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W waveform symmetry, 9.11–9.14 Y



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Electric Circuit Analysis by K. S. Suresh Kumar

W
waveform symmetry, 9.11–9.14
Y
Y-connected source, 8.6–8.9
Z
zero-input response, 11.3
zero input current principle, 2.29
zero sequence component, 8.26–8.27

Document Outline

  • Cover
  • Dedication
  • Brief Contents
  • Contents
  • Preface
  • Acknowledgements
  • Chapter 1 : Circuit Variables and Circuit Elements
    • 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 Farady’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 Ideal Dependent Sources
    • 1.9 Summary
    • 1.10 Problems
  • Chapter 2 : Basic Circuit Laws
    • 2.1 Kirchhoff’s Voltage Law (KVL)
    • 2.2 Kirchhoff’s Current Law
    • 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 KVL and KCL in Operational Amplifier Circuits
      • 2.7.1 The Practical Operational Amplifier
      • 2.7.2 Negative Feedback in Operational Amplifier Circuits
      • 2.7.3 The Principles of ‘Virtual Short’ and ‘Zero Input Current’
      • 2.7.4 Analysis of Operational Amplifier Circuits Using the IOA Model
    • 2.8 Summary
    • 2.9 Problems
  • Chapter 3 : Single Element Circuits
    • 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 Sinusoidal Voltage Input
        • 3.2.7 Linearity of Inductor
        • 3.2.8 Energy Storage in an Inductor
      • 3.3 Series Connection of Inductors
      • 3.4 Parallel Connection of Inductors
      • 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 Problems
  • Chapter 4 : Nodal Analysis and Mesh Analysis of Memoryless Circuits
    • 4.1 The Circuit Analysis Problem
    • 4.2 Nodal Analysis of Circuits Containing Resistors and 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 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
    • 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 : Power and Energy in Periodic Waveforms
    • 6.1 Why Sinusoids?
    • 6.2 The Sinusoidal Source Function
      • 6.2.1 Amplitude, Period, Cyclic Frequency, Angular Frequency
      • 6.2.2 Phase of a Sinusoidal Waveform
      • 6.2.3 Phase Difference Between Two Sinusoids
      • 6.2.4 Lag or Lead?
      • 6.2.5 Phase Lag/Lead Versus Time Delay/Advance
    • 6.3 Instantaneous Power in Periodic Waveforms
    • 6.4 Average Power in Periodic Waveforms
    • 6.5 Effective Value (RMS Value) of Periodic Waveforms
      • 6.5.1 RMS Value of Sinusoidal Waveforms
    • 6.6 The Power Superposition Principle
      • 6.6.1 RMS Value of a Composite Waveform
    • 6.7 Summary
    • 6.8 Problems
  • Chapter 7 : The Sinusoidal Steady-State Response
    • 7.1 Transient State and Steady-State in Circuits
      • 7.1.1 Governing Differential Equation of Circuits – Examples
      • 7.1.2 Solution of the Circuit Differential Equation
      • 7.1.3 Complete Response with Sinusoidal Excitation
    • 7.2 The Complex Exponential Forcing Function
      • 7.2.1 Sinusoidal Steady-State Response from Response to ejωt
      • 7.2.2 Steady-State Solution to ejωt and the j ω Operator
    • 7.3 Sinusoidal Steady-State Response Using Complex Exponential Input
    • 7.4 The Phasor Concept
      • 7.4.1 Kirchhoff’s Laws in Terms of Complex Amplitudes
      • 7.4.2 Element Relations in Terms of Complex Amplitudes
      • 7.4.3 The Phasor
    • 7.5 Transforming a Circuit into Phasor Equivalent Circuit
      • 7.5.1 Phasor Impedance, Phasor Admittance and Phasor Equivalent Circuit
    • 7.6 Sinusoidal Steady-State Response from Phasor Equivalent Circuit
      • 7.6.1 Comparison between Memoryless Circuits and Phasor Equivalent Circuits
      • 7.6.2 Nodal Analysis and Mesh Analysis of Phasor Equivalent Circuits – Examples
    • 7.7 Circuit Theorems in Sinusoidal Steady-State Analysis
      • 7.7.1 Maximum Power Transfer Theorem for Sinusoidal Steady-State Condition
    • 7.8 Phasor Diagrams
    • 7.9 Apparent Power, Active Power, Reactive Power and Power Factor
      • 7.9.1 Active and Reactive Components of Current Phasor
      • 7.9.2 Reactive Power and the Power Triangle
    • 7.10 Complex Power Under Sinusoidal Steady-State Condition
    • 7.11 Summary
    • 7.12 Problems
  • Chapter 8 : Sinusoidal Steady-State in Three-Phase Circuits
    • 8.1 Three-Phase System Versus Single-Phase System
    • 8.2 Three-Phase Sources and Three-Phase Power
      • 8.2.1 The Y-connected Source
      • 8.2.2 The Δ-connected Source
    • 8.3 Analysis of Balanced Three-Phase Circuits
      • 8.3.1 Equivalence Between a Y-connected Source and a Δ-connected Source
      • 8.3.2 Equivalence Between a Y-connected Load and a Δ-connected Load
      • 8.3.3 The Single-Phase Equivalent Circuit for a Balanced Three-Phase Circuit
    • 8.4 Analysis of Unbalanced Three-Phase Circuits
      • 8.4.1 Unbalanced Y–Y Circuit
      • 8.4.2 Circulating Current in Unbalanced Delta-connected Sources
    • 8.5 Symmetrical Components
      • 8.5.1 Three-Phase Circuits with Unbalanced Sources and Balanced Loads
      • 8.5.2 The Zero Sequence Component
      • 8.5.3 Active Power in Sequence Components
      • 8.5.4 Three-Phase Circuits with Balanced Sources and Unbalanced Loads
    • 8.6 Summary
    • 8.7 Problems
  • Chapter 9 : Dynamic Circuits with Periodic Inputs –Analysis by Fourier Series
    • 9.1 Periodic Waveforms in Circuit Analysis
      • 9.1.1 The Sinusoidal Steady-State Frequency Response Function
    • 9.2 The Exponential Fourier Series
    • 9.3 Trigonometric Fourier Series
    • 9.4 Conditions for Existence of Fourier Series
    • 9.5 Waveform Symmetry and Fourier Series Coefficients
    • 9.6 Properties of Fourier Series and Some Examples
    • 9.7 Discrete Magnitude and Phase Spectrum
    • 9.8 Rate of Decay of Harmonic Amplitude
    • 9.9 Analysis of Periodic Steady-State Using Fourier Series
    • 9.10 Normalised Power in a Periodic Waveform and Parseval’s Theorem
    • 9.11 Power and Power Factor in AC System with Distorted Waveforms
    • 9.12 Summary
    • 9.13 Problems
  • Chapter 10 : First-Order RL Circuits
    • 10.1 The Series RL Circuit
      • 10.1.1 The Series RL Circuit Equations
      • 10.1.2 Need for Initial Condition Specification
      • 10.1.3 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 Step Response of RL Circuit by Solving Differential Equation
      • 10.3.1 Interpreting the Input Forcing Functions in Circuit Differential Equations
      • 10.3.2 Complementary Function and Particular Integral
      • 10.3.3 Series RL Circuit Response in DC Voltage Switching Problem
    • 10.4 Features of RL Circuit Step Response
      • 10.4.1 Step Response Waveforms in Series RL Circuit
      • 10.4.2 The Time Constant ‘s ’ of a Series RL Circuit
      • 10.4.3 Rise Time and Fall Time in First-Order Circuits
      • 10.4.4 Effect of Non-Zero Initial Condition on DC Switching Response of RL Circuit
      • 10.4.5 Free Response of Series RL Circuit
    • 10.5 Steady-State Response and Forced Response
      • 10.5.1 The DC Steady-State
      • 10.5.2 The Sinusoidal Steady-State
      • 10.5.3 The Periodic Steady-State
    • 10.6 Linearity and Superposition Principle in Dynamic Circuits
    • 10.7 Unit Impulse Response of Series RL Circuit
      • 10.7.1 Zero-State Response for Other Inputs from Impulse Response
    • 10.8 Series RL Circuit with Exponential Inputs
      • 10.8.1 Zero-State Response for Real Exponential Input
      • 10.8.2 Zero-State Response for Sinusoidal Input
    • 10.9 General Analysis Procedure for Single Time Constant RL Circuits
    • 10.10 Summary
    • 10.11 Problems
  • Chapter 11 : First-Order RC Circuits
    • 11.1 RC Circuit Equations
    • 11.2 Zero-Input Response of RC Circuit
    • 11.3 Zero-State Response of RC Circuits for Various Inputs
      • 11.3.1 Impulse Response of First-Order RC Circuits
      • 11.3.2 Step Response of First-Order RC Circuits
      • 11.3.3 Ramp Response of Series RC Circuit
      • 11.3.4 Series RC Circuit with Real Exponential Input
      • 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 Frequency Response of First Order RC Circuits
      • 11.5.1 The Use of Frequency Response
      • 11.5.2 Frequency Response and Linear Distortion
      • 11.5.3 First-Order RC Circuits as Averaging Circuits
      • 11.5.4 Capacitor as a Signal Coupling Element
      • 11.5.5 Parallel RC Circuit for Signal Byassing
    • 11.6 Summary
    • 11.7 Problems
  • Chapter 12 : Series and Parallel RLC Circuits
    • 12.1 The Series RLC Circuit – Zero-Input Response
      • 12.1.1 Source-Free Response of Series RLC Circuit
    • 12.2 The Series LC Circuit – A Special Cas e
    • 12.3 The Series LC Circuit with Small Damping – Another Special Case
    • 12.4 Standard Formats for Second-Order Circuit Zero-Input Response
    • 12.5 Impulse Response of Series RLC Circuit
    • 12.6 Step Response of Series RLC Circuit
    • 12.7 Standard Time-Domain Specifications for Second-Order Circuits
    • 12.8 Examples on Impulse and Step Response of Series RLC Circuits
    • 12.9 Frequency Response of Series RLC Circuit
      • 12.9.1 Sinusoidal Forced-Response from Differential Equation
      • 12.9.2 Frequency Response from Phasor Equivalent Circuit
    • 12.10 Resonance in Series RLC Circuit
      • 12.10.1 The Voltage Across Resistor – The Band-pass Output
      • 12.10.2 The Voltage Across Capacitor – The Low-pass Output
      • 12.10.3 The Voltage Across Inductor – The High-Pass Output
      • 12.10.4 Bandwidth Versus Quality Factor of Series RLC Circuit
      • 12.10.5 Quality Factor of Inductor and Capacitor
      • 12.10.6 LC Circuit as an Averaging Filter
    • 12.11 The Parallel RLC Circuit
      • 12.11.1 Zero-Input Response and Zero-State Response of Parallel RLC Circuit
      • 12.11.2 Frequency Response of Parallel RLC Circuit
    • 12.12 Summary
    • 12.13 Problems
  • Chapter 13 : Analysis of Dynamic Circuits by Laplace Transforms
    • 13.1 Circuit Response to Complex Exponential Input
    • 13.2 Expansion of a Signal in terms of Complex Exponential Functions
      • 13.2.1 Interpretation of Laplace Transform
    • 13.3 Laplace Transforms of Some Common Right-Sided Functions
    • 13.4 The s-Domain System Function H(s)
    • 13.5 Poles and Zeros of System Function and Excitation Function
    • 13.6 Method of Partial Fractions for Inverting Laplace Transforms
    • 13.7 Some Theorems on Laplace Transforms
      • 13.7.1 Time-Shifting Theorem
      • 13.7.2 Frequency-Shifting Theorem
      • 13.7.3 Time-Differentiation Theorem
      • 13.7.4 Time-Integration Theorem
      • 13.7.5 s-Domain-Differentiation Theorem
      • 13.7.6 s-Domain-Integration Theorem
      • 13.7.7 Convolution Theorem
      • 13.7.8 Initial Value Theorem
      • 13.7.9 Final Value Theorem
    • 13.8 Solution of Differential Equations by Using Laplace Transforms
    • 13.9 The s-Domain Equivalent Circuit
      • 13.9.1 s-Domain Equivalents of Circuit Elements
      • 13.9.2 Is s-domain Equivalent Circuit Completely Equivalent to Original Circuit?
    • 13.10 Total Response of Circuits Using s-Domain Equivalent Circuit
    • 13.11 Network Functions and Pole-Zero Plots
      • 13.11.1 Driving-Point Functions and Transfer Functions
      • 13.11.2 The Three Interpretations for a Network Function H(s)
      • 13.11.3 Poles and Zeros of H(s) and Natural Frequencies of the Circuit
      • 13.11.4 Specifying a Network Function
    • 13.12 Impulse Response of Network Functions from Pole-Zero Plots
    • 13.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots
      • 13.13.1 Three Interpretations for H(jω)
      • 13.13.2 Frequency Response from Pole-Zero Plot
    • 13.14 Summary
    • 13.15 Problems
  • Chapter 14 : Magnetically Coupled Circuits
    • 14.1 The Mutual Inductance Element
      • 14.1.1 Why Should M12Be Equal to M21?
      • 14.1.2 Dot Polarity Convention
      • 14.1.3 Maximum Value of Mutual Inductance and Coupling Coefficient
    • 14.2 The Two-Winding Transformer
    • 14.3 The Perfectly Coupled Transformer and The Ideal Transformer
    • 14.4 Ideal Transformer and Impedance Matching
    • 14.5 Transformers in Single-Tuned and Double-Tuned Filters
      • 14.5.1 Single-Tuned Amplifier
      • 14.5.2 Double-Tuned Amplifier
    • 14.6 Analysis of Coupled Coils Using Laplace Transforms
      • 14.6.1 Input Impedance Function of a Two-Winding Transformer
      • 14.6.2 Transfer Function of a Two-Winding Transformer
    • 14.7 Flux Expulsion by a Shorted Coil
    • 14.8 Breaking the Primary Current in a Transformer
    • 14.9 Summary
    • 14.10 Problems
  • Index

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