Fundamentals of Electronics 2

Pierre Muret, Emeritus Professor of Universitei Grenoble-Alpes (now honorary professor) & free researcher at Institut Neiel CNRS Grenoble, France

Preface ix

Introduction   xiii

Chapter 1. Continuous-time Systems: General Properties, Feedback, Stability, Oscillators  1

1.1. Representation of continuous time signals 2

1.1.1. Sinusoidal signals   2

1.1.2. Periodic signals    4

1.1.3. Non-periodic real signals and Fourier transforms  5

1.2. Representations of linear and stationary systems and circuits built with localized elements   8

1.2.1. Representation using ordinary differential equation 8

1.2.2. Periodic permanent conditions and harmonic conditions   10

1.2.3. Unilateral Laplace transform of causal systems and study of the various regimes 12

1.3. Negative feedback    25

1.3.1. Inversion of a transfer function  26

1.3.2. Linearization of a nonlinear system  27

1.3.3. Gain-bandwidth product for first-order low-pass systems   28

1.3.4. Simultaneous negative and positive feedback   29

1.4. Study of system stability   30

1.4.1. Time response: pole mapping   31

1.4.2. Nyquist criterion in general case   33

1.4.3. Stability of looped systems assumed stable in open loop: Nyquist and Bode criteria    35

1.4.4. Stability of linear and nonlinear networks of any order, analyzed from state variables   37

1.5. State space form 40

1.6. Oscillators and unstable systems   42

1.6.1. Sinusoidal oscillators   42

1.6.2. Relaxation oscillators using a nonlinear dipole and other resonant circuit oscillators   49

1.6.3. General case of systems comprising a nonlinear dipole and study of oscillation in phase space   52

1.7. Exercises   66

1.7.1. Response and stability of an operational amplifier not compensated until unity gain and loaded by a capacitor  66

1.7.2. Active filters built with operational amplifiers   69

1.7.3. Study of a looped system and its stability: sample and hold circuit  72

1.7.4. Study of a Colpitts oscillator built with a JFET  78

1.7.5. Study of a system in state-space form  80

Chapter 2. Continuous-time Linear Systems: Quadripoles, Filtering and Filter Synthesis   85

2.1. Quadripoles or two-port networks  85

2.1.1. Quadripoles deduced from dynamic circuits  86

2.1.2. Quadripoles and transfer matrices  87

2.1.3. Modification of the parameters of the quadripoles using negative feedback   89

2.1.4. Passive quadripoles    91

2.1.5. Dipole impedances and admittances; iterative impedance   92

2.1.6. Scattering matrix (or s-matrix) and transfer matrix  102

2.1.7. Powers in quadripoles and matching  107

2.1.8. Image-impedances and image-matching   118

2.1.9. Representation of quadripoles by block diagrams  124

2.2. Analog filters  126

2.2.1. Definition and impulse response   126

2.2.2. Properties of real, causal and stable filters   131

2.3. Synthesis of analog active filters using operational amplifiers   146

2.3.1. Cascading second-order cell filters  146

2.3.2. Multiple feedback loop cell   148

2.4. Non-dissipative filters synthesis methods  150

2.4.1. Synthesis based on effective parameters   151

2.4.2. Synthesis based on image parameters  166

2.4.3. Filter sensitivity and Orchard’s argument   195

2.5. Exercises   196

2.5.1. Impedance matching by means of passive two-port networks; application to class B push–pull power RF amplifier with MOS transistors    196

2.5.2. Passive low-pass filtering of an ideal voltage source by a two-port network built with an LC ladder (single-ended ladder filter)   204

2.5.3. Dual-ended passive filter, synthesized by the image impedance method 211

2.5.4. Lattice filter 214

Appendix   223

Bibliography   233

Index 235