Optimization and CMOS design of chaotic oscillators robust to PVT variations: INVITED

Edward Lorenz was an early pioneer of the chaos theory. He discovered that small changes in initial conditions produce large changes in long-term outcome, and introduced a chaotic attractor already known as Lorenz chaotic oscillator, which produces a butterfly-like behavior. This and all kinds of continuous-time chaotic oscillators can be simulated with different numerical methods. However, a bad choice of the step size and/or parameters of the mathematical models can produce errors or even mitigate the chaotic behavior. These issues are related to the main property of chaotic oscillators, the high sensitivity to the initial conditions, which is quantified by evaluating the maximum Lyapunov exponent (MLE). The Lorenz and other representative oscillators like Lü, Chua's circuit and Rössler have been implemented using different discrete electronic devices and few ones with integrated circuits (IC) using CMOS technologies. Designing CMOS chaotic oscillators is challenging because a very small variation in their parameters from their mathematical models or in the sizes of the MOS transistors may suppress the chaotic behavior. This article describes how to perform a successful simulation and optimization, and how to synthesize the mathematical models using CMOS technology. The application of metaheuristics to optimize MLE by varying the parameters of the oscillators, and the optimization of the CMOS IC design to guarantee robustness to process, voltage and temperature (PVT) variations, are discussed. Finally, we discuss issues on the application of chaos generators in random number generators, robotics and chaotic secure communication systems.