Fundamentals of Modern Electric Circuit Analysis and Filter Synthesis: A Transfer Function Approach

Preface
Contents
Chapter 1: Introduction to Electric Circuits
	Introduction
	Electric Circuit Topologies
	Hinged Circuits
		Measurement Units
	Scales and Units
		Most Common Electric Circuit Symbols
	Problems
Chapter 2: Circuit Components, Voltage, and Current Laws
	Introduction
	Definition of Voltage
	Definition of Current
	Resistor
	Conductors, Insulators, and Semiconductors
	Effect of Temperature on Resistance
	Conductance
	Series Connection of Circuit Elements
	Parallel Connection of Circuit Elements
	Mixed Connection of Circuit Elements
		Mesh
		Node
	Ohm´s Law
	Kirchhoff Voltage Law (KVL)
	Kirchhoff Current Law (KCL)
	The Equivalent of Resistors in Series
	The Equivalent of Resistors in Parallel
	Delta (Δ) and Star (Y) Connection
		Y  Δ Conversion
		Δ  Y Conversion
	Power and Energy in Resistors
	Definition of a Short Circuit
	What Is an Inductor?
		Inductor´s Voltage and Current Relation
		Energy and Power of an Inductor
		The Equivalent of Inductors in Series
		The Equivalent of Inductors in Parallel
	What Is a Capacitor?
		Capacitor´s Voltage and Current Relation
		Energy and Power of a Capacitor
		The Equivalent of Capacitors in Series
		The Equivalent of Capacitors in Parallel
	Sources
		Independent Voltage Source
		Independent Current Source
		Dependent Sources
	Switches
	Mechanical Relays and Contactors
	Electrically Operated or Solid-State Switches
	Diode´s Peak Inverse Voltage (PIV)
	Diode Current Carrying Capacity and Operating Frequency
	Linear Time-Invariant Circuits
	Superposition in Circuits
	Problems
Chapter 3: Waveform and Source Analyses
	Introduction
	Waveform Analysis
		Impulse Function f(t) = δ(t)
		Unit Step Function f(t) = u(t)
		Ramp Function f(t) = r(t)
		Power Function
		Exponential Function f(t) = Aeαtu(t)
		Sinusoidal Function f(t) = A sin (ωt + φ)
		Polar to Cartesian (Rectangle) Conversion
		Cartesian (Rectangle) to Polar Conversion
		Mathematical Operation of Polar and Complex Numbers
			Adding Complex Numbers
			Product of Complex Numbers
			Product of Polar Numbers
			Division of Polar Numbers
			Summation of Polar Numbers
			Summation of Sinusoidal Functions
		Damped Sinusoidal Function
	Periodic Waveform Mathematical Expression
		Average of a Signal
		Root Mean Square (RMS)
	Circuit Simplification Techniques
		Voltage Division
		Current Division
		Source Conversion
	Thevenin Equivalent Circuit
	Norton Equivalent Circuit
	Norton and Thevenin Equivalent
	Power Calculations
		Consumption of Power
		Generation of Power
	Maximum Power Transfer to Load in Pure Resistive Circuits
	Problems
Chapter 4: Circuit Response Analysis
	Introduction
	Resistors
	Inductors
	Capacitors
	Order of a Circuit
		First-Order Circuits
			Natural Response: RL Circuits
			Natural Response: RC First-Order Circuit
			Forced Response of First-Order Circuits
			Step Response of RL Circuit
			Forced Response of First-Order RC Circuit
		Second-Order Circuits
			Natural Response of RLC Parallel Circuits
			Summary of RLC Parallel Circuit
			Natural Response of RLC Series Circuits
			Summary of RLC Series Circuit
	Problems
Chapter 5: Steady-State Sinusoidal Circuit Analysis
	Introduction
	How to Use Phasor in Circuit Analysis
	Circuit Response Stages
	Resistors in Steady State
	Power Factor of Resistive Circuits
	Inductors in Steady State
	Power Factor of Inductive Circuits
	Capacitors in Steady-State Sinusoidal
	Power Factor of Capacitive Circuits
	Resistive-Inductive Circuits
	Power Factor of Resistive-Inductive Circuits
	Vector Analysis of RL Circuits
	Resistive-Capacitive Circuits
	Using Admittance
	Using Impedance
	Power Factor of Resistive-Capacitive Circuits
	Vector Analysis of RC Circuits
	Steady-State Analysis of Circuits
	RLC Series
	RLC Parallel
	Resonance
	Power in Sinusoidal Steady-State Operation
	Apparent Power
	Active Power
	Reactive Power
	Reactive Power of an RC Circuit
	Nonideal Inductors
	Quality Factor (Qf)
	Nonideal Capacitors
	Model as RC Series
	Model as RC Parallel
	Dielectric Heating
	Thevenin Equivalent Circuits in Sinusoidal Steady State
	Norton Equivalent and Source Conversion
	Maximum Power Transfer
	Problem
Chapter 6: Mutual Inductance
	Introduction
	Self-Inductance and Mutual Inductance
	Induced Voltage
	Energy Stored in Coupled Circuits
	Limit of Mutual Inductance
	Turn Ratio
	Equivalent Circuit of Mutual Inductance
		T Equivalent Circuit
		Π Equivalent Circuit
	Ideal Mutual Inductance
	Ideal Transformer
	Problems
Chapter 7: Laplace Transform and Its Application in Circuits
	Introduction
	Mathematical Background
	Laplace of Unit Step Function
	Laplace of Impulse Function
	Laplace of Ramp Function
	Laplace of Exponential Function
	Laplace of Sinusoidal Function
	Laplace of Co-sinusoidal Function
	Laplace of Hyperbolic Sinusoidal Function
	Laplace of Hyperbolic Co-sinusoidal Function
	Laplace of Derivatives of Impulse
	Laplace of Differential Functions
	Laplace Operations
		Linear Combination of Functions
		Shift in Time
		Product by an Exponential
		Product by Time Factors
		Divide by Time Factors
	Complementary Laplace Inverse Techniques
		Long Division
		Partial Fraction Expansion
	Application of Laplace in Electric Circuits
		Resistors in Frequency Domain
		Inductors in Frequency Domain
		Capacitors in Frequency Domain
	Circuit Analysis Using Laplace Transform
	Problems
Chapter 8: Transfer Functions
	Definition of Transfer Function
	Multi-input-Multi-output Systems
	Obtaining Transfer Function of Electric Circuits
	Transfer Function Operations
	Parallel Connection
	Feedback Connection
	Feedback and Change of Order of Circuit
	Poles and Zeros
	Phase Plane
	Limit of Stability
	Initial Value and Final Value Theorems
	Order and Type of a System
		First-Order Systems
		Second-Order Systems
			Case 1. Oscillatory
			Case 2. Underdamped
			Case 3. Critically Damped
			Case 4. Overdamped
		Analysis of Step Response of Second-Order System
	The Effect of Controller on Type-Zero Systems
	Tracking Error Considering the Type and the Input as Reference Waveform
	Convolution Integral
	State Space Analysis
	Obtaining State-Space Equations from Differential Equations
	Obtaining a Block Diagram of a State-Space Equation
	Obtaining State-Space of Differential Equations that Involve Differential of the Input Signals
	Obtaining Transfer Function from State-Space Representation
	Bode Diagram
	Transfer Function Amplitude and Phase
	Bode Plot of A Transfer Function
	Problems
Chapter 9: Passive Filters
	Introduction
	Passive and Active Filters
		Category of Passive Filter Circuits
		Filter Gains
		Cutoff and Half-Power Point Frequencies
	Low-Pass Filter
		First-Order RL Low-Pass Filter
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
		First-Order RC Low-Pass Filter
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
		First-Order High-Pass Filter
			RL HPF
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
		First-Order RC High-Pass Filter
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
	Analysis of LC Circuits
		Parallel LC Circuit
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Parallel LC Circuit Using Laplace
		Series LC Circuit
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Series LC Circuit Using Laplace
		Summary of LC Series and Parallel Circuits
	Band-Pass Filters
		BPF Circuit 1: Using LC Series
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
		BPF Circuit 2: Using LC Parallel
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
	Band-Reject Filters
		BRF Circuit 1: LC Series
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequencies
		BRF Circuit 2: Using LC Parallel
			Identifying the Cutoff Frequency from the Ratio of the Output Over Input
			Using Laplace Transform to Find the Cutoff Frequency
		Summary of Filters in Laplace
	Higher-Order Filters
		Second-Order Low-Pass Filer
		Second-Order High-Pass Filer
		Higher-Order Filter by Repeated Circuits
			Repeated LPF
			Repeated HPF
			Repeated BPF
			Repeated BRF
	Butterworth Filters
		Butterworth Low-Pass Filter
		Butterworth Denominator Polynomials
		Butterworth High-Pass Filter
	Problems
		Low-Pass Filter
		Low-Pass Filter Using Laplace
		High-Pass Filter
		High-Pass Filter Using Laplace
		Series and Parallel LC Circuits
		Band-Pass Filters
		Band-Pass Filters Using Laplace
		Band-Reject Filters
		Band-Pass Filters Using Laplace
		Overall Filtration Process
		Butterworth Filters
		Higher-Order Filter
		Higher-Order Filter Using Laplace
Chapter 10: Operational Amplifiers
	Ideal Opamp
	Slew Rate
	Opamp in Circuits
	Mathematical Operations
		Adder
		Subtraction
		Integrator
		Differentiator
		Comparator
	Pulse Width Modulation (PWM)
	Unit Follower
	Function Builder
	Negative Immittance Converter
	Negative Impedance
	Negative Resistance (Fig. 10.27)
	Negative Capacitance (Fig. 10.28)
	Negative Inductance (Fig. 10.29)
	Gyrator
	Realization of a Gyrator in Circuits
	Problems
		Add and Subtract
		Differentiators
		Integrators
		Build Analog Computers
Chapter 11: Active Filters
	Introduction
	Active Low-Pass Filter
		Active Low-Pass Filters Using Feedback Impedance
		Active Low-Pass Filters Using Input Impedance
	Active High-Pass Filters
		Active High-Pass Filters Using Feedback Impedance
		Active High-Pass Filters Using Input Impedance
	Active Band-Pass Filters
		Active Band-Pass Filter Using a Combination of Low- and High-Pass Filters
		Transfer Function of a Band-Pass Filter
	Active Band-Reject Filters
	Multiple Feedback (MFB) Opamp Circuits
	Creating a Low-Pass Filter
	Creating a High-Pass Filter
	Creating a Band-Pass Filter
	Problems
Chapter 12: Two-Port Networks
	Introduction
	Impedance Matrix of a Two-Port Network
	The Equivalent of an Impedance Network
	Reciprocal Networks
		T Model
		Nonreciprocal Networks
		Separate Loop Model
		Element-Sharing Loops
	Alternative Approach in Impedance Matrix
	Finding Impedance Matrix in Multi-loop Networks
	Current and Voltage Considerations
	Finding the Matrix Dimension and Its Elements
	General Form of KVL Equations
	Matrix Size Reduction
	Impedance Matrix Existence
	Admittance Matrix of a Two-Port Network
	The Equivalent of Admittance Network
	Reciprocal Network
		Π Model
		Nonreciprocal Network
		Element-Sharing Nodes
	Alternative Approach in Admittance Matrix
	Finding Admittance Matrix in Multi-node Networks
	Current and Voltage Considerations
	Finding the Matrix Dimension and Its Elements
	General Form of KCL Equations
	Matrix Size Reduction
	Admittance to Impedance Conversion
	Admittance Matrix Existence
	Nonreciprocal Admittance Matrix
	Hybrid Parameters
	Inverse Hybrid Parameters
	Transmission Matrix Parameters
	Presenting the Transmission Matrix Parameters in Terms of Impedance and Admittance Matrices
	Parallel Connection of an Element
	Series Connection of an Element
	Transmission Matrix of Cascade Systems
	Finding Thevenin Equivalent Circuit from Transmission Matrix
	Problems
References
Index