A fixed-point homotopy method for solving modified nodal equations

Recently, the application of homotopy methods to practical circuit simulation has been remarkably developed, and bipolar analog integrated circuits with more than 10 000 elements are now solved efficiently by the homotopy methods. There are several approaches to applying the homotopy methods to large-scale circuit simulation. One of them is combining the publicly available software package of the homotopy methods (such as HOMPACK) with the general-purpose circuit simulators such as SPICE. However, the homotopy method using the fixed-point (FP) homotopy (that is provided as a default in HOMPACK) is not guaranteed to converge for the modified nodal (MN) equations that are used in SPICE. In this paper, we propose a modified algorithm of the homotopy method using the FP homotopy and prove that this algorithm is globally convergent for the MN equations. We also show that the proposed algorithm converges to a stable operating point with high possibility from any initial point.