A Globally Convergent Algorithm Using the Newton-Fixed-Point Homotopy for Finding DC Operating Points of Nonlinear Circuits

abstract In circuit simulation, many circuit designers experience difficulties in finding dc operating points of nonlinear circuits because the Newton-Raphson method often fails to converge unless the initial point is sufficiently close to the solution. To overcome this convergence problem, homotopy methods have been studied, and it has been proved that the homotopy methods are globally convergent for nonlinear circuit equations. Nowadays the homotopy methods are widely used in practical circuit simulation, and bipolar analog integrated circuits with more than 20,000 elements are solved efficiently with the theoretical guarantee of global convergence. In this paper, an efficient algorithm using a new homotopy function termed the Newton-fixed-point homotopy is proposed, and it is shown that this algorithm is more efficient than the conventional algorithms.