A Homotopy Method Using a Nonlinear Auxiliary Function for Solving Transistor Circuits

Finding DC operating points of transistor circuits is a very important and difficult task. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. For efficiency of homotopy methods, it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. In this paper, a homotopy method for solving transistor circuits using a nonlinear auxiliary function is proposed. The proposed method utilizes the nonlinear function closely related to circuit equations to be solved, so that it efficiently finds DC operating points of practical transistor circuits. Numerical examples show that the proposed method is several times more efficient than conventional three homotopy methods.