Global convergence of the newton fixed-point homotopy method for MOS transistor circuits

In circuit simulation, it is of great importance to compute DC operating points of nonlinear circuits. However, the Newton-Raphson method employed in some SPICE-like simulators often fails to obtain a solution. To solve the non-convergence problem, homotopy methods receive abundant attention and have been studied from various standpoints. As to homotopy methods, the convergence property is fundamentally important. However, the global convergence theorems and conditions of homotopy methods for MOS transistor circuits are still open problems. This paper presents the Newton fixed-point homotopy method (NFPH) for MOS transistor circuits and proves detailedly how to satisfy the uniqueness condition and the boundary free condition. Moreover, it is also proved that the MOS Newton fixed-point homotopy method is quite possible to converges to a stable operating point from any initial solution.