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.>

We formulate the state equations for tme- and frequency-domain aalysis of switched-capacitor networks (SCN's) using charges associated with topologically identifiable structures in a network as network variables. The method effectively combines variable elimination to reduce matrix sizes with redundancy elimination to reduce memory requirements for many-phases SCN's. The frequency-domain analysis equations are formulated in such a way that computation can be done in a simple iterative manner akin to time-domain analysis but without using discrete Fourier transform. Two speed-up algorithms based on the proposed formulation for input and output sampling are presented.