Classical Circuit Theory (eBook)

Preface 6
Contents 8
Introduction 14
1.1 A brief history 14
1.2 What drives circuit theory? 17
1.3 Scope of this book 18
1.4 Mathematical programming tools 19
1.5 Notable people in classical circuit theory 20
Fundamentals 23
2.1 Kirchhoff’s laws 23
2.2 Linear and nonlinear elements 24
2.3 Linear and nonlinear circuits 26
2.4 Small-signal equivalent circuits 27
2.5 Fundamental KVL equations 28
2.6 Fundamental KCL equations 31
2.7 Tellegen’s theorem 32
2.8 Energy in coupled inductors 33
2.9 Passive circuits 34
2.10 Modified node equations 35
2.11 Numerical solution 38
Problems 41
Circuit Dynamics 47
3.1 State equations 47
3.2 Independent state variables 50
3.3 Order of state equations 52
3.4 Formulation of state equations 52
3.5 Solution of state equations 56
3.6 Repeated eigenvalues 60
3.7 Symbolic solution 63
3.8 Numerical solution 64
3.9 Analog computer simulation 64
3.10 Exponential excitation 65
Problems 66
Properties in the Frequency Domain 71
4.1 Preliminaries 71
4.2 Modified node equations 72
4.3 Circuits with transconductances 73
4.4 Reciprocity 73
4.5 Impedance, admittance 74
4.6 Transfer function 78
4.7 Relation between real and imaginary parts 83
4.8 Gain and phase relation 86
4.9 Sensitivity function 88
4.10 Summary 94
Problems 95
The Impedance Function 101
5.1 Preliminaries 101
5.2 Positive real function 102
5.3 Properties of positive real function 104
5.4 Necessary and sufficient conditions 105
5.5 Useful theorems 106
5.6 Impedance removal 108
5.7 Remarks 108
Problems 109
Synthesis of Two-Element-Kind Impedances 111
6.1 LC impedance function 111
6.2 RC impedance function 117
6.3 RL impedance function 121
6.4 Remarks 122
Problems 124
Synthesis of RLC Impedances 127
7.1 Brune synthesis 127
7.2 Bott and Duffin synthesis 134
7.3 Miyata synthesis 139
7.4 General remarks 140
Problems 141
Scattering Matrix 143
8.1 Scattering matrix with resistive terminations 144
8.2 Scattering matrix with impedance terminations 151
8.3 Gain-bandwidth limitations of two-ports 157
8.4 Open-circuit impedance matrix 164
8.5 Short-circuit admittance matrix 167
Problems 168
Synthesis of Transfer Functions 175
9.1 The synthesis problem 175
9.2 Preliminaries 177
9.3 Input impedance and two-port parameters 178
9.4 Synthesis of two-port with imaginary transmission zeros 183
9.5 Brune section 191
9.6 Darlington C-section 194
9.7 Darlington D-section 197
9.8 Remarks 201
Problems 202
Filter Design 205
10.1 Filter functions 205
10.2 Maximally flat approximation 206
10.3 Chebyshev Filters 212
10.4 Elliptic filters 219
10.5 Remarks 237
10.6 Loss sensitivity of filters 239
10.7 Analog computer simulation of filters 244
10.8 Frequency transformation 245
Problems 250
Circuit Design by Optimization 255
11.1 Formulation of design problem 255
11.2 Solution strategy 257
11.3 Steepest descent 257
11.4 Newton’s method 260
11.5 Least squares method 261
11.6 Remarks 262
11.7 Computation of gradient and Hessian matrix 263
11.8 Examples of design by optimization 266
11.9 Remarks 269
Problems 270
All-Pass Circuits 273
12.1 Introduction 273
12.2 All-pass transfer function 273
12.3 Realizations of all-pass transfer functions 274
12.4 Lumped delay line 279
12.5 Wide-band 90° phase difference circuit 280
12.6 Delay Equalizer 290
12.7 Summary 293
Problems 294
Useful MATLAB functions 296
References 298
Index 301