The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Encontrar pontos de operação CC de circuitos não lineares é uma tarefa importante e difícil. O método Newton-Raphson empregado nos simuladores do tipo SPICE muitas vezes não consegue convergir para uma solução. Para superar este problema de convergência, métodos de homotopia têm sido estudados sob vários pontos de vista. O método de homotopia de ponto fixo é um dos métodos excelentes. No entanto, do ponto de vista da implementação, é importante estudá-lo mais a fundo para que o método possa ser fácil e amplamente utilizado por muitos projetistas de circuitos. Este artigo apresenta um método prático para implementar o método de homotopia de ponto fixo. Um circuito especial chamado circuito de rastreamento de solução para o método de homotopia de ponto fixo é proposto. Ao usar este circuito, as curvas de solução das equações de homotopia podem ser traçadas realizando a análise transitória SPICE. Portanto, nenhuma modificação nos programas existentes é necessária. Além disso, está provado que o método proposto é globalmente convergente. Exemplos numéricos mostram que a técnica proposta é eficaz e pode ser facilmente implementada. Pela técnica proposta, muitos usuários do SPICE podem implementar facilmente o método de homotopia de ponto fixo.
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Yasuaki INOUE, Saeko KUSANOBU, Kiyotaka YAMAMURA, "A Practical Approach for the Fixed-Point Homotopy Method Using a Solution-Tracing Circuit" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 1, pp. 222-233, January 2002, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_1_222/_p
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@ARTICLE{e85-a_1_222,
author={Yasuaki INOUE, Saeko KUSANOBU, Kiyotaka YAMAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Practical Approach for the Fixed-Point Homotopy Method Using a Solution-Tracing Circuit},
year={2002},
volume={E85-A},
number={1},
pages={222-233},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - A Practical Approach for the Fixed-Point Homotopy Method Using a Solution-Tracing Circuit
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 222
EP - 233
AU - Yasuaki INOUE
AU - Saeko KUSANOBU
AU - Kiyotaka YAMAMURA
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2002
AB - 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.
ER -