Chaotic Behavior in Simple Looped MOS Inverters

Cong-Kha PHAM  Mamoru TANAKA  Katsufusa SHONO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.3   pp.291-299
Publication Date: 1995/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Selected Papers from the 7th Karuizawa Workshop on Circuits and Systems)
Category: Nonlinear Problems
bifurcation,  chaos,  chaotic behavior,  sigmoid function,  inverter,  transfer characteristic,  nonlinear mapping function,  switched capacitor (SC),  CMOS switch,  hold capacitor,  

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In this paper, bifurcation and chaotic behavior which occur in simple looped MOS inverters with high speed operation are described. The most important point in this work is to change a nonlinear transfer characteristic of a MOS inverter to the nonlinearity generating a chaos. Three types of circuits which include four, three and one MOS inverters, respectively, are proposed. A switched capacitor (SC) circuit to operate sampling holding is added in the loop in each of the circuits. The bifurcation and chaotic behavior have been found along with a variation of an external input, and/or a sampling clock frequency. The bifurcation and chaotic behavior of the proposed simple looped MOS inverters are verified by employing SPICE circuit simulator as well as the experiments. For the first type of four looped CMOS inverters, Lyapunov exponent λ which has the positive regions for the chaotic behavior can be calculated by use of the fitting nonlinear function synthesized from two sigmoid functions. For the second type of three looped CMOS inverters and the third type of one looped MOS inverter, the nonlinear charge/discharge characteristics of the hold capacitor in the SC circuit is utilized efficiently for forming the nonlinearity generating the bifurcation and chaotic behavior. Their bifurcation can be generated by the sampling clock frequency parameter which is controlled easily.