Solution of a set of nonlinear algebraic equations for general-purpose CAD programs

A method is described for solving sets of nonlinear algebraic equations that arise in computer-aided circuit (CAD) programs in the steady-state mode of analysis. The method discriminates among different circuit elements in their contribution to the circuit equations. A logarithmic mapping is used on a subset of the correction vector involved in updating nonlinear current and voltage elements and their partial derivative contribution to the circuit equations. The values of nonlinear resistors, conductors, inductors, and capacitors are updated at every iterative step and then treated as though they were linear elements. However, in the steady-state mode, the values of capacitors and inductors are transformed into conductors and resistors, respectively. The values of these elements are made functions of the Newton iteration. The functional relation depends on the convergence behavior of the solution vector.