An equation for Generating Chaos and its monolithic Implementation

It is well known that chaotic signals are characterized by having a positive Lyapunov exponent and a noise-like power spectrum [Young, 1983]. These features have motivated researchers to investigate using chaotic signals in various applications and particularly in wide-band communication systems [Kolumbán et al., 1998; Setti et al., 1999]. In order to be compatible with other system elements, it is preferable to use chaotic oscillators that can be integrated on silicon. A number of attempts have been made to introduce discretetime as well as continuous-time CMOS chaotic oscillators. In most of these attempts, the resulting circuits were complicated and occupied a large silicon area. Discrete-time chaotic oscillators usually employ either switched-C or switched-current techniques. The utilization of a multiplier in addition to the many capacitors and op amps used in [Delgado-Restituto et al., 1992] automatically result in a large circuit. Meanwhile, CMOS continuous-time chaotic oscillators that are available in the literature are based on the classical Chua’s circuit oscillator. The designs proposed in [Cruz & Chua, 1993] and [Rodriguez-Vazquez & Delgado-Restituto, 1993] are copies of the architecture in [Kennedy, 1992] on silicon. In both designs, it can be clearly noticed that the involved nonlinear resistor, which is active and piecewiselinear, requires a considerable design effort that had to be done at a separate stage [Cruz & Chua, 1992]. The nonlinear resistor of [Cruz & Chua, 1992] has an area of 0.5 mm2 and requires dual ±9 V supplies; the complete Chua’s circuit [Cruz & Chua, 1993] has an area of 7 mm2. The design in [Rodriguez-Vazquez & Delgado-Restituto, 1993] is better in that it requires ±2.5 V supplies. A more