A fixed-point homotopy method for solving modified nodal equations

Recently, the application of homotopy methods to practical circuit simulati on has been remarkably developed, and bipolar analog integrated circuits wi th more than 10000 elements are now solved efficiently by the homotopy meth ods, 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 usi ng 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 a re used in SPICE. In this paper, we propose a modified algorithm of the hom otopy method using the FP homotopy and prove that this algorithm is globall y convergent for the MN equations. We also show that the proposed algorithm converges to a stable operating point with high possibility from any initi al point.