Acceleration plane method for analysis of a circuit with nonlinear inductance and nonlinear capacitance

Abstract

This paper analyses the transient behavior of a circuit with nonlinear resistance, inductance, and capacitance by the acceleration plane method developed recently by the author.1 The method as extended here is able to solve a nonlinear differential equation of the following type: ϕ(x)x + f(x, x) + f1(x) = F(t). Five examples are given, with F(t) equal to a constant or a time function. Either ϕ(x), f1(x, x), or f1(x) may be gven as a graph plotted from experimental data. The forcing function F(t) may be a sine wave or any time function. The method owes its simplicity to a close relation with physical boundary conditions. In one example, the phenomenon of ferroresonance is obtained. Also the possibility of applying the same method to a circuit with R(t), L(t), and C(t) is indicated.