book

Electric Circuits and Networks, Ist Edition by Pearson

Name: Electric Circuits and Networks, Ist Edition by Pearson
Author: K. S. Suresh Kumar
ISBN: 9781299447028

by K. S. Suresh Kumar

May 2024

Intermediate to advanced

840 pages

45h 20m

English

Pearson India

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Cover (1/3)
Cover (2/3)
Cover (3/3)
Contents (1/2)
Contents (2/2)
Preface (1/2)
Preface (2/2)
List of Reviewers
Part One: Basic Concepts
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 Effect1.1.2 Electric Potential and Voltage1.1.3 Electromotive Force and Terminal Voltage of a Steady Source
1.2 A Voltage Source with a Resistance Connected at its Terminals (1/2)
1.2.1 Steady-State Charge Distribution in the System1.2.2 Drift Velocity and Current Density1.2.3 Current Intensity1.2.4 Conduction and Energy Transfer Process1.2.5 Two-terminal Resistance Element
1.2 A Voltage Source with a Resistance Connected at its Terminals (2/2)
1.2.6 A Time-varying Voltage Source with Resistance Across it
1.3 Two-terminal Capacitance
1.4 Two-terminal Inductance (1/2)
1.4.1 Induced Electromotive Force and its Location in a Circuit1.4.2 Relation Between Induced Electromotive Force and Current1.4.3 Faraday’s Law and Induced Electromotive Force1.4.4 The Issue of a Unique Voltage Across a two-terminal Element1.4.5 The two-terminal Inductance
1.4 Two-terminal Inductance (2/2)
1.5 Ideal Independent two-terminal Electrical Sources
1.5.1 Ideal Independent Voltage Source1.5.2 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 (1/2)1.6.1 Passive Sign Convention1.6.2 Power and Energy in two-terminal Elements
1.6 Power and Energy Relations for two-terminal Elements (2/2)
1.7 Classification of Two-terminal Elements
1.7.1 Lumped and Distributed Elements1.7.2 Linear and Non-linear Elements1.7.3 Bilateral and Non-bilateral Elements1.7.4 Passive and Active Elements
1.7.5 Time-invariant and Time-variant Elements
1.8 Multi-terminal Circuit Elements1.8.1 Mutual Inductance Element1.8.2 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) (1/2)
2.1 Kirchhoff's Voltage Law (KVL) (2/2)
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 (1/2)
3.1.1 Series Connection of Resistors3.1.2 Parallel Connection of Resistors
3.1 The Resistor (2/2)
3.2 The Inductor (1/3)
3.2.1 Instantaneous Inductor Current versus Instantaneous Inductor Voltage3.2.2 Change in Inductor Current Function versus Area under Voltage Function3.2.3 Average Applied Voltage for a Given Change in Inductor Current3.2.4 Instantaneous Change in Inductor Current3.2.5 Inductor with Alternating Voltage Across it
3.2 The Inductor (2/3)
3.2.6 Inductor with Exponential and Sinusoidal Voltage Input3.2.7 Linearity of Inductor3.2.8 Energy Storage in an Inductor
3.2 The Inductor (3/3)
3.3 Series Connection of Inductors
3.3.1 Series Connection of Inductors with Same Initial Current3.3.2 Series Connection with Unequal Initial Currents
3.4 Parallel Connection of Inductors
3.4.1 Parallel Connection of Initially Relaxed Inductors3.4.2 Parallel Connection of Inductors with Initial Energy
3.5 The Capacitor (1/2)
3.5 The Capacitor (2/2)
3.6 Series Connection of Capacitors
3.6.1 Series Connection of Capacitors with Zero Initial Energy3.6.2 Series Connection of Capacitors with Non-zero Initial Energy
3.7 Parallel Connection of Capacitors
3.8 Summary
3.9 Questions
3.10 Problems
Part Two: Analysis of Memoryless Circuits
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 (1/2)
4.3 Nodal Analysis of Circuits Containing Independent Voltage Sources (2/2)
4.4 Source Transformation Theorem and its Use in Nodal Analysis
4.4.1 Source Transformation Theorem4.4.2 Applying Source Transformation Theorem in Nodal Analysis of Circuits
4.5 Nodal Analysis of Circuits Containin 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 Analysis4.7.2 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 (1/2)
5.1.1 Linearity of a Circuit
5.1 Linearity of a Circuit and Superposition Theorem (2/2)
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: The Operational Amplifier as a Circuit Element
Introduction
6.1 Ideal Amplifiers and their Features
6.1.1 Ground in Electronic Amplifiers
6.2 The Role of DC Power Supply in Amplifiers (1/2)6.2.1 Linear Amplification in Electronic Amplifiers6.2.2 Large-signal Operation of Amplifiers6.2.3 Output Limits in Amplifiers
6.2 The Role of DC Power Supply in Amplifiers (2/2)
6.3 The Operational Amplifier
6.3.1 The Practical Operational Amplifier
6.4 Negative Feedback in Operational Amplifier Circuits
6.5 The Principles of ‘Virtual Short’ and ‘Zero Input Current’
6.6 Analysis of Operational Amplifier Circuits using the IOA Model (1/2)
6.6.1 The Non-Inverting Amplifier Circuit6.6.2 The Voltage Follower Circuit6.6.3 The Inverting Amplifier Circuit6.6.4 The Inverting Summer6.6.5 The Non-Inverting Summer Amplifier6.6.6 The Subtractor Circuit6.6.7 The Instrumentation Amplifier
6.6 Analysis of Operational Amplifier Circuits using the IOA Model (2/2)
6.6.8 Voltage to Current Converters
6.7 Offset Model for an Operational Amplifier
6.8 Effect of Non-Ideal Properties of Opamp on Circuit Performance
6.9 Summary
6.10 Questions
6.11 Problems
Part Three: Sinusoidal Steady-State in Dynamic Circuits
Chapter 7: Power and Energy in Periodic Waveforms
Introduction
7.1 Why Sinusoids?
7.2 The Sinusoidal Source Function (1/2)
7.2.1 Amplitude, Period, Cyclic Frequency and Angular Frequency7.2.2 Phase of a Sinusoidal Waveform7.2.3 Phase Difference Between Two Sinusoids7.2.4 Lag or Lead?
7.2 The Sinusoidal Source Function (2/2)
7.2.5 Phase Lag/Lead Versus Time Delay/Advance
7.3 Instantaneous Power in Periodic Waveforms
7.4 Average Power in Periodic Waveforms (1/2)
7.4 Average Power in Periodic Waveforms (2/2)
7.5 Effective Value (RMS Value) of Periodic Waveforms
7.6 The Power Superposition Principle
7.6.1 RMS Value of a Composite Waveform
7.7 Summary
7.8 Question
7.9 Problems
Chapter 8: The Sinusoidal Steady-State Response
Introduction
8.1 Transient State and Steady-State in Circuits
8.1.1 Governing Differential Equation of Circuits – Examples8.1.2 Solution of the Circuit Differential Equation8.1.3 Complete Response with Sinusoidal Excitation
8.2 The Complex Exponential Forcing Function
8.2.1 Sinusoidal Steady-State Response from Response to8.2.2 Steady-State Solution to and the Operator
8.3 Sinusoidal Steady-State Response using Complex Exponential Input
8.4 The Phasor Concept
8.4.1 Kirchhoff’s Laws in terms of Complex Amplitudes8.4.2 Element Relations in terms of Complex Amplitudes
8.4.3 The Phasor
8.5 Transforming a Circuit into A Phasor Equivalent Circuit8.5.1 Phasor Impedance, Phasor Admittance and Phasor Equivalent Circuit
8.6 Sinusoidal Steady-State Response from Phasor Equivalent Circuit (1/3)
8.6.1 Comparison Between Memoryless Circuits and Phasor Equivalent Circuits8.6.2 Nodal Analysis and Mesh Analysis of Phasor Equivalent Circuits – Examples
8.6 Sinusoidal Steady-State Response from Phasor Equivalent Circuit (2/3)
8.6 Sinusoidal Steady-State Response from Phasor Equivalent Circuit (3/3)
8.7 Circuit Theorems in Sinusoidal Steady-State Analysis
8.7.1 Maximum Power Transfer Theorem for Sinusoidal Steady-State Condition
8.8 Phasor Diagrams (1/2)
8.8 Phasor Diagrams (2/2)
8.9 Apparent Power, Active Power, Reactive Power and Power Factor
8.9.1 Active and Reactive Components of Current Phasor8.9.2 Reactive Power and the Power Triangle
8.10 Complex Power under Sinusoidal Steady-State Condition
8.11 Sinusoidal Steady-State in Circuits with Coupled Coils (1/2)
8.11.1 Dot Polarity Convention8.11.2 Maximum Value of Mutual Inductance and Coupling Coefficient8.11.3 A Two-Winding Transformer – Equivalent Models
8.11 Sinusoidal Steady-State in Circuits with Coupled Coils (2/2)
8.11.4 The Perfectly Coupled Transformer and The Ideal Transformer
8.12 Summary
8.13 Questions
8.14 Problems
Chapter 9: Sinusoidal Steady-State in Three-Phase Circuits
Introduction
9.1 Three-Phase System versus Single-Phase System
9.2 Three-Phase Sources and Three-Phase Power
9.2.1 The Y-connected Source9.2.2 The Δ-connected Source
9.3 Analysis of Balanced Three-Phase Circuits (1/2)
9.3.1 Equivalence Between a Y-connected Source and a Δ-connected Source9.3.2 Equivalence Between a Y-connected Load and a Δ-connected Load9.3.3 The Single-Phase Equivalent Circuit for a BalancedThree-Phase Circuit
9.3 Analysis of Balanced Three-Phase Circuits (2/2)
9.4 Analysis of Unbalanced Three-Phase Circuits
9.4.1 Unbalanced Y–Y Circuit9.4.2 Circulating Current in Unbalanced Δ-connected Sources
9.5 Symmetrical Components (1/3)
9.5.1 Three-Phase Circuits with Unbalanced Sources and Balanced Loads9.5.2 The Zero Sequence Component9.5.3 Active Power in Sequence Components9.5.4 Three-Phase Circuits with Balanced Sources and Unbalanced Loads
9.5 Symmetrical Components (2/3)
9.5 Symmetrical Components (3/3)
9.6 Summary
9.7 Questions
9.8 Problems
Part Four: Time-Domain Analysis of Dynamic Circuits
Chapter 10: Simple RL Circuits in Time-Domain
Introduction
10.1 The Series RL Circuit
10.1.1 The Series RL Circuit Equations10.1.2 Need for Initial Condition Specification10.1.3 Sufficiency of Initial Condition
10.2 Series RL Circuit with Unit Step Input – Qualitative Analysis
10.2.1 From t = 0– to t = 0+10.2.2 Inductor Current Growth Process
10.3 Series RL Circuit with Unit Step Input – Power Series Solution
10.3.1 Series RL Circuit Current as a Power Series
10.4 Step Response of an RL Circuit by Solving Differential Equation
10.4.1 Interpreting the Input Forcing Functions in Circuit Differential Equations10.4.2 Solving the Series RL Circuit Equation by Integrating Factor Method10.4.3 Complementary Function and Particular Integral
10.5 Features of RL Circuit Step Response (1/3)
10.5.1 Step Response Waveforms in Series RL Circuit10.5.2 The Time Constant ‘τ’ of a Series RL Circuit10.5.3 Rise Time and Fall Time in First Order Circuits
10.5 Features of RL Circuit Step Response (2/3)
10.5.4 Effect of Non-Zero Initial Condition on Step Response of RL Circuit10.5.5 Free Response of Series RL Circuit
10.5 Features of RL Circuit Step Response (3/3)
10.6 Steady-State Response and Forced Response
10.6.1 The DC Steady-State10.6.2 The Sinusoidal Steady-State10.6.3 The Periodic Steady-State
10.7 Linearity and Superposition Principle in Dynamic Circuits
10.8 Unit Impulse Response of Series RL Circuit (1/2)
10.8.1 Unit Impulse Response of RL Circuit with Non-Zero Initial Current10.8.2 Zero-State Response for Other Inputs from Zero-State Impulse Response
10.8 Unit Impulse Response of Series RL Circuit (2/2)
10.9 Series RL Circuit with Exponential Inputs
10.9.1 Zero-State Response for a Real Exponential Input10.9.2 Zero-State Response for Sinusoidal Input
10.10 General Analysis Procedure for Single Time Constant RL Circuits (1/2)
10.10 General Analysis Procedure for Single Time Constant RL Circuits (2/2)
10.11 Summary
10.12 Questions
10.13 Problems
Chapter 11: RC and RLC Circuits in Time-Domain
Introduction
11.1 RC Circuit Equations
11.2 Zero-Input Response of RC Circuit
11.3 Zero-State Response of RC Circuits for Various Inputs (1/2)
11.3.1 Impulse Response of First-Order RC Circuits11.3.2 Step Response of First-Order RC Circuits11.3.3 Ramp Response of Series RC Circuit11.3.4 Series RC Circuit with Real Exponential Input
11.3 Zero-State Response of RC Circuits for Various Inputs (2/2)
11.3.5 Zero-State Response of Parallel RC Circuit for Sinusoidal Input
11.4 Periodic Steady-State in a Series RC Circuit
11.5 Sinusoidal Steady-State Frequency Response of First-Order RC Circuits (1/2)
11.5.1 The Use of Frequency Response11.5.2 Frequency Response and Linear Distortion11.5.3 Jean Baptiste Joseph Fourier and Frequency Response11.5.4 First-Order RC Circuits as Averaging Circuits
11.5 Sinusoidal Steady-State Frequency Response of First-Order RC Circuits (2/2)
11.5.5 Capacitor as a Signal-Coupling Element11.5.6 Parallel RC Circuit for Signal Bypassing
11.6 The Series RLC Circuit – Zero-Input Response (1/3)
11.6.1 Source-free Response of Series RLC Circuit
11.6 The Series RLC Circuit – Zero-Input Response (2/3)
11.6.2 The Series LC Circuit – A Special Case
11.6 The Series RLC Circuit – Zero-Input Response (3/3)
11.6.3 The Series LC Circuit with Small Damping – Another Special Case11.6.4 Standard Formats for Second-order Circuit Zero-input Response
11.7 Impulse Response of Series RLC Circuit
11.8 Step Response of Series RLC Circuit
11.9 Standard Time-Domain Specifications for Second-Order Circuits
11.10 Examples on Impulse and Step Response of Series RLC Circuits (1/2)
11.10 Examples on Impulse and Step Response of Series RLC Circuits (2/2)
11.11 Frequency Response of Series RLC Circuit (1/3)
11.11.1 Sinusoidal Forced-Response from Differential Equation11.11.2 Frequency Response from Phasor Equivalent Circuit11.11.3 Qualitative Discussion on Frequency Response of Series RLC Circuit
11.11 Frequency Response of Series RLC Circuit (2/3)
11.11.4 A More Detailed Look at the Band-pass Output of Series RLC Circuit11.11.5 Quality Factor of Inductor and Capacitor
11.11 Frequency Response of Series RLC Circuit (3/3)
11.12 The Parallel RLC Circuit (1/2)
11.12.1 Zero-Input Response and Zero-State Response of Parallel RLC Circuit
11.12 The Parallel RLC Circuit (2/2)
11.12.2 Sinusoidal Steady-State Frequency Response of Parallel RLC Circuit
11.13 Summary
11.14 Questions
11.15 Problems
Chapter 12: Higher Order Circuits in Time-Domain
Introduction
12.1 Analysis of Multi-Mesh and Multi-Node Dynamic Circuits (1/3)
12.1 Analysis of Multi-Mesh and Multi-Node Dynamic Circuits (2/3)
12.1 Analysis of Multi-Mesh and Multi-Node Dynamic Circuits (3/3)
12.2 Generalisations for an nth Order Linear Time-Invariant Circuit
12.3 Time-Domain Convolution Integral (1/3)
12.3.1 Zero-State Response to Narrow Rectangular Pulse Input12.3.2 Expansion of an Arbitrary Input Function in Terms of Impulse Functions12.3.3 The Convolution Integral
12.3 Time-Domain Convolution Integral (2/3)
12.3.4 Graphical Interpretation of Convolution in Time-Domain12.3.5 Frequency Response Function from Convolution Integral12.3.6 A Circuit with Multiple Sources – Applying Convolution Integral
12.3 Time-Domain Convolution Integral (3/3)
12.3.7 Zero-Input Response by Convolution Integral
12.4 Summary
12.5 Questions
12.6 Problems
Part Five: Frequency-Domain Analysis of Dynamic Circuits
Chapter 13: Dynamic Circuits with Periodic Inputs – Analysis by Fourier Series
Introduction
13.1 Periodic Waveforms in Circuit Analysis
13.2 The Exponential Fourier Series
13.3 Trigonometric Fourier Series
13.4 Conditions for Existence of Fourier Series
13.5 Waveform Symmetry and Fourier Series Coefficients
13.6 Properties of Fourier Series and Some Examples (1/2)
13.6 Properties of Fourier Series and Some Examples (2/2)
13.7 Discrete Magnitude and Phase Spectrum
13.8 Rate of Decay of Harmonic Amplitude
13.9 Analysis of Periodic Steady-State Using Fourier Series
13.10 Normalised Power in a Periodic Waveform and Parseval’s Theorem
13.11 Power and Power Factor in AC System with Distorted Waveforms
13.12 Summary
13.13 Questions
13.14 Problems
Chapter 14: Dynamic Circuits with Aperiodic Inputs - Analysis by Fourier Transforms
Introduction
14.1 Aperiodic Waveforms
14.1.1 Finite-Duration Aperiodic Signal As One Period of a Periodic Waveform
14.2 Fourier Transform of an Aperiodic Waveform (1/2)
14.2.1 Fourier Transform of a Finite-Duration Aperiodic Waveform14.2.2 Fourier Transform of Infinite-Duration Aperiodic Waveforms14.2.3 Interpretation of Fourier Transforms
14.2 Fourier Transform of an Aperiodic Waveform (2/2)
14.3 Convergence of Fourier transforms
14.3.1 Uniqueness of Fourier Transform Pair
14.4 Some Basic Properties of Fourier transforms
14.4.1 Linearity of Fourier Transform14.4.2 Duality in Fourier Transform14.4.3 Time Reversal Property14.4.4 Time Shifting Property
14.5 Symmetry Properties of Fourier transforms
14.5.1 Conjugate Symmetry Property14.5.2 Fourier Transform of an Even Time-Function14.5.3 Fourier Transform of an Odd Time-Function14.5.4 Fourier Transforms of Even Part and Odd Part of a Real Time-Function
14.5.5 v(0) and V(j0)
14.6 Time-Scaling Property and Fourier transform of Impulse Function14.6.1 Compressing a Triangular Pulse in Time-Domain with its Area Content Constant
14.7 Fourier Transforms of Periodic Waveforms
14.8 Fourier Transforms of Some Semi-Infinite Duration Waveforms
14.8.1 Fourier Transform of e–α t u(t)14.8.2 Fourier Transform of Signum Function14.8.3 Fourier Transform of Unit Step Function14.8.4 Fourier Transform of Functions of the Form
14.9 Zero-State Response by Frequency-Domain Analysis (1/2)
14.9.1 Why Should the System Function and Fourier Transform of Impulse Response be the Same?
14.9 Zero-State Response by Frequency-Domain Analysis (2/2)
14.10 The System Function and Signal Distortion
14.10.1 The Signal Transmission Context14.10.2 Linear Distortion in Signal Transmission Context14.10.3 Pulse Distortion in First Order Channels
14.11 Parseval’s Relation for a Finite-Energy Waveform
14.12 Summary
14.13 Questions
14.14 Problems
Chapter 15: Analysis of Dynamic Circuits by Laplace Transforms
Introduction
15.1 Circuit Response to Complex Exponential Input
15.2 Expansion of a Signal in Terms of Complex Exponential Functions
15.2.1 Interpretation of Laplace Transform
15.3 Laplace Transforms of Some Common Right-Sided Functions
15.4 The s-Domain System Function H(S)
15.5 Poles and Zeros of System Function and Excitation Function
15.6 Method of Partial Fractions for Inverting Laplace Transforms
15.7 Some Theorems on Laplace Transforms
15.7.1 Time-shifting Theorem15.7.2 Frequency-shifting Theorem15.7.3 Time-Differentiation Theorem15.7.4 Time-integration Theorem15.7.5 s-Domain-Differentiation Theorem15.7.6 s-Domain-Integration Theorem15.7.7 Convolution Theorem15.7.8 Initial Value Theorem15.7.9 Final Value Theorem
15.8 Solution of Differential Equations by Laplace Transforms
15.9 The s-Domain Equivalent Circuit
15.9.1 s-Domain Equivalents of Circuit Elements
15.10 Total Response of Circuits Using s-Domain Equivalent Circuit (1/3)
15.10 Total Response of Circuits Using s-Domain Equivalent Circuit (2/3)
15.10 Total Response of Circuits Using s-Domain Equivalent Circuit (3/3)
15.11 Network Functions and Pole-Zero Plots (1/2)
15.11.1 Driving-point Functions and Transfer Functions15.11.2 The Three Interpretations for a Network Function H(s)15.11.3 Poles and Zeros of H(s) and Natural Frequencies of the Circuit15.11.4 Specifying a Network Function
15.11 Network Functions and Pole-Zero Plots (2/2)
15.12 Impulse Response of Network Functions from Pole-Zero Plots
15.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots
15.13.1 Three Interpretations for H15.13.2 Frequency Response from Pole-Zero Plot
15.14 Analysis of Coupled Coils Using Laplace Transforms (1/2)
15.14.1 Input Impedance Function and Transfer Function of a Two-Winding Transformer15.14.2 Flux Expulsion by a Shorted Coil
15.14 Analysis of Coupled Coils Using Laplace Transforms (2/2)
15.14.2 Breaking the Primary Current in a Transformer
15.15 Summary
15.16 Problems
Part Six: Introduction to Network Analysis
Chapter 16: Two-Port Networks and Passive Filters
Introduction
16.1 Describing Equations and Parameter Sets for Two-Port Networks (1/2)
16.1.1 Short-Circuit Admittance Parameters for a Two-Port Network16.1.2 Open-Circuit Impedance Parameters for a Two-Port Network
16.1 Describing Equations and Parameter Sets for Two-Port Networks (2/2)
16.1.3 Hybrid Parameters and Inverse-Hybrid Parameters for a Two-Port Network
16.2 Equivalent Circuits for a Two-Port Network
16.3 Transmission Parameters (ABCD Parameters) of a Two-Port Network
16.4 Inter-relationships between Various Parameter Sets
16.5 Interconnections of Two-Port Networks
16.6 Reciprocity and Symmetry in Two-Port Networks
16.7 Standard Symmetric T and Pi Equivalents
16.8 Image Parameter Description of a Reciprocal Two-Port Network
16.8.1 Image Parameters for a Symmetric Reciprocal Two-Port Network16.8.2 Image Parameters in terms of Open-Circuit and Short-Circuit Impedances
16.9 Characteristic Impedance and Propagation Constant of Symmetric T and Pi Networks Under Sinusoidal Steady-State
16.9.1 Attenuation Constant α and Phase Constant β
16.10 Constant-k Low-pass Filter
16.10.1 Ideal Low-pass Filter Versus Constant-k Low-pass Filter16.10.2 Prototype Low-pass Filter Design
16.11 m-Derived Low-pass Filter Sections for Improved Attenuation
16.12 m-Derived Half-Sections for Filter Termination
16.12.1 m-Derived Half-Sections for Input Termination16.12.2 Half-Π Termination Sections for Π-Section Filters
16.13 Constant-k and m-Derived High-Pass Filters
16.13.1 Design Equations for Prototype High-Pass Filter16.13.2 m-Derived Sections for Infinite Attenuation16.13.3 Termination Sections for High-Pass Filter
16.14 Constant-k Band-Pass Filter
16.14.1 Design Equations of Prototype Band-Pass Filter
16.15 Constant-k Band-Stop Filter
16.16 Resistive Attenuators
16.16.1 Attenuation provided by a Symmetric Resistive Attenuator16.16.2 The Symmetrical T-Section Attenuator16.16.3 The Symmetrical Π-Section Attenuator16.16.4 The Symmetrical Lattice-Section Attenuator16.16.5 The Symmetrical Bridged-T-Section Attenuator16.16.6 Asymmetrical T-Section and Π-Section Attenuators
16.17 Summary
16.18 Questions
16.19 Problems
Chapter 17: Introduction to Network Topology
Introduction
17.1 Linear Oriented Graphs
17.1.1 Connected Graph, Subgraphs and Some Special Subgraphs
17.2 The Incidence Matrix of a Linear Oriented Graph
17.2.1 Path Matrix and its Relation to Incidence Matrix
17.3 Kirchhoff’s Laws in Incidence Matrix Formulation
17.3.1 KCL Equations from A Matrix17.3.2 KVL Equations and the A Matrix
17.4 Nodal Analysis of Networks (1/2)
17.4.1 The Principle of v-Shift17.4.2 Nodal Analysis of Networks Containing Ideal Dependent Sources
17.4 Nodal Analysis of Networks (2/2)
17.5 The Circuit Matrix of a Linear Oriented Graph
17.5.1 The Fundamental Circuit Matrix Bf17.5.2 Relation between All Incidence Matrix Aa and All Circuit Matrix Ba
17.6 Kirchhoff’s Laws in Fundamental Circuit Matrix Formulation
17.6.1 Kirchhoff’s Voltage Law and the Bf Matrix17.6.2 Kirchhoff’s Current Law and the Bf Matrix
17.7 Loop Analysis of Electrical Networks (1/2)
17.7.1 The Principle of i-Shift17.7.2 Loop Analysis of Networks Containing Ideal Dependent Sources
17.7 Loop Analysis of Electrical Networks (2/2)
17.7.3 Planar Graphs and Mesh Analysis17.7.4 Duality
17.8 The Cut-Set Matrix of a Linear Oriented Graph
17.8.1 Cut-sets17.8.2 The All Cut-set Matrix17.8.3 Orthogonality Relation Between Cut-set Matrix and Circuit Matrix17.8.4 The Fundamental Cut-set Matrix17.8.5 Relation Between Qf, A and Bf
17.9 Kirchhoff’s Laws in Fundamental Cut-Set Formulation
17.9.1 Kirchhoff’s Current Law and the Qf Matrix
17.9.2 Kirchhoff’s Voltage Law and the Qf Matrix
17.10 Node-Pair Analysis of Networks17.10.1 Node-Pair Analysis of Networks Containing Ideal Dependent Sources
17.11 Analysis Using Generalised Branch Model
17.11.1 Node Analysis17.11.2 Loop Analysis17.11.3 Node-pair Analysis
17.12 Tellegen’s Theorem
17.13 Summary
17.14 Problems
Answers to Selected Problems (1/3)
Answers to Selected Problems (2/3)
Answers to Selected Problems (3/3)
Index

Content preview from Electric Circuits and Networks, Ist Edition by Pearson

17.3 KIRCHHOFF’S LAWS IN INCIDENCE MATRIX FORMULATION

17.3.1 KCL Equations from A Matrix

Kirchhoff’s Current Law states that the sum of currents leaving a node in a network is zero

on an instant-to-instant basis at all nodes in the network. The orientation of a particular

branch in the graph of a network was taken to be the same as the reference direction for cur-

rent in that branch. The incidence matrix entry is +1 if a branch is incident at a node with

orientation away from the node. It is 1 if a branch is incident at a particular node and is

oriented towards it. Therefore, the KCL equation at a node can be obtained by multiplying

the entries in ...

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