Chaotic Solitary Wavelets in 45nm CMOS Adaptive Bias Controlled Ring Oscillators

A novel kind of iterative map, the frequency dependent map, offering the crucial advantages of easy tunability and signal dependent control is formulated from the standard circle map, and is studied using the bifurcation and cobweb plots. Following this, the nonlinearity of a MOSFET is explored and a novel modification to a conventional ring oscillator is proposed by adding a potential divider in its feedback path, achieving adaptive bias control. It is seen that such a design gives outputs most closely resembling hyperbolic secant based solitons. The ring oscillators, nonlinearly coupled to a ‘split-gate’ CMOS inverter is seen to generate chaotic signals, which are characterized using standard measures such as phase portrait, Kolmogorov Entropy and Lyapunov Exponent, following which the effect of number of ring oscillator stages on the nature if generated chaos is studied. Finally, the chaotic signal is merged with a hyperbolic secant pulse to form a ‘chaotic solitary wavelet’, which is seen to possess a high number of vanishing moments with a distinct and unique negative logarithmic slope, a very desirable quality in wavelets, leading to applications such as secure communications, image compression and efficient detection of burst-type signals.