Department of Physics and Astronomy University of Manchester
Contents
Preface page xi
List of symbols and abbreviations xvi
Part 1 Mathematical techniques
1.1 Trigonometry 3
1.2 Geometry 6
1.3 Series expansions 9
1.4 Logarithms 12
1.5 Exponentials 16
1.6 Vectors 19
1.7 Complex numbers 28
1.8 Differentiation 34
1.9 Integration 37
1.10 Equations and determinants 42
1.11 Fourier transforms 49
1.12 Laplace transforms 60
1.13 Differential equations 76
1.14 Convolution 87
Part 2 Physics
2.1 Current flow 93
2.2 Energies 97
2.3 Kirchhoff’s laws 101
2.4 Faraday’s law and Lenz’s law 104
2.5 Currents and fields 107
2.6 Magnetism and relativity 113
vii
2.7 Maxwell’s equations 119
2.8 Conductivity and the skin effect 125
2.9 Quantization 131
2.10 Dielectrics and permittivity 135
2.11 Magnetic materials 139
2.12 Units of electromagnetism 147
2.13 Noise 150
Part 3 Introduction to circuit mathematics
3.1 Circuit laws 159
3.2 A.C. theory 166
3.3 Phasors 173
3.4 Phase and amplitude 178
3.5 Resonance 183
3.6 Bandwidth and risetime 196
3.7 Pulse and transient response 206
3.8 Equivalent circuits 217
3.9 Cauchy’s dog bodes well 225
3.10 Feedback 230
3.11 Noise in circuits 241
3.12 Hysteresis 252
3.13 Bridges 259
3.14 Approximation 263
3.15 Control systems 271
3.16 Filters 278
3.17 Transmission lines 293
Part 4 Circuit elements
4.1 Resistors 307
4.2 Capacitors 312
4.3 Inductance 323
4.4 Transformers 331
4.5 Diodes 340
4.6 Bipolar transistors 349
4.7 Field effect transistors 357
viii Contents
4.8 Temperature dependent resistors 368
4.9 Coaxial cables 377
4.10 Crystals 383
Part 5 SPICE circuit applications
5.1 Absolute value circuit 393
5.2 Oscilloscope probes 398
5.3 Operational amplifier circuits 403
5.4 Rectifier circuits 422
5.5 Integrators 431
5.6 Differentiator 436
5.7 Two-phase oscillator 444
5.8 Wien-bridge oscillator 449
5.9 Current sources and mirrors 458
5.10 Power supplies 464
5.11 Current-feedback amplifiers 479
5.12 Fast operational picoammeter 488
5.13 Three-pole, single amplifier filter 505
5.14 Open-loop response 511
5.15 Lumped or distributed? 523
5.16 Immittance Through the Looking Glass: gyrators,
negative
immittance converters and frequency dependent negative resistors
527
5.17 Maser gain simulation 535
5.18 Frequency-independent phase shifter 539
5.19 Ratemeter 542
5.20 Baluns and high frequency transformers 545
5.21 Directional coupler 555
5.22 Power control or hotswitch 561
5.23 Modulation control of a resonant circuit 566
5.24 Photomultiplier gating circuit 571
5.25 Transatlantic telegraph cable 580
5.26 Chaos 588
5.27 Spice notes 598
Bibliography 615
Name index 621
Subject index 629
Part index 649
ix Contents
