In this paper, a piecewise approximate analytical solution for transient circuits of a general nonlinear capacitor model characterized by a quintic polynomial voltage-charge dependence is presented. The method is based on a piecewise quadratic approximation of the transient circuit’s differential equation and its locally exact integration. The integration step size is determined according to the variation of the solution in the transient layer. The mesh selection strategy has the advantage of self selecting initial step size. The method results in an explicit analytical adaptive step size integration scheme. The accuracy and stability properties of the method are investigated and shown to yield at least third-order and L-stability property. Analytical and Simulink numerical solutions of two case-study problems are compared and showed that both solutions are in very good agreement.

piecewise Taylor approximation, locally exact integration, stability, nonlinear transient circuits.