Artificial parameter homotopy methods for the dc operating point problem

Abstract

A new class of circuit simulation methods comprises a homotopy that is constructed by employing particular models of the nonlinear elements of the circuit and by including a randomizing component in the homotopy equation. In particular, the models of the non-linear elements are passive, in the sense that they contain no negative resistors and no voltage dependent sources. Also, the models are smooth enough to at least have well-defined first and second order derivatives. One such homotopy is (1-t)(Bx+a)+tF(x)=0, where B is a randomizing matrix and a is a randomizing vector, t is the continuation parameter, x is a vector of the circuit's node voltages, and F(x) is a set of equations such that F(x)=0 describes the circuit. Another is the homotopy (1-t)(F.sub.A (x)+a)+tF.sub.B (x)+.sigma.(t)(x-a) where F.sub.B (x)=0 describes the circuit whose dc operating point is sought, F.sub.A (x)=0 describes a circuit whose dc operating point is known, and .sigma.(t) is a function that is 0 at t=0 and t=1. The randomizing portion reduces the chances of a bifurcation occurring in the course of analysis to essentially zero.