Equivalent circuits for implicit Runge-Kutta methods in circuit simulators for nonlinear circuits

Abstract

This paper describes a method of implementing RadauIIA and LobattoIIIA of implicit Runge-Kutta formulas into circuit simulators for nonlinear circuits as numerical integration. These implicit Runge-Kutta methods have high orders and are A-stable. Equivalent circuits at discrete time for linear and nonlinear elements are proposed. Circuits at times between past and present time are needed in addition to the equivalent circuit at present time. Solutions at intermediate and present times must be estimated simultaneously. So, the size of equivalent circuit becomes larger than the numerical integration in conventional circuit simulators. However, since the orders of these algorithms are high, this problem is solved by using larger time step for numerical integration compared to conventional methods to save calculation time. The implicit Runge-Kutta and conventional methods are compared in terms of accuracy and computational costs using example circuits.