An efficient and globally convergent homotopy method for finding DC operating points of nonlinear circuits

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. 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. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, an improved version of the homotopy method is proposed that can find DC operating points of practical nonlinear circuits smoothly and efficiently. It is also shown that the proposed method can be easily implemented on SPICE without programming.