Symbolically-aided simulation of nonlinear passive components

This paper describes a symbolically-aided computational procedure for building algebraic companion form (ACF) models of nonlinear passive components for use in time-domain circuit simulators. This procedure is based on the automatic differentiation technique (ADT) and requires the computation of the sensitivity or Jacobian matrices as do many other implicit integration algorithms. The ADT is utilized for the effective computation of the required sensitivity matrices, which leads to significant savings of the CPU time compared to other commonly employed numerical differentiation techniques. To demonstrate its capabilities, ACF models of nonlinear passive components are built employing ADT and are used in practical power electronic circuits. Specifically, the effects of nonlinear capacitors and inductors in PWM inverter circuits are analyzed.