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Electric Circuit Analysis

Book Description

Electric Circuit Analysis is designed for undergraduate course on basic electric circuits. The book builds on the subject from its basic principles. Spread over fourteen chapters, the book can be taught with varying degree of emphasis based on the course requirement. Written in a student-friendly manner, its narrative style places adequate stress on the principles that govern the behaviour of electric circuits.

Table of Contents

  1. Cover
  2. Title Page
  3. Brief Contents
  4. Contents
  5. Dedication
  6. Preface
  7. Chapter 1: Circuit Variables and Circuit Elements
    1. 1.1 Electromotive Force, Potential and Voltage
      1. 1.1.1 Force between two moving point charges and Retardation Effect
      2. 1.1.2 Electric Potential and Voltage
      3. 1.1.3 Electromotive Force and Terminal Voltage of a Steady Source
    2. 1.2. A Voltage Source with a Resistance Connected at its Terminals
      1. 1.2.1 Steady-State Charge Distribution in the System
      2. 1.2.2 Drift Velocity and Current Density
      3. 1.2.3 Current Intensity
      4. 1.2.4 Conduction and Energy Transfer Process
      5. 1.2.5 Two-Terminal Resistance Element
      6. 1.2.6 A Time-Varying Voltage Source with Resistance Across it
    3. 1.3 Two-Terminal Capacitance
    4. 1.4 Two-Terminal Inductance
      1. 1.4.1 Induced Electromotive Force and its Location in a Circuit
      2. 1.4.2 Relation Between Induced Electromotive Force and Current
      3. 1.4.3 Farady’s Law and Induced Electromotive Force
      4. 1.4.4 The Issue of a Unique Voltage Across a Two-Terminal Element
      5. 1.4.5 The Two-Terminal Inductance
    5. 1.5 Ideal Independent Two-Terminal Electrical Sources
      1. 1.5.1 Ideal Independent Voltage Source
      2. 1.5.2 Ideal Independent Current Source
      3. 1.5.3 Ideal Short-Circuit Element and Ideal Open-Circuit Element
    6. 1.6 Power and Energy Relations for Two-Terminal Elements
      1. 1.6.1 Passive Sign Convention
      2. 1.6.2 Power and Energy in Two-Terminal Elements
    7. 1.7 Classification of Two-Terminal Elements
      1. 1.7.1 Lumped and Distributed Elements
      2. 1.7.2 Linear and Non-linear Elements
      3. 1.7.3 Bilateral and Non-bilateral Elements
      4. 1.7.4 Passive and Active Elements
      5. 1.7.5 Time-Invariant and Time-Variant Elements
    8. 1.8 Multi-Terminal Circuit Elements
      1. 1.8.1 Ideal Dependent Sources
    9. 1.9 Summary
    10. 1.10 Problems
  8. Chapter 2: Basic Circuit Laws
    1. 2.1 Kirchhoff ’s Voltage Law (KVL)
    2. 2.2 Kirchhoff ’s Current Law
    3. 2.3 Interconnections of Ideal Sources
    4. 2.4 Analysis of a Single-Loop Circuit
    5. 2.5 Analysis of a Single-Node-Pair Circuit
    6. 2.6 Analysis of Multi-Loop, Multi-Node Circuits
    7. 2.7 KVL and KCL in Operational Amplifier Circuits
      1. 2.7.1 The Practical Operational Amplifier
      2. 2.7.2 Negative Feedback in Operational Amplifier Circuits
      3. 2.7.3 The Principles of ‘Virtual Short’ and ‘Zero Input Current’
      4. 2.7.4 Analysis of Operational Amplifier Circuits Using the IOA Model
    8. 2.8 Summary
    9. 2.9 Problems
  9. Chapter 3: Single Element Circuits
    1. 3.1 The Resistor
      1. 3.1.1 Series Connection of Resistors
      2. 3.1.2 Parallel Connection of Resistors
    2. 3.2 The Inductor
      1. 3.2.1 Instantaneous Inductor Current versus Instantaneous Inductor Voltage
      2. 3.2.2 Change in Inductor Current Function versus Area under Voltage Function
      3. 3.2.3 Average Applied Voltage for a Given Change in Inductor Current
      4. 3.2.4 Instantaneous Change in Inductor Current
      5. 3.2.5 Inductor with Alternating Voltage Across it
      6. 3.2.6 Inductor with Exponential and Sinusoidal Voltage Input
      7. 3.2.7 Linearity of Inductor
      8. 3.2.8 Energy Storage in an Inductor
    3. 3.3 Series Connection of Inductors
    4. 3.4 Parallel Connection of Inductors
    5. 3.5 The Capacitor
    6. 3.6 Series Connection of Capacitors
      1. 3.6.1 Series Connection of Capacitors with Zero Initial Energy
      2. 3.6.2 Series Connection of Capacitors with Non-zero Initial Energy
    7. 3.7 Parallel Connection of Capacitors
    8. 3.8 Summary
    9. 3.9 Problems
  10. Chapter 4: Nodal Analysis and Mesh Analysis of Memoryless Circuits
    1. 4.1 The Circuit Analysis Problem
    2. 4.2 Nodal Analysis of Circuits Containing Resistors and Independent Current Sources
    3. 4.3 Nodal Analysis of Circuits Containing Independent Voltage Sources
    4. 4.4 Source Transformation Theorem and its Use in Nodal Analysis
      1. 4.4.1 Source Transformation Theorem
      2. 4.4.2 Applying Source Transformation in Nodal Analysis of Circuits
    5. 4.5 Nodal Analysis of Circuits Containing Dependent Current Sources
    6. 4.6 Nodal Analysis of Circuits Containing Dependent Voltage Sources
    7. 4.7 Mesh Analysis of Circuits with Resistors and Independent Voltage Sources
      1. 4.7.1 Principle of Mesh Analysis
      2. 4.7.2 Is Mesh Current Measurable?
    8. 4.8 Mesh Analysis of Circuits with Independent Current Sources
    9. 4.9 Mesh Analysis of Circuits Containing Dependent Sources
    10. 4.10 Summary
    11. 4.11 Problems
  11. Chapter 5: Circuit Theorems
    1. 5.1 Linearity of a Circuit and Superposition Theorem
      1. 5.1.1 Linearity of a Circuit
    2. 5.2 Star–Delta Transformation Theorem
    3. 5.3 Substitution Theorem
    4. 5.4 Compensation Theorem
    5. 5.5 Thevenin’s Theorem and Norton’s Theorem
    6. 5.6 Determination of Equivalents for Circuits with Dependent Sources
    7. 5.7 Reciprocity Theorem
    8. 5.8 Maximum Power Transfer Theorem
    9. 5.9 Millman’s Theorem
    10. 5.10 Summary
    11. 5.11 Problems
  12. Chapter 6: Power and Energy in Periodic Waveforms
    1. 6.1 Why Sinusoids?
    2. 6.2 The Sinusoidal Source Function
      1. 6.2.1 Amplitude, Period, Cyclic Frequency, Angular Frequency
      2. 6.2.2 Phase of a Sinusoidal Waveform
      3. 6.2.3 Phase Difference Between Two Sinusoids
      4. 6.2.4 Lag or Lead?
      5. 6.2.5 Phase Lag/Lead Versus Time Delay/Advance
    3. 6.3 Instantaneous Power in Periodic Waveforms
    4. 6.4 Average Power in Periodic Waveforms
    5. 6.5 Effective Value (RMS Value) of Periodic Waveforms
      1. 6.5.1 RMS Value of Sinusoidal Waveforms
    6. 6.6 The Power Superposition Principle
      1. 6.6.1 RMS Value of a Composite Waveform
    7. 6.7 Summary
    8. 6.8 Problems
  13. Chapter 7: The Sinusoidal Steady-State Response
    1. 7.1 Transient State and Steady-State in Circuits
      1. 7.1.1 Governing Differential Equation of Circuits – Examples
      2. 7.1.2 Solution of the Circuit Differential Equation
      3. 7.1.3 Complete Response with Sinusoidal Excitation
    2. 7.2 The Complex Exponential Forcing Function
      1. 7.2.1 Sinusoidal Steady-State Response from Response to e jωt
      2. 7.2.2 Steady-State Solution to ejωt and the jω Operator
    3. 7.3 Sinusoidal Steady-State Response Using Complex Exponential Input
    4. 7.4 The Phasor Concept
      1. 7.4.1 Kirchhoff ’s Laws in Terms of Complex Amplitudes
      2. 7.4.2 Element Relations in Terms of Complex Amplitudes
      3. 7.4.3 The Phasor
    5. 7.5 Transforming a Circuit into Phasor Equivalent Circuit
      1. 7.5.1 Phasor Impedance, Phasor Admittance and Phasor Equivalent Circuit
    6. 7.6 Sinusoidal Steady-State Response from Phasor Equivalent Circuit
      1. 7.6.1 Comparison between Memoryless Circuits and Phasor Equivalent Circuits
      2. 7.6.2 Nodal Analysis and Mesh Analysis of Phasor Equivalent Circuits – Examples
    7. 7.7 Circuit Theorems in Sinusoidal Steady-State Analysis
      1. 7.7.1 Maximum Power Transfer Theorem for Sinusoidal Steady-State Condition
    8. 7.8 Phasor Diagrams
    9. 7.9 Apparent Power, Active Power, Reactive Power and Power Factor
      1. 7.9.1 Active and Reactive Components of Current Phasor
      2. 7.9.2 Reactive Power and the Power Triangle
    10. 7.10 Complex Power Under Sinusoidal Steady-State Condition
    11. 7.11 Summary
    12. 7.12 Problems
  14. Chapter 8: Sinusoidal Steady-State in Three-Phase Circuits
    1. 8.1 Three-Phase System versus Single-Phase System
    2. 8.2 Three-Phase Sources and Three-Phase Power
      1. 8.2.1 The Y-connected Source
      2. 8.2.2 The ∆-connected Source
    3. 8.3 Analysis of Balanced Three-Phase Circuits
      1. 8.3.1 Equivalence Between a Y-connected Source and a ∆-connected Source
      2. 8.3.2 Equivalence Between a Y-connected Load and a ∆-connected Load
      3. 8.3.3 The Single-Phase Equivalent Circuit for a Balanced Three-Phase Circuit
    4. 8.4 Analysis of Unbalanced Three-Phase Circuits
      1. 8.4.1 Unbalanced Y–Y Circuit
      2. 8.4.2 Circulating Current in Unbalanced Delta-connected Sources
    5. 8.5 Symmetrical Components
      1. 8.5.1 Three-Phase Circuits with Unbalanced Sources and Balanced Loads
      2. 8.5.2 The Zero Sequence Component
      3. 8.5.3 Active Power in Sequence Components
      4. 8.5.4 Three-Phase Circuits with Balanced Sources and Unbalanced Loads
    6. 8.6 Summary
    7. 8.7 Problems
  15. Chapter 9: Dynamic Circuits with Periodic Inputs – Analysis by Fourier Series
    1. 9.1 Periodic Waveforms in Circuit Analysis
      1. 9.1.1 The Sinusoidal Steady-State Frequency Response Function
    2. 9.2 The Exponential Fourier Series
    3. 9.3 Trigonometric Fourier Series
    4. 9.4 Conditions for Existence of Fourier Series
    5. 9.5 Waveform Symmetry and Fourier Series Coefficients
    6. 9.6 Properties of Fourier Series and Some Examples
    7. 9.7 Discrete Magnitude and Phase Spectrum
    8. 9.8 Rate of Decay of Harmonic Amplitude
    9. 9.9 Analysis of Periodic Steady-State Using Fourier Series
    10. 9.10 Normalised Power in a Periodic Waveform and Parseval’s Theorem
    11. 9.11 Power and Power Factor in AC System with Distorted Waveforms
    12. 9.12 Summary
    13. 9.13 Problems
  16. Chapter 10: First-Order RL Circuits
    1. 10.1 The Series RL Circuit
      1. 10.1.1 The Series RL Circuit Equations
      2. 10.1.2 Need for Initial Condition Specification
      3. 10.1.3 Sufficiency of Initial Condition
    2. 10.2 Series RL Circuit with Unit Step Input – Qualitative Analysis
      1. 10.2.1 From t = 0− to t = 0+
      2. 10.2.2 Inductor Current Growth Process
    3. 10.3 Step Response of RL Circuit by Solving Differential Equation
      1. 10.3.1 Interpreting the Input Forcing Functions in Circuit Differential Equations
      2. 10.3.2 Complementary Function and Particular Integral
      3. 10.3.3 Series RL Circuit Response in DC Voltage Switching Problem
    4. 10.4 Features of RL Circuit Step Response
      1. 10.4.1 Step Response Waveforms in Series RL Circuit
      2. 10.4.2 The Time Constant ‘τ ’ of a Series RL Circuit
      3. 10.4.3 Rise Time and Fall Time in First-Order Circuits
      4. 10.4.4 Effect of Non-Zero Initial Condition on DC Switching Response of RL Circuit
      5. 10.4.5 Free Response of Series RL Circuit
    5. 10.5 Steady-State Response and Forced Response
      1. 10.5.1 The DC Steady-State
      2. 10.5.2 The Sinusoidal Steady-State
      3. 10.5.3 The Periodic Steady-State
    6. 10.6 Linearity and Superposition Principle in Dynamic Circuits
    7. 10.7 Unit Impulse Response of Series RL Circuit
      1. 10.7.1 Zero-State Response for Other Inputs from Impulse Response
    8. 10.8 Series RL Circuit with Exponential Inputs
      1. 10.8.1 Zero-State Response for Real Exponential Input
      2. 10.8.2 Zero-State Response for Sinusoidal Input
    9. 10.9 General Analysis Procedure for Single Time Constant RL Circuits
    10. 10.10 Summary
    11. 10.11 Problems
  17. Chapter 11: First-Order RC Circuits
    1. 11.1 RC Circuit Equations
    2. 11.2 Zero-Input Response of RC Circuit
    3. 11.3 Zero-State Response of RC Circuits for Various Inputs
      1. 11.3.1 Impulse Response of First-Order RC Circuits
      2. 11.3.2 Step Response of First-Order RC Circuits
      3. 11.3.3 Ramp Response of Series RC Circuit
      4. 11.3.4 Series RC Circuit with Real Exponential Input
      5. 11.3.5 Zero-State Response of Parallel RC Circuit for Sinusoidal Input
    4. 11.4 Periodic Steady-State in a Series RC Circuit
    5. 11.5 Frequency Response of First Order RC Circuits
      1. 11.5.1 The Use of Frequency Response
      2. 11.5.2 Frequency Response and Linear Distortion
      3. 11.5.3 First-Order RC Circuits as Averaging Circuits
      4. 11.5.4 Capacitor as a Signal Coupling Element
      5. 11.5.5 Parallel RC Circuit for Signal Bypassing
    6. 11.6 Summary
    7. 11.7 Problems
  18. Chapter 12: Series and Parallel RLC Circuits
    1. 12.1 The Series RLC Circuit – Zero-Input Response
      1. 12.1.1 Source-Free Response of Series RLC Circuit
    2. 12.2 The Series LC Circuit – A Special Case
    3. 12.3 The Series LC Circuit with Small Damping – Another Special Case
    4. 12.4 Standard Formats for Second-Order Circuit Zero-Input Response
    5. 12.5 Impulse Response of Series RLC Circuit
    6. 12.6 Step Response of Series RLC Circuit
    7. 12.7 Standard Time-Domain Specifications for Second-Order Circuits
    8. 12.8 Examples on Impulse and Step Response of Series RLC Circuits
    9. 12.9 Frequency Response of Series RLC Circuit
      1. 12.9.1 Sinusoidal Forced-Response from Differential Equation
      2. 12.9.2 Frequency Response from Phasor Equivalent Circuit
    10. 12.10 Resonance in Series RLC Circuit
      1. 12.10.1 The Voltage Across Resistor – The Band-pass Output
      2. 12.10.2 The Voltage Across Capacitor – The Low-pass Output
      3. 12.10.3 The Voltage Across Inductor – The High-Pass Output
      4. 12.10.4 Bandwidth Versus Quality Factor of Series RLC Circuit
      5. 12.10.5 Quality Factor of Inductor and Capacitor
      6. 12.10.6 LC Circuit as an Averaging Filter
    11. 12.11 The Parallel RLC Circuit
      1. 12.11.1 Zero-Input Response and Zero-State Response of Parallel RLC Circuit
      2. 12.11.2 Frequency Response of Parallel RLC Circuit
    12. 12.12 Summary
    13. 12.13 Problems
  19. Chapter 13: Analysis of Dynamic Circuits by Laplace Transforms
    1. 13.1 Circuit Response to Complex Exponential Input
    2. 13.2 Expansion of a Signal in terms of Complex Exponential Functions
      1. 13.2.1 Interpretation of Laplace Transform
    3. 13.3 Laplace Transforms of Some Common Right-Sided Functions
    4. 13.4 The s-Domain System Function H(s)
    5. 13.5 Poles and Zeros of System Function and Excitation Function
    6. 13.6 Method of Partial Fractions for Inverting Laplace Transforms
    7. 13.7 Some Theorems on Laplace Transforms
      1. 13.7.1 Time-Shifting Theorem
      2. 13.7.2 Frequency-Shifting Theorem
      3. 13.7.3 Time-Differentiation Theorem
      4. 13.7.4 Time-Integration Theorem
      5. 13.7.5 s-Domain-Differentiation Theorem
      6. 13.7.6 s-Domain-Integration Theorem
      7. 13.7.7 Convolution Theorem
      8. 13.7.8 Initial Value Theorem
      9. 13.7.9 Final Value Theorem
    8. 13.8 Solution of Differential Equations by Using Laplace Transforms
    9. 13.9 The s-Domain Equivalent Circuit
      1. 13.9.1 s-Domain Equivalents of Circuit Elements
      2. 13.9.2 Is s-domain Equivalent Circuit Completely Equivalent to Original Circuit?
    10. 13.10 Total Response of Circuits Using s-Domain Equivalent Circuit
    11. 13.11 Network Functions and Pole-Zero Plots
      1. 13.11.1 Driving-Point Functions and Transfer Functions
      2. 13.11.2 The Three Interpretations for a Network Function H(s)
      3. 13.11.3 Poles and Zeros of H(s) and Natural Frequencies of the Circuit
      4. 13.11.4 Specifying a Network Function
    12. 13.12 Impulse Response of Network Functions from Pole-Zero Plots
    13. 13.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots
      1. 13.13.1 Three Interpretations for H( jω)
      2. 13.13.2 Frequency Response from Pole-Zero Plot
    14. 13.14 Summary
    15. 13.15 Problems
  20. Chapter 14: Magnetically Coupled Circuits
    1. 14.1 The Mutual Inductance Element
      1. 14.1.1 Why Should M12 Be Equal to M21?
      2. 14.1.2 Dot Polarity Convention
      3. 14.1.3 Maximum Value of Mutual Inductance and Coupling Coefficient
    2. 14.2 The Two-Winding Transformer
    3. 14.3 The Perfectly Coupled Transformer and the Ideal Transformer
    4. 14.4 Ideal Transformer and Impedance Matching
    5. 14.5 Transformers in Single-Tuned and Double-Tuned Filters
      1. 14.5.1 Single-Tuned Amplifier
      2. 14.5.2 Double-Tuned Amplifier
    6. 14.6 Analysis of Coupled Coils Using Laplace Transforms
      1. 14.6.1 Input Impedance Function of a Two-Winding Transformer
      2. 14.6.2 Transfer Function of a Two-Winding Transformer
    7. 14.7 Flux Expulsion by a Shorted Coil
    8. 14.8 Breaking the Primary Current in a Transformer
    9. 14.9 Summary
    10. 14.10 Problems
  21. Acknowledgements
  22. Copyright
  23. Back Cover