Periodic steady-state solutions of nonlinear circuits based on a differentiation matrix

A discrete time-domain method suitable to compute stable, periodic steady-state solutions of nonlinear systems is presented in this paper. This approach applies a discrete-time representation of the differentiation operator, which estimates the exact derivative of a trigonometric polynomial. The set of ordinary differential equations that represents the dynamic behavior of the nonlinear problem is transformed into a nonlinear algebraic formulation and solved with a Newton algorithm. Furthermore, a direct method for solving sparse systems is incorporated in the Newton method to improve its efficiency in both storage and time. Two test cases based on the Duffing circuit and a power supply illustrate the applicability and effectiveness of this method to determine periodic steady-state solutions. Comparative results are reported with the proposal presented in this work and the well-known finite-difference method.