Elegant Circuits

The following sections are included:

• Dedication
• Preface
• Contents

This chapter contains the motivation and background for the book, a brief history of chaotic circuits, what we mean by a circuit being ‘elegant,’ and details that are common to all the circuits in the book, their construction, and their analysis. The subsequent chapters are organized according to the essential nonlinear component that is responsible for the chaos.

The diode is the simplest and most fundamental of the semiconductor devices. This chapter will describe ideal diodes and conventional silicon-based diodes. It will also describe some simple circuits using such diodes as the nonlinear component to generate chaos.

The transistor is the oldest three-terminal semiconductor device, and its development revolutionized the electronics industry. This chapter describes the device and shows how it can operate as an amplifier or as a switch to produce chaotic signals.

The tunnel diode is one of the most fascinating of the semiconductor devices, invented by Physics Nobel laureate (1973) Leo Esaki. This two-terminal device exploits quantum tunneling to produce a negative resistance and hysteresis, allowing it to be used as an active device in chaotic circuits.

The thyristor is a semiconductor switch that is often used to control high-voltage and high-current circuits. Since the thyristor exhibits hysteresis, it can also be used as the nonlinear element in a wide range of chaotic circuits, several elegant examples of which are shown in this chapter.

Previously, we used the operational amplifier in its linear region to amplify, buffer, or integrate a signal. However, this is insufficient to produce chaos unless a nonlinear device such as a diode is added or if the operational amplifier becomes nonlinear when it saturates. Here we briefly review the operational amplifier and show examples of chaotic circuits that rely solely on its saturation.

Perhaps the most versatile nonlinear device is the analog multiplier. Many standard chaotic systems involve polynomial nonlinearities and thus lend themselves to electronic implementation using such devices. This chapter gives a small selection of some of the most elegant examples of such systems and their corresponding circuits.

Although inductors are usually considered to be linear circuit components, they can behave in a very nonlinear manner when they use a ferromagnetic core. The previous circuits have largely avoided such nonlinearities, but they can be exploited to produce chaos, much like the circuits in Chapter 6 used the saturation of operational amplifiers for that purpose. This short chapter describes nonlinear inductors and gives three examples of circuits that employ them to produce chaos.

The memristor is a two-terminal device that can be programmed to change its resistance when a voltage is applied to it, whereupon it will either increase or decrease its resistance depending on the polarity of the voltage. If this voltage is removed, the memristor retains its resistance value, making it useful as a computer memory element that can implement neural network algorithms. In this chapter, we use the resistance switching properties of a real solid-state memristor for several chaotic circuits that previously used memristor emulators.

The following sections are included:

• Bibliography
• Index
• About the Authors