Pulse Modulation Techniques for Nonlinear Dynamical Systems and a CMOS Chaos Circuit with Arbitrary 1-D Maps

Takashi MORIE  Kenichi MURAKOSHI  Makoto NAGATA  Atsushi IWATA  

IEICE TRANSACTIONS on Electronics   Vol.E87-C   No.11   pp.1856-1862
Publication Date: 2004/11/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on New System Paradigms for Integrated Electronics)
CMOS analog integrated circuits,  nonlinear circuits,  nonlinear functions,  pulse width modulation,  pulse phase modulation,  chaos,  

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This paper presents circuit techniques using pulse-width and pulse-phase modulation (PWM/PPM) approaches for VLSI implementation of nonlinear dynamical systems. The proposed circuits implement discrete-time continuous-state dynamics by means of analog processing in a time domain, and also approximately implement continuous-time dynamics. Arbitrary nonlinear transformation functions are generated by the process in which a PPM signal samples a voltage or current source whose waveform in the time domain has the same shape as the desired transformation function. Because a shared arbitrary nonlinear voltage or current waveform generator can be constructed by digital circuits and D/A converters, high flexibility and real-time controllability are achieved. By using one of these new techniques, we have designed and fabricated a CMOS chaos circuit with arbitrary 1-D maps using a 0.6 µm CMOS process, and demonstrate from the experimental results that the new chaos circuit successfully generated various chaos with 7.5-7.8 bit precision by using logistic, tent and chaotic-neuron maps.