Generic RC realizations of Chua's Circuit

Since its discovery, Chua’s circuit has served as the main prototype circuit for studying chaos in electronic systems [Matsumoto, 1984]. Several realizations of this circuit have been introduced in the literature [Cruz & Chua, 1992; Kennedy, 1992, 1995; Rodriguez-Vazquez & Delgado-Restituto, 1993; Zhong, 1994; Morgul, 1995; Elwakil & Kennedy, 1999a, 1999b, 2000]. These various implementations were concerned with two main design aspects of Chua’s circuit. The first aspect is the realization of the voltage-controlled nonlinear resistor [Cruz & Chua, 1992; Kennedy, 1992; Zhong, 1994; Elwakil & Kennedy, 1999b, 2000] and the second aspect is the removal of the inductor as it is generally difficult to integrate [RodriguezVazquez & Delgado-Restituto, 1993; Morgul, 1995; Elwakil & Kennedy, 1999a]. We have contributed to both of these research topics. In the case of the voltage-controlled nonlinear resistor, we have proposed a simple high performance realization based on the current-feedback op amp [Elwakil & Kennedy, 2000]. We then replaced this active nonlinearity by a simple diode [Elwakil & Kennedy, 1999b]. Of course, with the diode one cannot produce double-scroll dynamics, but can produce chaos with qualitative dynamics similar to those of the chaotic Colpitts oscillator [Kennedy, 1995]. Concerning the removal of the inductor, our approach was significantly different from the previous attempts [Rodriguez-Vazquez & Delgado-Restituto, 1993; Morgul, 1995] which were basically replacing the inductor by an RC circuit that emulates its function. Our approach was based on the conjecture proposed in [Elwakil & Kennedy, 1999a] which suggested that at the heart of any autonomous chaotic oscillator, there lies a core sinusoidal oscillator engine. Thus, instead of replacing the inductor alone one can in fact replace the entire active tank resonator (also known as the negative-resistance oscillator) which is the core engine of Chua’s circuit. Replacing this engine with any RC sinusoidal oscillator will automatically result in an inductorless Chua’s circuit. The significance of this approach lies in its ability to isolate the mechanism by which oscillations are produced. Hence, important features of the chaotic oscillator, such as its spectral bandwidth and the relationship between the values of particular circuit components, can be derived [Elwakil & Kennedy, 1999a]. Furthermore, oscillators based on different nonlinear resistor characteristics can be freely investigated.