Multistable Circuits Using Nonlinear Reactances

This paper presents some results in the asymmetric resonant circuit, which is constructed by applying a dc voltage
E_0
and a sinusoidal voltage
E_1 \sin {\omega}t
to a series resonant circuit containing a nonlinear capacitance. The circuit is analyzed using the Ritz-Galerkin method. Assuming that the first approximation for the charge
q
takes on the form
Q_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 voltage
E_0
upon the circuit is studied in particular, and an interesting phenomenon, called "residual jump phenomenon," may occur in the circuit only when
E_0
is 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.