Mathematical Physics

   

Frequency Dependent Chaos in a Single CMOS Inverter: Two Related Perspectives

Authors: Sai Venkatesh Balasubramanian

The generation of Chaos in Electronics has largely been implemented using the Chua circuits, where the initial conditions are described by system parameters such as resistors and capacitors. The present work provides a radical shift in approach by proposing signal based chaos generators. The essential design here is the coupling of two sinusoidal signal sources to a CMOS inverter circuit, which is seen to exhibit nonlinear behavior thanks to its transfer characteristics and non-quasi static behavior. The Standard Circle Map, ideally suited to describing nonlinear coupling of oscillations with competing frequencies is studied and a ‘frequency map’ is derived from it. The latter is studied using bifurcation and cobweb plots. A second perspective, the amplitude map is created by forming a difference equation using the CMOS inverter transfer function. This map is explored using the bifurcation plots and phase portraits. Finally, the proposed design is implemented experimentally and the generated chaotic output is validated using phase portraits and Fourier spectra. The effect of driving frequency on the output is characterized using Kolmogorov Entropy and Lyapunov Exponents, giving rise to the term ‘Frequency Dependent Chaos’. The fresh perspectives of a signal oriented chaos discussed in the present work exhibits the advantages of simple circuitry and easy tunability, and this forms the novelty of the present work.

Comments: 12 Pages.

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Submission history

[v1] 2015-10-28 20:31:46

Unique-IP document downloads: 340 times

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