Artificial parameter homotopy methods for the DC operating point problem

Efficient and robust computation of one or more of the operating points of a nonlinear circuit is a necessary first step in a circuit simulator. The application of globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation is discussed. The coercivity conditions required for such methods are established using concepts from circuit theory. The theoretical claims of global convergence for such methods are substantiated by experiments with a collection of examples that have proved difficult for commercial simulation packages that do not use homotopy methods. Moreover, by careful design of the homotopy equations, the performance of the homotopy methods can be made quite reasonable. An extension to the steady-state problem in the time domain is also discussed.