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A Practical Approach for the FixedPoint Homotopy Method Using a SolutionTracing Circuit
Yasuaki INOUE Saeko KUSANOBU Kiyotaka YAMAMURA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E85A
No.1
pp.222233 Publication Date: 2002/01/01
Online ISSN:
DOI:
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Nonlinear Problems Keyword: homotopy method, fixedpoint homotopy, DC operatingpoint, circuit simulation, SPICE,
Full Text: PDF(540.9KB)>>
Summary:
Finding DC operatingpoints of nonlinear circuits is an important and difficult task. The NewtonRaphson method employed in the SPICElike simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixedpoint 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 fixedpoint homotopy method. A special circuit called the solutiontracing circuit for the fixedpoint 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 fixedpoint homotopy method.

