A practical approach for the fixed-point homotopy method using a solution-tracing circuit

Yasuaki Inoue*, Saeko Kusanobu, Kiyotaka Yamamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Finding DC operating-points of nonlinear circuits is an important and difficult task. The Newton-Raphson method employed in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixed-point homotopy method is one of the excellent methods. However, from the viewpoint of implementation, it is important to study it further so that the method can be easily and widely used by many circuit designers. This paper presents a practical method to implement the fixed-point homotopy method. A special circuit called the solution-tracing circuit for the fixed-point homotopy method is proposed. By using this circuit, the solution curves of homotopy equations can be traced by performing the SPICE transient analysis. Therefore, no modification to the existing programs is necessary. Moreover, it is proved that the proposed method is globally convergent. Numerical examples show that the proposed technique is effective and can be easily implemented. By the proposed technique, many SPICE users can easily implement the fixed-point homotopy method.

Original languageEnglish
Pages (from-to)222-233
Number of pages12
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2002 Jan
Externally publishedYes


  • Circuit simulation
  • DC operating-point
  • Fixed-point homotopy
  • Homotopy method

ASJC Scopus subject areas

  • Hardware and Architecture
  • Information Systems
  • Electrical and Electronic Engineering


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