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

Finding the DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often falls 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 20,000 elements with the theoretical guarantee of global convergence. We propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method.