A nonlinear homotopy method 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 globally convergent homotopy methods, it is important to construct an appropriate homotopy function. In conventional homotopy methods, linear auxiliary functions have been commonly used. A homotopy method using some nonlinear auxiliary function is proposed. The method utilizes a nonlinear function closely related to the circuit equations to be solved. Hence it efficiently finds the DC operating points of practical transistor circuits. Numerical examples show the effectiveness of the proposed algorithm.