An Effective and Globally Convergent Newton Fixed-Point 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, the 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 a Newton fixed-point homotopy method for MOS transistor circuits and proposes an embedding algorithm in the implementation as well. Moreover, the global convergence theorems of the proposed Newton fixed-point homotopy method for MOS transistor circuits are also proved. Numerical examples show that the efficiencies for finding DC operating points of MOS transistor circuits by the proposed MOS Newton fixed-point homotopy method with the two embedding types can be largely enhanced (can larger than 50%) comparing with the conventional MOS homotopy methods, especially for some large-scale MOS transistor circuits which can not be easily solved by the SPICE3 and HSPICE simulators.