New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials

Abstract In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem. This paper aims to introduce Chebyshev polynomial of the second kind to improve the equivalent resistance for...

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Published inScientific reports Vol. 14; no. 1; pp. 1 - 14
Main Authors Wang, Ru, Jiang, Xiaoyu, Zheng, Yanpeng, Jiang, Zhaolin, Xiang, Deliang
Format Journal Article
LanguageEnglish
Published Nature Portfolio 27.11.2024
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Abstract Abstract In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem. This paper aims to introduce Chebyshev polynomial of the second kind to improve the equivalent resistance formula of $$m\times n$$ rectangular resistor network, thereby improving the calculation efficiency. Additionally, the discrete sine transform of the first kind (DST-I) is utilized to solve the modeling equation. Under the condition of applying the new equivalent resistance formula, several equivalent resistance formulas with different parameters are given, and three-dimensional views are used to illustrate them. Six comparison tables are provided to showcase the advantages of the improved explicit formula in terms of computational efficiency, as well as the relationship between resistivity and the maximum size of the resistor network that the formula can effectively handle. This may provide more convenient and effective technical support for research and practice in electronic engineering and other related fields.
AbstractList Abstract In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem. This paper aims to introduce Chebyshev polynomial of the second kind to improve the equivalent resistance formula of $$m\times n$$ rectangular resistor network, thereby improving the calculation efficiency. Additionally, the discrete sine transform of the first kind (DST-I) is utilized to solve the modeling equation. Under the condition of applying the new equivalent resistance formula, several equivalent resistance formulas with different parameters are given, and three-dimensional views are used to illustrate them. Six comparison tables are provided to showcase the advantages of the improved explicit formula in terms of computational efficiency, as well as the relationship between resistivity and the maximum size of the resistor network that the formula can effectively handle. This may provide more convenient and effective technical support for research and practice in electronic engineering and other related fields.
ArticleNumber 29461
Author Jiang, Zhaolin
Jiang, Xiaoyu
Wang, Ru
Zheng, Yanpeng
Xiang, Deliang
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Snippet Abstract In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network...
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Title New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials
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