Multistable Circuits Using Nonlinear Reactances

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Abstract
This paper presents some results in the asymmetric resonant circuit, which is constructed by applying a dc voltageE_0and a sinusoidal voltageE_1 \sin {\omega}tto a series resonant circuit containing a nonlinear capacitance. The circuit is analyzed using the Ritz-Galerkin method. Assuming that the first approximation for the chargeqtakes on the formQ_0 + Q_1 sin({\omega}t + \theta), the curves\omega - Q_1,{E_1} - {Q_1}, and{E_0} - {Q_1}, are obtained. It is shown that the asymmetric circuit is a tristable circuit with respect to these parameters, while the usual ferroresonant circuit is a bistable circuit. The influence of the dc voltageE_0upon the circuit is studied in particular, and an interesting phenomenon, called "residual jump phenomenon," may occur in the circuit only whenE_0is changed and others fixed. Furthermore, the study shows how to construct a multistable circuit using nonlinear reactances. Combining some nonlinear reactances with suitable bias voltages, circuits having two, three, four or five stable solutions are obtained.

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