Introducing chaotic circuits in an undergraduate electronic course

For decades, the engineering undergraduate education in the area of circuit and design has been mainly focused in linear models. The reason is that linear system theory has been thoroughly developed and mathematical tools are available to analyze such systems. This philosophy has led to disregard many observed phenomena such as unusual complicated waveforms, commonly known as strange attractors. Therefore, it is important for today's students to be exposed to this complex chaos phenomenon. In this paper several chaotic circuits are presented. Electronics Workbench [1] is used to simulate circuits and show the presence of chaos. Complete circuits implementation and oscilloscope plots are all given. Introduction For decades, the engineering undergraduate education in the area of circuit and design has been mainly focused in linear models. The reason is that linear system theory has been thoroughly developed and mathematical tools are available to analyze such systems. This philosophy has led many scientists and experimentalists to disregard many observed phenomena because linear system theory cannot explain them. In the last decade, there is a strong interest in exploring systems that display unusual complicated waveforms, commonly known as strange attractors. These attractors have been increasingly observed in several nonlinear deterministic systems . Therefore, it is important for today's students to be exposed to these complex chaos phenomena. From the educational aspect, students need to learn not only how to control and avoid chaos but also how to design chaotic circuits and develop applications, which explore these phenomena. Realizing the educational value to introduce undergraduate students to the phenomena of chaos, Lonngren 1 describes an interesting electronics experiment to illustrate the existence of chaos. The described laboratory experiment with the accompanying theory is a good start for the student to grasp and understand chaos. As a continuation of this goal and to enhance the student understanding of chaos, Hamill 2 presented a collection of ten chaotic circuits simulated using PSpice. These circuits, some being quite simple, illustrate how chaos can be generated. 1 This work was supported by the Louisiana BORSF contract No. LEQSF(1999-2001)-RD-A-47 Proceedings of the 2002 ASEE Gulf-Southwest Annual Conference, The University of Louisiana at Lafayette, March 20-22, 2002. Copyright © 2002, American Society for Engineering Education In this paper, two chaotic circuits are presented for the student and the practicing engineer to study and experiment with. It is worthwhile to mention that one of the presented circuits, such as the Colpitts oscillator, is taught to students in electronics courses. Yet, there is no mention that chaotic behavior may occur. We have chosen to stay away from circuits that require a degree of mathematical sophistication beyond the undergraduate level. We have selected to use Electronics Workbench (EW) to simulate circuits since it provides an interface as close as to the real implementation environment. In addition, complete circuits implementation and oscilloscope graphical plots are all presented. It is our hope that this paper will raise many questions in the minds of students and practicing engineers. Example of autonomous chaotic circuit Colpitts oscillator: The first example is the Colpitts oscillator 10,11 shown in Fig. 1(a). Fig. 1(a). Colpitts oscillator. It is described by a system of three state equations: L L BE CE CC L B L BE EE BE C L CE R i V V V dt di L i i V V dt dV C i i dt dV C − + − = − − + − = − =