Linear and Nonlinear Circuits

Cover......Page 0000_0001.djvu
Title......Page 0002_0001.djvu
CONTENTS......Page 0006_0001.djvu
Preface......Page 0016_0001.djvu
1 The Discipline of Circuit Theory......Page 0020_0001.djvu
2 Lumped-Circuit Approximation......Page 0021_0001.djvu
3 Electric Circuits. Models. and Circuit Elements......Page 0023_0001.djvu
4.1 Reference Directions......Page 0025_0001.djvu
4.2 Kirchhoff\'s Voltage Law (KVL)......Page 0026_0001.djvu
4.3 Kirchhoff\'s Current Law (KCL)......Page 0029_0001.djvu
5 From Circuits to Graphs......Page 0031_0001.djvu
5.1 The Element Graph: Branch Currents, Branch Voltages. and the Associated Reference Directions......Page 0032_0001.djvu
5.2 The Circuit Graph: Digraph......Page 0035_0001.djvu
5.3 Two-Ports Multiports and Hinged Graphs......Page 0037_0001.djvu
5.4 Cut Sets and KCL......Page 0040_0001.djvu
6.1 Linear Independence......Page 0042_0001.djvu
6.2 Independent KCL Equations......Page 0043_0001.djvu
6.3 Independent KVL Equations......Page 0045_0001.djvu
7.1 Theorem, Proof, and Remarks......Page 0046_0001.djvu
7.2 Tellegen\'s Theorem and Conservation of Energy......Page 0048_0001.djvu
7.3 The Relation between Kirchhoff\'s Laws and Tellegen\'s Theorem......Page 0049_0001.djvu
7.4 Geometric Interpretation......Page 0050_0001.djvu
Summary......Page 0053_0001.djvu
2 Two-Terminal Resistors......Page 0064_0001.djvu
1.l From binear Resistor to Resistor......Page 0065_0001.djvu
1.2 The Nonlinear Resistor......Page 0069_0001.djvu
1.3 Independent Sources......Page 0075_0001.djvu
1.4 Time-Invariant and Time-Varying Resistors......Page 0078_0001.djvu
2 Series and Parallel Connections......Page 0080_0001.djvu
2.1 Series Connection of Resistors......Page 0081_0001.djvu
2.2 Parallel Connection of Resistors......Page 0086_0001.djvu
2.3 Series-Parallel Connection of Resistors......Page 0092_0001.djvu
3 Piecewise-linear Techniques......Page 0095_0001.djvu
3.1 The Concave and Convex Resistors......Page 0097_0001.djvu
3.2 Approximation and Synthesis......Page 0099_0001.djvu
4 dc Operating Points......Page 0102_0001.djvu
5 Small-Signal Analysis......Page 0111_0001.djvu
6 Transfer Characteristics......Page 0115_0001.djvu
Summary......Page 0119_0001.djvu
3 Multiterminal Resistors......Page 0135_0001.djvu
1 Resistive Two-Ports......Page 0136_0001.djvu
1.1 A Linear Resistive Two Port Example......Page 0137_0001.djvu
1.2 Six Representations......Page 0138_0001.djvu
1.3 Physical Interpretations......Page 0140_0001.djvu
2.1 Linear Controlled Sources......Page 0145_0001.djvu
2.2 Ideal Transformer......Page 0149_0001.djvu
2.3 Gyrator......Page 0151_0001.djvu
3 Nonlinear Resistive Two-Ports......Page 0152_0001.djvu
4.1 v-i Characteristics and Modeling......Page 0156_0001.djvu
4.2 dc Operating Points and Double Load Lines......Page 0161_0001.djvu
4.3 Small-Signal Analysis......Page 0164_0001.djvu
5 The MOS Transistor and the Basic Inverter......Page 0169_0001.djvu
6.1 The Three-Port Ideal Transformer......Page 0174_0001.djvu
6.2 The Three-Port Circulator......Page 0175_0001.djvu
6.3 Analog Multiplier......Page 0177_0001.djvu
Summary......Page 0178_0001.djvu
1 Device Description, Characteristics, and Model......Page 0190_0001.djvu
2.1 Virtual Short Circuits......Page 0196_0001.djvu
A Voltage Follower (Buffer)......Page 0197_0001.djvu
B Inverting Amplifier......Page 0198_0001.djvu
C Noninverting Amplifier......Page 0199_0001.djvu
D Resistance Measurement without Surgery......Page 0200_0001.djvu
E Nonlinear Feedback......Page 0201_0001.djvu
2.3 Systematic Method......Page 0203_0001.djvu
3.1 + Saturation and - Saturation Equivalent Circuits......Page 0206_0001.djvu
A Comparator (Threshold Detector)......Page 0207_0001.djvu
B Negative vs. Positive Feedback Circuit......Page 0209_0001.djvu
C Negative-Resistive Converter......Page 0211_0001.djvu
D Concave and Convex Resistors......Page 0214_0001.djvu
3.3 Systematic Method......Page 0218_0001.djvu
4 Comparison with Finite-Gain model......Page 0219_0001.djvu
Summary......Page 0221_0001.djvu
5 General Resistive Circuits......Page 0232_0001.djvu
1 Node Analysis for Resistive Circuits......Page 0233_0001.djvu
1.1 Node Equation Formulation: Linear Resistive Circuits......Page 0234_0001.djvu
1.2 Linear Circuits Containing Two-Terminal Resistors and Independent Sources......Page 0240_0001.djvu
1.3 Existence and Uniqueness of Solution......Page 0241_0001.djvu
1.4 Node Equation Formulation: Nonlinear Resistive Circuits......Page 0242_0001.djvu
2 Tableau Analysis for Resistive Circuits......Page 0244_0001.djvu
2.1 Tableau Equation Formulation: Linear Resistive Circuits......Page 0245_0001.djvu
2.2 Tableau Equation Formulation: Nonlinear Resistive Circuits......Page 0249_0001.djvu
3 Computer-Aided Solution of Nonlinear Algebraic Equations......Page 0251_0001.djvu
3.1 The Newton-Raphson Algorithm......Page 0252_0001.djvu
3.2 Newton-Raphson Discrete Equivalent Circuit......Page 0255_0001.djvu
4 General Properties of Linear Resistive Circuits......Page 0262_0001.djvu
4.l Superposition Theorem......Page 0263_0001.djvu
4.2 The Thévenin-Norton Theorem......Page 0270_0001.djvu
4.3 Two-Port Representation Theorem......Page 0278_0001.djvu
5 General Properties of Nonlinear Resistive Circuits......Page 0285_0001.djvu
5.1 Substitution Theorem......Page 0286_0001.djvu
5.2 Loop-Cut-Set Exclusion Property......Page 0288_0001.djvu
5.3 Consequences of Strict Passivity......Page 0290_0001.djvu
5.4 Consequences of Strict Monotonicity......Page 0295_0001.djvu
Summary......Page 0298_0001.djvu
1 Two-Terminal Capacitors and Inductors......Page 0314_0001.djvu
1.1 q-v and phi-i Characteristics......Page 0316_0001.djvu
1.2 Time-Varying Capacitors and Inductors......Page 0322_0001.djvu
2.1 Memory Property......Page 0325_0001.djvu
2.2 Continuity Property......Page 0328_0001.djvu
2.3 Lossless Property......Page 0331_0001.djvu
2.4 Energy Stored in a Linear Time-Invariant Capacitor or Inductor......Page 0335_0001.djvu
2.5 Energy Stored in a Nonlinear Time-Invariant Capacitor or Inductor......Page 0336_0001.djvu
3 First-Order Linear Circuits......Page 0339_0001.djvu
3.1 Circuits Driven by de Sources......Page 0340_0001.djvu
A Properties of Exponential Waveforms......Page 0341_0001.djvu
C Inspection Method (First-Order Linear Time-Invariant Circuits Driven by dc Sources)......Page 0346_0001.djvu
3.2 Circuits Driven by Piecewise-Constant Signals......Page 0348_0001.djvu
3.3 Linear Time-Invariant Circuits Driven by an Impulse......Page 0353_0001.djvu
3.4 Circuits Driven by Arbitrary Signals......Page 0355_0001.djvu
4 First-Order Linear Switching Circuits......Page 0358_0001.djvu
5 First-Order Piecewise-Linear Circuits......Page 0359_0001.djvu
5.1 The Dvnamic Route......Page 0360_0001.djvu
5.2 Jump Phenomenon and Relaxation Oscillation......Page 0363_0001.djvu
5.3 Triggering a Bistable Circuit (Flip-Flop)......Page 0366_0001.djvu
Summary......Page 0369_0001.djvu
7 Second-Order Circuits......Page 0382_0001.djvu
1.1 Two Standard Forms etc.......Page 0383_0001.djvu
1.2 State Equation and State Variables......Page 0387_0001.djvu
A Two-Capacitor Configuration......Page 0390_0001.djvu
C Capacitor-Inductor Configuration......Page 0392_0001.djvu
2 Zero-Input Response......Page 0393_0001.djvu
2.1 Determining Zero-Input Response from etc.......Page 0394_0001.djvu
B Physical Interpretation via Parallel RLC Circuits......Page 0397_0001.djvu
C Quality Factor......Page 0400_0001.djvu
2.2 Determining Zero-Input Response from etc.......Page 0402_0001.djvu
3 Qualitative Behavior of x\' = Ax......Page 0405_0001.djvu
3.1 Two Distinct Real Eigenvalues etc.......Page 0407_0001.djvu
A Stable Node: Two Real Negative Eigenvalues etc.......Page 0408_0001.djvu
B Unstable Node: Two Real Positive Eigenvalues etc.......Page 0409_0001.djvu
C Saddle Point: One Negative and One Positive Eigenvalue etc.......Page 0410_0001.djvu
3.2 Two Complex-Conjugate Eigenvalues etc.......Page 0411_0001.djvu
A Center: Two Imaginary Eigenvalues etc.......Page 0412_0001.djvu
B Stable Focus: Two Complex-Conjugate Eigenvalues with a Negative Real Part etc.......Page 0414_0001.djvu
C Unstable Focus: Two Complex-Conjugate Eigenvalues with a Positive Real Part etc.......Page 0415_0001.djvu
3.3 Summary of Equilibrium State Classification......Page 0416_0001.djvu
4 Nonlinear State Equation Formulation......Page 0418_0001.djvu
4.l Tunnel Diode and Josephson Junction Circuits......Page 0419_0001.djvu
4.2 How to Write Nonlinear State Equations......Page 0421_0001.djvu
5 Qualitative Behavior of x\' = f(x)......Page 0426_0001.djvu
5.1 Phase Portrait......Page 0428_0001.djvu
5.2 Equilibrium States and Operating Points......Page 0436_0001.djvu
5.3 Qualitative Behavior Near Equilibrium States......Page 0440_0001.djvu
6 Nonlinear Oscillation......Page 0444_0001.djvu
6.1 Basic Negative-Resistance Oscillator......Page 0445_0001.djvu
6.2 Physical Mechanisms for Oscillation......Page 0447_0001.djvu
A Linear Oscillator......Page 0450_0001.djvu
B Van der Pol Oscillator......Page 0451_0001.djvu
C Jump Phenomenon Revisited......Page 0455_0001.djvu
Summary......Page 0458_0001.djvu
8 General Dynamic Circuits......Page 0472_0001.djvu
A Characterization......Page 0473_0001.djvu
B Stored Energy......Page 0475_0001.djvu
C Sign of M......Page 0477_0001.djvu
D More Than Two Inductors......Page 0478_0001.djvu
E Relation with Ideal Transformers......Page 0479_0001.djvu
1.2 Nonlinear Time-Invariant Coupled Inductors......Page 0480_0001.djvu
A Linear Time-Invariant Circuits......Page 0481_0001.djvu
B Linear Time-Varying Circuit......Page 0483_0001.djvu
2.2 Nonlinear Dynamic Circuits......Page 0485_0001.djvu
3 Modified Node Analysis......Page 0487_0001.djvu
4 Small-Signal Analysis......Page 0491_0001.djvu
5 General Properties of Dynamic Circuits......Page 0500_0001.djvu
5.1 Superposition Theorem for Linear Dynamic Circuits......Page 0501_0001.djvu
5.2 Substitution Theorem for Dynamic Circuits......Page 0505_0001.djvu
6 Numerical Solution of Circuit Equations......Page 0507_0001.djvu
6.1 The Forward Euler Method......Page 0508_0001.djvu
6.2 The Backward Euler Method......Page 0510_0001.djvu
6.3 The Backward Euler Method Applied to Circuit Equations......Page 0512_0001.djvu
Summary......Page 0515_0001.djvu
Introduction......Page 0524_0001.djvu
0 Review of Complex Numbers......Page 0525_0001.djvu
Operations with Complex Numbers......Page 0526_0001.djvu
1.1 Sinusoids and Phasors......Page 0527_0001.djvu
1.2 Three Lemmas......Page 0528_0001.djvu
1.3 Example of Sinusoidal Steady-State Solution......Page 0531_0001.djvu
A Kirchhoff\'s Current Law: KCL......Page 0533_0001.djvu
B Kirchhoff\'s Voltage Law: KVL......Page 0534_0001.djvu
2.2 Branch Equations......Page 0535_0001.djvu
2.3 The Concept of Impedance and Admittance......Page 0536_0001.djvu
2.4 Tableau Equations......Page 0539_0001.djvu
A Analogy with Resistive Circuit Analysis......Page 0541_0001.djvu
B Example of Node Analysis in the Sinusoidal Steady State......Page 0542_0001.djvu
3.1 The Concept of Network Function......Page 0543_0001.djvu
3.2 Symmetry Property of Network Functions......Page 0547_0001.djvu
3.4 Superposition of Sinusoidal Steady State......Page 0550_0001.djvu
3.5 Impedance and Frequency Normalization......Page 0552_0001.djvu
4.1 Time-Domain Analysis......Page 0554_0001.djvu
B Beharior of Z(jw)......Page 0555_0001.djvu
C Circuit at Resonance......Page 0557_0001.djvu
D Behavior Near Resonance......Page 0559_0001.djvu
A Examples......Page 0561_0001.djvu
B Power into a One-Port......Page 0563_0001.djvu
A Definition......Page 0564_0001.djvu
B Conservation of Complex Power......Page 0565_0001.djvu
5.3 Maximum Power Transfer Theorem......Page 0566_0001.djvu
A Analysis......Page 0567_0001.djvu
B Conclusions......Page 0568_0001.djvu
5.4 Average Power Due to Several Sinusoidal Inputs......Page 0569_0001.djvu
5.5 Driving-Point Impedance, Stored Energy, and Dissipated Power......Page 0571_0001.djvu
6.1 General Considerations......Page 0573_0001.djvu
6.2 Elementary One-Phase Generator......Page 0574_0001.djvu
6.3 Elementary Three-Phase Generator......Page 0576_0001.djvu
6.4 Three-Phase Generator Under Balanced Load......Page 0578_0001.djvu
6.5 Analysis of a Balanced Three.Phase Circuit......Page 0579_0001.djvu
Summary......Page 0581_0001.djvu
Introduction......Page 0594_0001.djvu
1.1 Definition......Page 0595_0001.djvu
1.2 Two Important Examples......Page 0597_0001.djvu
2.2 Linearity Property......Page 0600_0001.djvu
A Property and Proof......Page 0602_0001.djvu
2.5 Laplace Transform Rules and Phasor Calculation Rules......Page 0604_0001.djvu
3.1 Reduction Step......Page 0607_0001.djvu
3.2 Simple Poles......Page 0608_0001.djvu
3.3 Multiple Poles......Page 0609_0001.djvu
3.4 Example: Circuit Analysis Using Laplace Transform......Page 0610_0001.djvu
A Laplace Transform of Kirchhoff\'s Laws......Page 0612_0001.djvu
C The Tableau Equations in the Frequency Domain......Page 0613_0001.djvu
D The Properties of Linear Time-Invariant Circuits......Page 0614_0001.djvu
4.2 Modified Node Analysis in the Frequency Domain......Page 0615_0001.djvu
A Characteristic Polynomial and Natural Frequencies......Page 0619_0001.djvu
B Physical Interpretation of Natural Frequencies......Page 0620_0001.djvu
C The Zero-Input Response......Page 0624_0001.djvu
4.4 Zero-State Response, Network Functions and Impulse Response......Page 0628_0001.djvu
A Network Functions......Page 0629_0001.djvu
B Remark on Cancellations......Page 0631_0001.djvu
C Impulse Response and Network Functions......Page 0632_0001.djvu
5 The Fundamental Theorem of the Sinusoidal Steady State......Page 0634_0001.djvu
A The Convolution Operation......Page 0638_0001.djvu
C Proof of Eq.(6.5) Based on Linearity and Time-lnvariance......Page 0639_0001.djvu
D Graphical Interpretation: Flip and Drag......Page 0642_0001.djvu
E Example......Page 0643_0001.djvu
6.2 The Convolution Theorem......Page 0645_0001.djvu
6.3 The Sinusoidal Steady State Analyzed by Convolution......Page 0646_0001.djvu
Summary......Page 0648_0001.djvu
1 Magnitude Phase and Pole Zeros......Page 0663_0001.djvu
A Analysis......Page 0664_0001.djvu
B Magnitude and Phase Curves......Page 0665_0001.djvu
C Bode Plots......Page 0667_0001.djvu
D Nyquist Plot of etc.......Page 0669_0001.djvu
E Step and Impulse Response of H(s) = etc.......Page 0670_0001.djvu
1.2 Second-Order Circuits......Page 0671_0001.djvu
1.3 General Case......Page 0674_0001.djvu
2 Zeros of Network Functions......Page 0677_0001.djvu
3 Nyquist Criterion......Page 0679_0001.djvu
3.1 Example......Page 0680_0001.djvu
3.2 Stability Analvsis......Page 0684_0001.djvu
3.3 Graphic Interpretation and the Key Theorem......Page 0686_0001.djvu
3.4 Nyquist Criterion......Page 0690_0001.djvu
3.5 The Nyquist Plot and Root Loci......Page 0692_0001.djvu
3.6 The Nyquist Criterion in Terms of the Bode Plot......Page 0694_0001.djvu
4 Open-Crcuit Stability and Short-Circuit Stability of One-Ports......Page 0696_0001.djvu
4.1 An Illustrative Example......Page 0697_0001.djvu
4.2 Short-Circuit Stability and Open-Circuit Stability Defined......Page 0698_0001.djvu
4.3 Remark on Polynomials......Page 0701_0001.djvu
A Analysis......Page 0702_0001.djvu
B Nyquist-Type Test Assuming ZI(S) Open-Circuit Stable......Page 0703_0001.djvu
Summary......Page 0705_0001.djvu
12 Circuit Topology and General Circuit Analysis......Page 0714_0001.djvu
1 Source Transformations......Page 0715_0001.djvu
1.1 The v -Shift Property......Page 0716_0001.djvu
1.2 The i -Shift Property......Page 0717_0001.djvu
2.1 KCL Equations Based on Cut Sets......Page 0719_0001.djvu
2.3 KVL Equations Based on Loops......Page 0721_0001.djvu
3.1 Tree......Page 0724_0001.djvu
3.2 The Fundamental Cut-Set Matrix Associated with a Tree......Page 0726_0001.djvu
3.3 The Fundamental Loop Matrix Associated with a Tree......Page 0729_0001.djvu
3.4 Relation between Q and B......Page 0733_0001.djvu
4 Tableau Analysis......Page 0734_0001.djvu
A Branch Equations......Page 0738_0001.djvu
B Cut-Set Equations......Page 0741_0001.djvu
5.2 Loop Analysis......Page 0743_0001.djvu
5.3 Mesh Analysis......Page 0745_0001.djvu
6 State Equations......Page 0746_0001.djvu
Summary......Page 0750_0001.djvu
13 Two-Ports, Multiports, and Reciprocity......Page 0759_0001.djvu
1.1 One-Port......Page 0761_0001.djvu
1.2 Two-Ports......Page 0763_0001.djvu
2 Linear Time-Invariant Two-Ports......Page 0765_0001.djvu
2.1 The Impedance and Admittance Matrices......Page 0766_0001.djvu
2.2 Hybrid Matrices......Page 0771_0001.djvu
2.3 The Transmission Matrices......Page 0773_0001.djvu
3.1 Terminated Two-Ports......Page 0775_0001.djvu
3.2 Interconnected Two-Ports......Page 0777_0001.djvu
4.1 n-Port Characterization......Page 0781_0001.djvu
4.2 The Indefinite Admittance Matrix......Page 0784_0001.djvu
5 The Soldering Iron Entry and Pliers Entry......Page 0789_0001.djvu
6 The Reciprocity Theorem......Page 0790_0001.djvu
Summary......Page 0798_0001.djvu
1 Simple Low-Pass Filter Design......Page 0809_0001.djvu
1.1 The Butterworth Approximation......Page 0810_0001.djvu
1.2 Synthesis of All-Pole Transfer Functions......Page 0814_0001.djvu
B Frequency Scaling......Page 0820_0001.djvu
C Impedance Scaling......Page 0821_0001.djvu
2 Sensitivity Analvsis......Page 0822_0001.djvu
A In Terms of Network Function Components......Page 0824_0001.djvu
B In Terms of the Node Admittance Matrix......Page 0827_0001.djvu
2.2 Calculating Sensitivity Via the Adjoint Equation......Page 0832_0001.djvu
A Physical Interpretation of the Adjoint Equation......Page 0833_0001.djvu
B Calculating ... in Terms of E and E*......Page 0834_0001.djvu
C LU Decomposition Method for Solving E and E*......Page 0837_0001.djvu
Summary......Page 0838_0001.djvu
A Symbols......Page 0845_0001.djvu
B Notation......Page 0847_0001.djvu
Index......Page 0850_0001.djvu