A fixed-point homotopy method for solving modified nodal equations

Kiyotaka Yamamura*, Tooru Sekiguchi, Yasuaki Inoue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)


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 largescale 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.

Original languageEnglish
Pages (from-to)654-665
Number of pages12
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Issue number6
Publication statusPublished - 1999
Externally publishedYes


  • Circuit simulation
  • DC operating point analysis
  • Global convergence
  • Homotopy method
  • Modified nodal equation
  • Stable operating point

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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