electromotive Force and Current
		1.4.3 Faraday’s Law and Induced Electromotive Force
		1.4.4 The Issue of a Unique Voltage Across a Two-terminal Element
		1.4.5 The Two-terminal Inductance
	1.5 Ideal Independent Two-terminal Electrical Sources
		1.5.1 Ideal Independent Voltage Source
		1.5.2 Ideal Independent Current Source
		1.5.3 Ideal Short-Circuit Element and Ideal Open-circuit Element
	1.6 Power and Energy Relations for Two-terminal Elements
		1.6.1 Passive Sign Convention
		1.6.2 Power and Energy in Two-terminal Elements
	1.7 Classification of Two-terminal Elements
		1.7.1 Lumped and Distributed Elements
		1.7.2 Linear and Non-Linear Elements
		1.7.3 Bilateral and Non-Bilateral Elements
		1.7.4 Passive and Active Elements
		1.7.5 Time-Invariant and Time-Variant Elements
	1.8 Multi-terminal Circuit Elements
		1.8.1 Mutual Inductance Element
		1.8.2 Why Should M12 be Equal to M21?
		1.8.3 Ideal Dependent Sources
	1.9 Summary
	1.10 Problems
Chapter 2: Basic Circuit Laws
	Introduction
	2.1 Kirchhoff's  Voltage Law (KVL)
	2.2 Kirchhoff's Current Law (KCL
)
	2.3 Interconnections of Ideal Sources
	2.4 Analysis of a Single-Loop Circuit
	2.5 Analysis of a Single-Node-Pair Circuit
	2.6 Analysis of Multi-Loop, Multi-Node Circuits
	2.7 Summary
	2.8 Problems
Chapter 3: Single Element Circuits
	Introduction
	3.1 The Resistor
		3.1.1 Series Connection of Resistors
		3.1.2 Parallel Connection of Resistors
	3.2 The Inductor
		3.2.1 Instantaneous Inductor Current Versus Instantaneous Inductor Voltage
		3.2.2 Change in Inductor Current Function Versus Area Under Voltage Function
		3.2.3 Average Applied Voltage for a Given Change in Inductor Current
		3.2.4 Instantaneous Change in Inductor Current
		3.2.5 Inductor with Alternating Voltage Across it
		3.2.6 Inductor with Exponential and Sinu so Idal Voltage Input
		3.2.7 Linearity of Inductor
		3.2.8 Energy Storage in an Inductor
	3.3 Series Connection of Inductors
		3.3.1 Series Connection of Inductors with Same Initial Current
		3.3.2 Series Connection with Unequal Initial Currents
	3.4 Parallel Connection of Inductors
		3.4.1 Parallel Connection of Initially Relaxed Inductors
		3.4.2 Parallel Connection of Inductors with Initial Energy
	3.5 The Capacitor
	3.6 Series Connection of Capacitors
		3.6.1 Series Connection of Capacitors with Zero Initial Energy
		3.6.2 Series Connection of Capacitors with Non-Zero Initial Energy
	3.7 Parallel Connection of Capacitors
	3.8 Summary
	3.9 Questions
	3.10 Problems
Chapter 4: Nodal Analysis and Mesh Analysis of Memoryless Circuits
	Introduction
	4.1 The Circuit Analysis Problem
	4.2 Nodal Analysis of Circuits Containing Resistors with Independent Current Sources
	4.3 Nodal Analysis of Circuits Containing Independent Voltage Sources
	4.4 Source Transformation Theorem and its Use in Nodal Analysis
		4.4.1 Source Transformation Theorem
		4.4.2 Applying Source Transformation Theorem in Nodal Analysis of Circuits
	4.5 Nodal Analysis of Circuits Containing Dependent Current Sources
	4.6 Nodal Analysis of Circuits Containing Dependent Voltage Sources
	4.7 Mesh Analysis of Circuits with Resistors and Independent Voltage Sources
		4.7.1 Principle of Mesh Analysis
		4.7.2 Is Mesh Current Measurable?
	4.8 Mesh Analysis of Circuits with Independent Current Sources
	4.9 Mesh Analysis of Circuits Containing Dependent Sources
	4.10 Summary
	4.11 Problems
Chapter 5: Circuit Theorems
	Introduction
	5.1 Linearity of a Circuit and Superposition Theorem
		5.1.1 Linearity of a Circuit
	5.2 Star-Delta Transformation Theorem
	5.3 Substitution Theorem
	5.4 Compensation Theorem
	5.5 Thevenin’s Theorem and Norton’s Theorem
	5.6 Determination of Equivalents for Circuits with Dependent Sources
	5.7 Reciprocity Theorem
	5.8 Maximum Power Transfer Theorem
	5.9 Millman’s Theorem
	5.10 Summary
	5.11 Problems
Chapter 6: Simple RL Circuits in Time-Domain
	Introduction
	6.1 The Series RL Circuit
		6.1.1 The Series RL Circuit Equations
		6.1.2 Need for Initial Condition Specification
		6.1.3 Sufficiency of Initial Condition
	6.2 Series RL Circuit with Unit Step Input – Qualitative Analysis
		6.2.1 From T = 0– to T = 0+
		6.2.2 Inductor Current Growth Process
	6.3 Series RL Circuit with Unit Step Input – Power Series Solution
		6.3.1 Series RL Circuit Current as a Power Series
	6.4 Step Response of an RL Circuit by Solving Differential Equation
		6.4.1 Interpreting the Input Forcing Functions in Circuit Differential Equations
		6.4.2 Solving the Series RL Circuit Equation by Integrating Factor Method
		6.4.3 Complementary Function and Particular Integral
	6.5 Features of RL Circuit Step Response
		6.5.1 Step Response Waveforms in Series RL Circuit
		6.5.2 The Time Constant of a Series RL Circuit
		6.5.3 Rise Time and Fall Time in First Order Circuits
		6.5.4 Effect of Non-Zero Initial Condition on Step Response of RL Circuit
		6.5.5 Free Response of Series RL Circuit
	6.6 Steady-State Response and Forced Response
		6.6.1 The DC Steady-State
		6.6.2 The Sinusoidal Steady-State
		6.6.3 The Periodic Steady-State
	6.7 Linearity and Superposition Principle in Dynamic Circuits
	6.8 Unit Impulse Response of Series RL Circuit
		6.8.1 Unit Impulse Response of RL Circuit with Non-Zero Initial Current
		6.8.2 Zero-State Response for Other Inputs from Zero-State Impulse Response
	6.9 Series RL Circuit with Exponential Inputs
		6.9.1 Zero-State Response for a Real Exponential Input
		6.9.2 Zero-State Response for Sinusoidal Input
	6.10 General Analysis Procedure for Single Time Constant RL Circuits
	6.11 Summary
	6.12 Questions
	6.13 Problems
Chapter 7: RC and RLC Circuits in Time-Domain
	Introduction
	7.1 RC Circuit Equations
	7.2 Zero-Input Response of RC Circuit
	7.3 Zero-State Response of RC Circuits for Various Inputs
		7.3.1 Impulse Response of First-Order RC Circuits
		7.3.2 Step Response of First-Order RC Circuits
		7.3.3 Ramp Response of Series RC Circuit
		7.3.4 Series RC Circuit with Real Exponential Input
		7.3.5 Zero-State Response of Parallel RC Circuit for Sinu Soidal Input
	7.4 Periodic Steady-State in a Series RC Circuit
	7.5 Sinusoidal Steady-State Frequency Response of First-Order RC Circuits
		7.5.1 The Use of Frequency Response
		7.5.2 Frequency Response and Linear Distortion
		7.5.3 Jean Baptiste Joseph Fourier and Frequency Response
		7.5.4 First-Order RC Circuits as Averaging Circuits
		7.5.5 Capacitor as a Signal-Coupling Element
		7.5.6 Parallel RC Circuit for Signal Bypassing
	7.6 The Series RLC Circuit – Zero-Input Response
		7.6.1 Source-Free Response of Series RLC Circuit
		7.6.2 The Series LC Circuit – A Special Case
		7.6.3 The Series LC Circuit with Small Damping –Another Special Case
		7.6.4 Standard Formats for Second-Order Circuit Zero-Input Response
	7.7 Impulse Response of Series RLC Circuit
	7.8 Step Response of Series RLC Circuit
	7.9 Standard Time-Domain Specifications for Second-Order Circuits
	7.10 Examples on Impulse and Step Response of Series RLC Circuits
	7.11 Frequency Response of Series RLC Circuit
		7.11.1 Sinusoidal Forced-Response from Differential Equation
		7.11.2 Frequency Response from Phasor Equivalent Circuit
		7.11.3 Qualitative Discussion on Frequency Response of Series RLC Circuit
		7.11.4 A More Detailed Look at the Band-Pass Output of Series RLC Circuit
		7.11.5 Quality Factor of Inductor and Capacitor
	7.12 The Parallel RLC Circuit
		7.12.1 Zero-Input Response and Zero-State Response of Parallel RLC Circuit
		7.12.2 Sinusoidal Steady-State Frequency Response of Parallel RLC Circuit
	7.13 Summary
	7.14 Questions
	7.15 Problems
Chapter 8: Higher Order Circuits in Time-Domain
	Introduction
	8.1 Analysis of Multi-Mesh and Multi-Node Dynamic Circuits
	8.2 Generalisations for an nth Order Linear Time-Invariant Circuit
	8.3 Time-Domain Convolution Integral
		8.3.1 Zero-State Response to Narrow Rectangular Pulse Input
		8.3.2 Expansion of an Arbitrary Input Function in Terms of Impulse Functions
		8.3.3 The Convolution Integral
		8.3.4 Graphical Interpretation of Convolution in Time-Domain
		8.3.5 Frequency Response Function from Convolution Integral
		8.3.6 A Circuit with Multiple Sources – Applying Convolution Integral
		8.3.7 Zero-Input Response by Convolution Integral
	8.4 Summary
	8.5 Questions
	8.6 Problems
Chapter 9: Analysis of Dynamic Circuits by Laplace Transforms
	Introduction
	9.1 Circuit Response to Complex Exponential Input
	9.2 Expansion of a Signal in Terms of Complex Exponential Functions
		9.2.1 Interpretation of Laplace Transform
	9.3 Laplace Transforms of Some Common Right-Sided Functions
	9.4 The s-Domain System Function H(S)
	9.5 Poles and Zeros of System Function and Excitation Function
	9.6 Method of Partial Fractions for Inverting Laplace Transforms
	9.7 Some Theorems on Laplace Transforms
		9.7.1 Time-Shifting Theorem
		9.7.2 Frequency-Shifting Theorem
		9.7.3 Time-Differentiation Theorem
		9.7.4 Time-Integration Theorem
		9.7.5 s-Domain-Differentiation Theorem
		9.7.6 s-Domain-Integration Theorem
		9.7.7 Convolution Theorem
		9.7.8 Initial Value Theorem
		9.7.9 Final Value Theorem
	9.8 Solution of Differential Equations by Laplace Transforms
	9.9 The s-Domain Equivalent Circuit
		9.9.1 s-Domain Equivalents of Circuit Elements
	9.10 Total Response of Circuits Using s-Domain Equivalent Circuit
	9.11 Network Functions and Pole-Zero Plots
		9.11.1 Driving-Point Functions and Transfer Functions
		9.11.2 The Three Interpretations for a Network Function H(S)
		9.11.3 Poles and Zeros of H(S) and Natural Frequencies of the Circuit
		9.11.4 Specifying a Network Function
	9.12 Impulse Response of Network Functions from Pole-Zero Plots
	9.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots
		9.13.1 Three Interpretations for H(Jω)
		9.13.2 Frequency Response from Pole-Zero Plot
	9.14 Analysis of Coupled Coils Using Laplace Transforms
		9.14.1 Input Impedance Function and Transfer Function of a Two-Winding Transformer
		9.14.2 Flux Expulsion by a Shorted Coil
		9.14.2 Breaking the Primary Current in a Transformer
	9.15 Summary
	9.16 Problems
Chapter 10: Two-Port Networks and Passive Filters
	Introduction
	10.1 Describing Equations and Parameter Sets for Two-Port Networks
		10.1.1 Short-Circuit Admittance Parameters for a Two-Port Network
		10.1.2 Open-Circuit Impedance Parameters for a Two-Port Network
		10.1.3 Hybrid Parameters and Inverse-Hybrid Parameters for a Two-Port Network
	10.2 Equivalent Circuits for a Two-Port Network
	10.3 Transmission Parameters (ABCD Parameters) of a Two-Port Network
	10.4 Inter-Relationships Between Various Parameter Sets
	10.5 Interconnections of Two-Port Networks
	10.6 Reciprocity and Symmetry in Two-Port Networks
	10.7 Standard Symmetric T and Pi Equivalents
	10.8 Image Parameter Description of a Reciprocal Two-Port Network
		10.8.1 Image Parameters for a Symmetric Reciprocal Two-Port Network
		10.8.2 Image Parameters in Terms of Open-Circuit and Short-Circuit Impedances
	10.9 Characteristic Impedance and Propagation Constant of Symmetric T and Pi Networks Under Sinusoidal Steady-State
		10.9.1 Attenuation Constant α and Phase Constant β
	10.10 Constant-k Low-Pass Filter
		10.10.1 Ideal Low-Pass Filter Versus Constant-k Low-pass Filter
		10.10.2 Prototype Low-pass Filter Design
	10.11 m-Derived Low-pass Filter Sections for Improved Attenuation
	10.12 m-Derived Half-Sections for Filter Termination
		10.12.1 m-Derived Half-Sections for Input Termination
		10.12.3 Half-II Termination Sections for II-Section Filters
	10.13 Constant-k and m-Derived High-Pass Filters
		10.13.1 Design Equations for Prototype High-Pass Filter
		10.13.2 m-Derived Sections for Infinite Attenuation
		10.13.3 Termination Sections for High-Pass Filter
	10.14 Constant-k Band-Pass Filter
		10.14.1 Design Equations of Prototype Band-Pass Filter
	10.15 Constant-k Band-Stop Filter
	10.16 Resistive Attenuators
		10.16.1 Attenuation Provided by a Symmetric Resistive Attenuator
		10.16.2 The Symmetrical T-Section Attenuator
		10.16.3 The Symmetrical II-Section Attenuator
		10.16.4 The Symmetrical Lattice-Section Attenuator
		10.16.5 The Symmetrical Bridged-T-Section Attenuator
		10.16.6 Asymmetrical T-Section and II-Section Attenuators
	10.17 Summary
	10.18 Questions
	10.19 Problems
Chapter 11: Introduction to Network Topology
	Introduction
	11.1 Linear Oriented Graphs
		11.1.1 Connected Graph, Subgraphs and Some Special Subgraphs
	11.2 The Incidence Matrix of a Linear Oriented Graph
		11.2.1 Path Matrix and its Relation to Incidence Matrix
	11.3 Kirchhoff’s Laws in Incidence Matrix Formulation
		11.3.1 KCL Equations from a Matrix
		11.3.2 KVL Equations and the a Matrix
	11.4 Nodal Analysis of Networks
		11.4.1 The Principle of v-Shift
		11.4.2 Nodal Analysis of Networks Containing Ideal Dependent Sources
	11.5 The Circuit Matrix of a Linear Oriented Graph
		11.5.1 The Fundamental Circuit Matrix Bf
		11.5.2 Relation Between All Incidence Matrix Aa and All Circuit Matrix Ba
	11.6 Kirchhoff’s Laws in Fundamental Circuit Matrix Formulation
		11.6.1 Kirchhoff’s Voltage Law and the Bf Matrix
		11.6.2 Kirchhoff’s Current Law and the Bf Matrix
	11.7 Loop Analysis of Electrical Networks
		11.7.1 The Principle of i-Shift
		11.7.2 Loop Analysis of Networks Containing Ideal Dependent Sources
		11.7.3 Planar Graphs and Mesh Analysis
		11.7.4 Duality
	11.8 The Cut-Set Matrix of a Linear Oriented Graph
		11.8.1 Cut-Sets
		11.8.2 The All Cut-Set Matrix Qa
		11.8.3 Orthogonality Relation Between Cut-Set Matrix and Circuit Matrix
		11.8.4 The Fundamental Cut-Set Matrix Qf
		11.8.5 Relation Between Qf, a and Bf
	11.9 Kirchhoff’s Laws in Fundamental Cut-Set Formulation
		11.9.1 Kirchhoff’s Current Law and the Qf Matrix
		11.9.2 Kirchhoff’s Voltage Law and the Qf Matrix
	11.10 Node-Pair Analysis of Networks
		11.10.1 Node-Pair Analysis of Networks Containing Ideal Dependent Sources
	11.11 Analysis Using Generalised Branch Model
		11.11.1 Node Analysis
		11.11.2 Loop Analysis
		11.11.3 Node-Pair Analysis
	11.12 Tellegen’s Theorem
	11.13 Summary
	11.14 Problems
Answers to Selected Problems