Elegant Circuits: Simple Chaotic Oscillators

✍ Scribed by Julien Clinton Sprott, Wesley Joo-chen Thio

• Publisher: World Scientific Publishing
• Year: 2021
• Tongue: English
• Leaves: 357
• Category: Library

✦ Synopsis

Chaos is the study of the underlying determinism in the seemingly random phenomena that occur all around us. One of the best experimental demonstrations of chaos occurs in electrical circuits when the parameters are chosen carefully. We will show you how to construct such chaotic circuits for use in your own studies and demonstrations while teaching you the basics of chaos. This book should be of interest to researchers and hobbyists looking for a simple way to produce a chaotic signal. It should also be useful to students and their instructors as an engaging way to learn about chaotic dynamics and electronic circuits. The book assumes only an elementary knowledge of calculus and the ability to understand a schematic diagram and the components that it contains. You will get the most out of this book if you can construct the circuits for yourself. There is no substitute for the thrill and insight of seeing the output of a circuit you built unfold as the trajectory wanders in real time across your oscilloscope screen. A goal of this book is to inspire and delight as well as to teach.

✦ Table of Contents

Contents
Preface
1. Introduction
1.1 Electronic Oscillators
1.2 Relaxation Oscillators
1.3 van der Pol Oscillator
1.4 Sinusoidally Forced van der Pol Oscillator
1.5 Primer on Chaos
1.6 Basins of Attraction and Robustness
1.7 Early Chaotic Oscillators
1.8 Circuit Dynamical Equations
1.9 Theoretical Analysis
1.10 Parameter Scaling
1.11 Construction and Analysis
1.12 Circuit Elegance
2. Conventional Diode Circuits
2.1 Diode Characteristics
2.1.1 Ideal diode
2.1.2 PN junction diode at equilibrium
2.1.3 PN junction with an applied voltage
2.1.4 I-V characteristic of the PN junction
2.1.5 Capacitance of the PN junction
2.2 Forced Diode Resonator
2.3 Vilnius Oscillator
2.4 Banlue–Rattikarn Circuit
2.5 Banlue–Buncha Diode Circuit
2.6 Chaotic Wien Bridge Oscillator
2.7 Elwakil–Kennedy Diode Oscillator
2.8 Saito Family Diode Circuit
2.9 Diode Jerk Circuit
3. Transistor Circuits
3.1 Transistor Characteristics
3.1.1 Bipolar junction transistor (BJT)
3.1.2 BJT I-V characteristic
3.1.3 Field effect transistor
3.1.4 FET I-V characteristic
3.2 Chaotic Colpitts Oscillator
3.3 Minati Circuit
3.4 Minati–Frasca Double-scroll Circuit
3.5 Minati–Frasca Spiking Circuit
3.6 Chaotic BJT Switch
3.7 Lindberg–Murali–Tamasevicius Circuit
3.8 Chaotic Hartley Oscillator
3.9 JFET-based Wien Bridge Oscillator
3.10 Chaotic MOS Amplier
4. Tunnel Diode Circuits
4.1 Tunnel Diode Junction
4.1.1 Tunnel diode I-V characteristic
4.1.2 Tunnel diode emulator
4.2 Forced Relaxation Oscillator
4.3 Autonomous Relaxation Oscillator
4.4 Chua Tunnel Diode Oscillator
4.5 Coupled Relaxation Oscillator
5. Thyristor Circuits
5.1 Thyristor Characteristics
5.1.1 Silicon controlled rectifier
5.1.2 Silicon bilateral switch
5.1.3 Thyristor I-V characteristic
5.2 Forced Thyristor Circuit
5.3 van der Pol Relaxation Oscillator
5.4 Autonomous Relaxation Oscillator
5.5 Coupled Relaxation Oscillators
5.6 Many Coupled Oscillators
5.7 Saito Family Thyristor Circuit
6. Saturating Amplifier Circuits
6.1 Operational Amplifiers
6.1.1 Operational amplifier transfer characteristic
6.1.2 Comparators
6.2 Saturating Wien Bridge Oscillator
6.3 Murali–Lakshmanan–Chua Circuit
6.4 Wang–Zhang–Bao Circuit
6.5 Coupled RC Circuits
6.6 Ketthong–Banlue Circuit
6.7 Saito Family Hysteresis Circuit
6.8 Saito Family Switch Circuit
6.9 Simplified Piper–Sprott Circuit
7. Analog Multiplier Circuits
7.1 Analog Multipliers
7.1.1 Analog computers
7.1.2 AD633 multiplier
7.2 Lorenz System
7.3 RŁossler Prototype-4 System
7.4 Original Ueda System
7.5 Simple Jerk System
7.6 Petrzela–Polak Circuit
7.7 Dissipative Nosé–Hoover System
7.8 Signum Thermostat
8. Nonlinear Inductor Circuits
8.1 Ferromagnetism
8.1.1 Magnetic properties of ferromagnets
8.1.2 Saturating inductor model
8.1.3 Ferrite-core inductor construction
8.1.4 Ferrite-core inductor measurement
8.2 Forced Ferroresonant Circuit
8.3 Saito Family Inductor Circuit
8.4 Minimal 3D Autonomous Inductor Circuit
9. Memristor Circuits
9.1 Memristors
9.1.1 Memristor I-V characteristic
9.1.2 Ag-chalcogenide memristor
9.1.3 Memristor measurement and model
9.2 Forced Memristor Circuit
9.3 Saito Family Memristor Circuit
9.4 Memristive Wien Bridge Oscillator
9.5 Elwakil–Kennedy Memristor Oscillator
9.6 Senani–Singh Memristor Oscillator
Bibliography
Index
About the Authors