A globally convergent and highly efficient homotopy method for MOS transistor circuits

Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. However, most previous studies are mainly focused on the bipolar transistor circuits. Also the efficiencies of the previous homotopy methods for MOS transistor circuits are not satisfactory. Therefore, finding a more efficient homotopy method for MOS transistor circuits becomes necessary and important. This paper proposes the Newton Fixed-Point homotopy method for MOS transistor circuits and also proposes the embedding algorithm in the implementation. Numerical examples show that the proposed MOS Newton Fixed-Point homotopy methods with two embedding types are more effective for finding DC operating points of MOS transistor circuits than the conventional MOS homotopy methods. Moreover, the global convergence of the proposed Newton Fixed-Point homotopy method for MOS transistor circuits has also been proved.