Analytical approximate solutions for a general nonlinear resistor–nonlinear capacitor circuit model

Abstract

In this paper, the analytical approximate solutions of a general RC circuit comprised of a nonlinear resistor in series with a nonlinear capacitor are addressed. In the studied circuit, the capacitor is characterized by a quintic polynomial voltage–charge dependence and the resistor obeys a cubic polynomial voltage–current relation. An efficient and easy-to-implement algorithm based on a hybrid analytical–numerical mathematical technique, namely the multistage Adomian decomposition method (MADM) is applied for solving the nonlinear differential equation governing the circuit performance. It is shown that the classic Adomian decomposition method fails to provide accurate convergent solutions for the posed problem over the whole semi-infinite time domain; however, the MADM can easily achieve convenient solutions with any desired degree of accuracy for both the transient and steady state time zones by exploiting its two embedded precision adjustment parameters. For the sake of illustration, two relevant numerical examples are solved by the MADM and simulated by the MATLAB–Simulink, as well. The results by the MADM are evaluated as highly accurate, based on comparison. In addition to the circuit theory aspects, the present work might be of particular interest from a practical point of view as the quintic nonlinear capacitor typically represents the widely used ferroelectric ceramic capacitors.