Introduction to Linear Circuit Analysis and Modelling (eBook)

Front cover 1
Table of contents 6
Preface 
10 
Acknowledgements 
12 
1 Elementary electrical circuit analysis 
14 
1.1 Introduction 14
1.2 Voltage and current 14
1.2.1 Voltage sources 15
1.2.2 Current sources 16
1.3 Electrical passive elements 18
1.3.1 Resistance and conductance 18
1.3.2 Capacitance 21
1.3.3 Inductance 22
1.4 Kirchhoff's laws 23
1.4.1 Series and parallel combinations of passive elements 24
1.4.2 Other types of circuit element connections 30
1.4.3 Electrical network analysis - Nodal analysis 31
1.4.4 Resistive voltage and current dividers 33
1.4.5 Controlled sources 34
1.5 Thévenin's theorem 35
1.6 Norton's theorem 36
1.7 Super-position theorem 38
1.8 Bibliography 39
1.9 Problems 40
2 Complex numbers: An introduction 
45 
2.1 Introduction 45
2.2 Definition 45
2.3 Elementary algebra 47
2.3.1 Addition 47
2.3.2 Subtraction 47
2.3.3 Multiplication 48
2.3.4 Division 50
2.3.5 Complex equations 51
2.3.6 Quadratic equations 51
2.4 Polar representation 52
2.4.1 Multiplication and division 53
2.5 The exponential form 54
2.5.1 Trigonometric functions and the exponential form 55
2.6 Powers and roots 56
2.7 Bibliography 59
2.8 Problems 59
3 Frequency domain electrical signal and circuit analysis 
61 
3.1 Introduction 61
3.2 Sinusoidal AC electrical analysis 61
3.2.1 Effective electrical values 62
3.2.2 I-V characteristics for passive elements 63
3.2.3 Phasor analysis 67
3.2.4 The generalised impedance 69
3.2.5 Maximum power transfer 77
3.3 Generalised frequency domain analysis 78
3.3.1 The Fourier series 78
3.3.2 Fourier coefficients, phasors and line spectra 85
3.3.3 Electrical signal and circuit bandwidths 86
3.3.4 Linear distortion 92
3.3.5 Bode plots 93
3.3.6 The Fourier transform 101
3.3.7 Transfer function and impulse response 111
3.3.8 The convolution operation 113
3.4 Bibliography 119
3.5 Problems 119
4 Natural and forced responses ciruit analysis 
122 
4.1 Introduction 122
4.2 Time domain analysis 122
4.3 Transient analysis using Fourier transforms 126
4.3.1 Differentiation theorem 126
4.3.2 Integration theorem 127
4.3.3 I-V characteristics for passive elements 127
4.4 The Laplace transform 130
4.4.1 Theorems of the Laplace transform 132
4.4.2 Partial-fraction expansion 136
4.5 Analysis using Laplace transforms 140
4.5.1 Solving differential equations 140
4.5.2 I-V characteristics for passive elements 141
4.5.3 Natural response 143
4.5.4 Response to the step function 149
4.6 Bibliography 160
4.7 Problems 160
5 Electrical two-port network analysis 163
5.1 Introduction 163
5.2 Electrical representa-tions 163
5.2.1 Electrical impedance representation 163
5.2.2 Electrical admittance representation 166
5.2.3 Electrical chain representation 170
5.2.4 Conversion between electrical representations 172
5.2.5 Miller's theorem 174
5.3 Computer-aided electrical analysis 176
5.4 Bibliography 180
5.5 Problems 180
6 Basic electronic amplifier building blocks 182
6.1 Introduction 182
6.2 Modelling the amplification process 182
6.3 Operational amplifiers 190
6.3.1 Open-loop and feedback concepts 190
6.3.2 Other examples and applications 192
6.4 Active devices 196
6.4.1 The junction or p-n diode 196
6.4.2 The bipolar junction transistor 196
6.4.3 The insulated gate field-effect transistor 205
6.4.4 The common-emitter amplifier 209
6.4.5 The differential pair amplifier 228
6.5 Bibliography 234
6.6 Problems 234
7 RF circuit analysis techniques 237
7.1 Introduction 237
7.2 Lumped versus distributed 237
7.3 Electrical model for ideal transmission lines 240
7.3.1 Voltage Standing Wave Ratio - VSWR 247
7.3.2 The lambda=4 transformer 252
7.3.3 Lossy transmission lines 255
7.3.4 Microstrip transmission lines 260
7.4 Scattering parameters 261
7.4.1 S-parameters and power waves 267
7.4.2 Power waves and generalised S-parameters 271
7.4.3 Conversions between different two-port parameters 276
7.5 The Smith chart 277
7.5.1 The impedance and the reflection coefficient planes 277
7.5.2 Representation of impedances 279
7.5.3 Introduction to impedance matching 285
7.6 Bibliography 289
7.7 Problems 289
8 Noise in electronic circuits 292
8.1 Introduction 292
8.2 Random variables 292
8.2.1 Moments of a random variable 298
8.2.2 The characteristic function 301
8.2.3 The central limit theorem 303
8.2.4 Bivariate Gaussian distributions 306
8.3 Stochastic processes 308
8.3.1 Ensemble averages 308
8.3.2 Stationary random processes 309
8.3.3 Ergodic random processes 309
8.3.4 Power spectrum 311
8.3.5 Cross-power spectrum 314
8.3.6 Gaussian random processes 315
8.3.7 Filtered random signals 316
8.4 Noise in electronic circuits 318
8.4.1 Thermal noise 318
8.4.2 Electronic shot-noise 319
8.4.3 1/f noise 319
8.4.4 Noise models for passive devices 320
8.4.5 Noise models for active devices 321
8.4.6 The equivalent input noise sources 323
8.4.7 The noise figure 332
8.5 Computer-aided noise modelling and analysis 336
8.5.1 Noise representations 336
8.5.2 Calculation of the correlation matrices 338
8.5.3 Elementary two-port interconnections 340
8.5.4 Transformation matrices 341
8.6 Bibliography 352
8.7 Problems 353
A Mathematical formulae for electrical engineering 355
Function definition 355
Fourier transform 356
Fourier transforms 357
Laplace transforms 358
Trigonometric identities 360
Series 360
Error functions 362
B Elementary matrix algebra 363
Definitions 363
C Two-port electrical parameters 365
Index 368