Linear & NonLinear Circuits_ Basic & Advanced Concepts Volume 2

✍ Scribed by Mauro Parodi , Marco Storace

• Tongue: English
• Leaves: 520
• Series: Volume 2
• Category: Library

✦ Table of Contents

Preface
Contents
About the Authors
Acronyms
Part V Components with Memory and First-Order Dynamical Circuits
9 Basic Concepts: Two-Terminal Linear Elements with Memory and First-Order Linear Circuits
9.1 Two-Terminal Linear Elements with Memory
9.1.1 Capacitor
9.1.2 Inductor
9.2 Capacitor and Inductor Properties
9.2.1 Energetic Behavior
9.2.2 Gyrator and Two-Terminals with Memory
9.2.3 Series and Parallel Connections
9.3 State and State Variables
9.3.1 Wide-Sense and Strict-Sense State Variables
9.3.2 Circuit Models of Algebraic Constraints
9.3.3 State Variables Method
9.4 Solution of First-Order Linear Circuits with One WSV
9.4.1 General Solution of the State Equation
9.4.2 Free Response and Forced Response
9.4.3 Circuit Stability
9.5 Forced Response to Sinusoidal Inputs
9.5.1 Sinusoids and Phasors
9.5.2 Phasor-Based Method for Finding a Particular Integral
9.5.3 Multiple Periodic Inputs: Periodic and Quasiperiodic Waveforms
9.6 Generalized Functions (Basic Elements)
9.7 Discontinuity Balance
9.8 Response of Linear Circuits with One WSV and One SSV to Discontinuous Inputs
9.8.1 Step Response
9.8.2 Impulse Response
9.9 Convolution Integral
9.10 Circuit Response to More Complex Inputs
9.10.1 Multi-input Example
9.11 Normalizations
9.12 Solution for Nonstate Output Variables
9.13 Thévenin and Norton Equivalent Representations of a Charged Capacitor/Inductor
9.13.1 Charged Capacitor
9.13.2 Charged Inductor
9.14 First-Order Linear Circuits with Several WSVs
9.15 Problems
References
10 Advanced Concepts: First-Order Nonlinear Circuits
10.1 Asymptotic Solution of a Particular Class of First-Order Nonlinear Circuits
10.1.1 First-Order Circuits with More Than One WSV
10.1.2 Impossibility of Oscillations
10.1.3 Equilibrium Stability Analysis Through Linearization
10.2 Equilibrium Points and Potential Functions for First-Order Circuits
10.3 Analysis of First-Order Circuits with PWL Memoryless Components
10.3.1 Clamper
10.3.2 Half-Wave Rectifier
10.3.3 Hysteretic Circuit
10.3.4 Circuit Containing an Operational Amplifier
10.3.5 Circuit Containing a BJT
10.4 Bifurcations
10.4.1 Linear Case
10.4.2 Nonlinear Case
10.5 A Summarizing Example
10.5.1 Inverting Schmitt Trigger
10.5.2 Dimensionless Formulation
10.5.3 Analysis with Constant Input
10.5.4 Potential Functions
10.6 Problems
References
Part VI Second- and Higher-Order Dynamical Circuits
11 Basic Concepts: Linear Two-Ports with Memory and Higher-Order Linear Circuits
11.1 Coupled Inductors
11.2 Properties of Coupled Inductors
11.2.1 Series Connection
11.2.2 Passivity
11.2.3 Coupling Coefficient and Closely Coupled Inductors
11.2.4 Energy Conservation
11.2.5 Equivalent Models
11.2.6 Thévenin and Norton Equivalent Representations of Charged Coupled Inductors
11.3 Higher-Order Linear Circuits
11.3.1 General Method
11.3.2 Complementary Component Method and State Equations
11.3.3 State Equations in Canonical Form and I/O Relationships
11.4 Discontinuity Balance
11.5 Solution of the State Equations: Free Response and Forced Response
11.5.1 Free Response
11.5.2 Forced Response
11.6 Circuit Stability
11.7 Normalizations and Comparisons with Mechanical Systems
11.7.1 A Double Mass–Spring Chain and Its Circuit Model
11.8 Solution for Nonstate Output Variables
11.9 Response of LTI Dynamical Circuits to Discontinuous Inputs
11.10 Generic Periodic Inputs
11.10.1 Fourier Series
11.10.2 Some Supplementary Notes About Fourier Series
11.10.3 Mean Value of Circuit Variables
11.10.4 Root Mean Square Value
11.11 Multi-input Example
11.12 Problems
References
12 Advanced Concepts: Higher-Order Nonlinear Circuits—State Equations and Equilibrium Points
12.1 Nonlinear State Equations
12.1.1 Existence of the State Equation
12.2 Linear Autonomous Circuits Revisited
12.2.1 Second-Order Circuits
12.2.2 nth-Order Circuits
12.3 Nonlinear Dynamical Circuits: Assumptions and General Properties
12.4 Equilibrium Stability Analysis Through Linearization
12.5 Bifurcations
12.5.1 Fold Bifurcation of Equilibria
12.5.2 Hopf Bifurcation
12.6 Wien Bridge Oscillator
12.6.1 Normalized State Equations
12.6.2 Hopf Bifurcation of the Equilibrium Point
12.7 Colpitts Oscillator
12.7.1 Normalized State Equations
12.7.2 Hopf Bifurcation of the Equilibrium Point
12.8 Small-Signal Analysis
12.8.1 Relationship with the Supercritical Hopf Bifurcation
References
Part VII Analysis of Periodic Solutions
13 Basic Concepts: Analysis of LTI Circuits in Sinusoidal Steady State
13.1 Sinusoidal Steady State
13.2 Circuit Equations in Terms of Phasors
13.2.1 Topological Equations
13.2.2 Descriptive Equations
13.3 Impedance and Admittance of Two-Terminal Elements
13.3.1 Impedance
13.3.2 Admittance
13.3.3 Relation Between Impedance and Admittance of a Two-Terminal Component
13.3.4 Series and Parallel Connections of Two-Terminal Elements
13.3.5 Reciprocity
13.4 Thévenin and Norton Equivalent Representations of Two-Terminal Elements
13.5 Two-Port Matrices
13.6 Thévenin and Norton Equivalent Representations of Two-Port Elements
13.7 Sinusoidal Steady-State Power
13.7.1 Two-Terminal Components
13.7.2 Generic Components
13.8 Boucherot's Theorem
13.9 Power Factor Correction
13.9.1 Advantages for the Consumer
13.9.2 Advantages for the Utility Company and Motivation for High-Voltage Transmission Lines
13.10 Theorem on the Maximum Power Transfer
13.11 Frequency Response
13.11.1 Network Functions of a Circuit
13.11.2 Some Properties of the Network Functions
13.12 Resonant Circuits and the Q Factor
13.13 Problems
14 Advanced Concepts: Analysis of Nonlinear Oscillators
14.1 Periodic Solutions and (Limit) Cycles
14.2 Poincaré Section
14.3 Floquet Multipliers
14.4 Poincaré Map
14.5 Stability of Generic Invariant Sets: Lyapunov Exponents
14.5.1 Particular Cases
14.6 Bifurcations
14.6.1 Fold Bifurcation of Limit Cycles
14.6.2 Flip Bifurcation
14.6.3 Neimark–Sacker Bifurcation
14.6.4 Homoclinic Bifurcations
14.7 Hindmarsh–Rose Neural Oscillator
14.7.1 Analysis of Equilibrium Points
14.7.2 Analysis of Limit Cycles
14.7.3 Equivalent Circuit
14.8 Forced Oscillators
14.9 Networks of Coupled Oscillators
14.9.1 Example 1: 3-Cell Network
14.9.2 Example 2: 4-Cell Network
14.9.3 Example 3: 30-Cell Network
14.10 Summarizing Comments
References
Appendix A Complex Numbers
A.1 Imaginary Unit
A.2 Representations of Complex Numbers
A.2.1 Standard Form and Geometric Representation
A.2.2 Polar Form
A.2.3 A Particular Case
A.3 Some Elementary Operations
A.3.1 Complex Conjugate
A.3.2 Sum
A.3.3 Multiplication
Appendix B Synoptic Tables
B.1 Metric System Prefixes
B.2 Properties of the Main Memoryless Components
B.3 Reciprocity and Symmetry Conditions for Linear, Time-Invariant, and Memoryless Two-Ports
Appendix Solutions
Index