Advances in Electronic Chaotic Oscillators with Applications in Communication Systems and Radar System

Abstract

Chaos theory is an emerging topic in electronics due to some of the inherent properties that can be considered advantageous in particular applications. Some of these properties include topological mixing, continuous power spectral density, and long-term aperiodic behavior. In particular, the topological mixing and long-term aperiodic behavior can be useful in generating random numbers for security or encryption applications. Similarly, the continuous power spectral density could be advantageous in communication and radar systems. Many of these systems are often defined mathematically using an ideal set of ordinary differential equations. These systems are usually classified as either autonomous or non-autonomous systems. An autonomous system is not explicitly dependent on any variable, where as a non-autonomous system is explicitly dependent on a variable. This variable is often a time dependency. These dependencies can lead to both systems being implemented in electronics with different types of challenges. An autonomous system might have an elegant mathematical solution or can be implemented in a single PCB, but often requires high component count in addition to dealing with finite switching times and propagation delays in the feedback path. These limitations can lead to difficulty in scaling the hardware realizations to higher frequency applications. A non-autonomous system may be somewhat difficult to find a closed-form solution to, but it can be realized in a variety of very simple electronic circuits. These simple circuits are externally excited, which can be a problem in some applications. This work investigates these challenges by designing, simulating, and implementing both autonomous and non-autonomous systems in hardware. Three different systems are presented here in this work. The first is an autonomous exactly solvable chaotic system with a second-order filter. The second is a similar autonomous exactly solvable chaotic system with a first-order filter. The third system is a non-autonomous nonlinear transistor circuit where the forcing function is integrated onto a single PCB.