Abstract
Fractional-order chaotic oscillators (FOCOs) have shown more complexity than integer-order chaotic ones. However, the majority of electronic implementations were performed using embedded systems; compared to analog implementations, they require huge hardware resources to approximate the solution of the fractional-order derivatives. In this manner, we propose the design of FOCOs using fractional-order integrators based on operational transconductance amplifiers (OTAs). The case study shows the implementation of FOCOs by cascading first-order OTA-based filters designed with complementary metal-oxide-semiconductor (CMOS) technology. The OTAs have programmable transconductance, and the robustness of the fractional-order integrator is verified by performing process, voltage and temperature variations as well as Monte Carlo analyses for a CMOS technology of 180 nm from the United Microelectronics Corporation. Finally, it is highlighted that post-layout simulations are in good agreement with the simulations of the mathematical model of the FOCO.
Highlights
It is well known that chaotic systems can occur in various natural and man-made systems, and are known to have great sensitivity to initial conditions
We show the complementary metal-oxide-semiconductor (CMOS) operational transconductance amplifiers (OTAs)-based design of a fractional-order integrator that is approximated by a Laplace transfer function, as shown in [1]
The second case study FOCO2 has three derivatives of fractional-order 0.9 [32], and its model is given in (5). It consists of three state variables—X (s), Y (s), and Z (s)—and a nonlinear function denoted by f ( x ) that can be approximated by saturated nonlinear function (SNLF) series
Summary
It is well known that chaotic systems can occur in various natural and man-made systems, and are known to have great sensitivity to initial conditions. A new category of fractional-order filters, realized without employing a fractional-order Laplacian operator, was introduced in [11], where the procedure resulted in a rational integer-order transfer function, and its implementation was possible, using conventional integer-order realization techniques This is the focus of this work, following the design of FOCOs by cascading active filters, as shown in [12]. The voltage level of opamp-based implementations of FOCOs can be scaled down to allow FPAA implementations [12] but still, the silicon area is huge In this manner, and as already demonstrated in [2], the CMOS operational transconductance amplifier (OTA) is helpful to reduce the silicon area when designing chaotic systems.
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