Frequency behavior of saturated nonlinear function series based on opamps

Abstract

In multiscroll chaotic circuit design based on active devices, piece-wise linear (PWL) approaches are often used to model the behavior of nonlinear functions, thereby that the behavior of a chaotic system can be forecasted through numerical simulations. However, although PWL models are relatively easy to build, they do not include any information related on the performance parameters of the active devices to be used. This a serious shortcoming, since PWL-models introduces a level of inaccuracy into a numerical analysis which is more evident when numerical simulations and experimental results are compared. These differences are more pronounced when the chaotic waveforms to be generated are pushed to operate at high-frequency. This paper introduces experimental results on the frequency behavior of a nonlinear function called saturated nonlinear function series based on operational amplifiers. These new results are key not only on the automatic synthesis of chaotic attractors and on the synchronization schemes used in secure communication systems based on chaos, but also on the metrics used to evaluate the complexity of a chaotic system. A mathematical model to characterize the behavior of the nonlinear function is also derived, showing a better accuracy compared with the PWL approach. The theoretical derivations and related results are experimentally validated through implementations from commercially available devices.