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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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-80899-w |
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| _version_ | 1832571651296854016 |
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| author | Ru Wang Xiaoyu Jiang Yanpeng Zheng Zhaolin Jiang Deliang Xiang |
| author_facet | Ru Wang Xiaoyu Jiang Yanpeng Zheng Zhaolin Jiang Deliang Xiang |
| author_sort | Ru Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4bb22873937f4d388a9983e7c8089bda |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-4bb22873937f4d388a9983e7c8089bda2025-02-02T12:25:03ZengNature PortfolioScientific Reports2045-23222024-11-0114111410.1038/s41598-024-80899-wNew equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomialsRu Wang0Xiaoyu Jiang1Yanpeng Zheng2Zhaolin Jiang3Deliang Xiang4School of Information Science and Engineering, Linyi UniversitySchool of Information Science and Engineering, Linyi UniversitySchool of Automation and Electrical Engineering, Linyi UniversitySchool of Mathematics and Statistics, Linyi UniversitySchool of Automation and Electrical Engineering, Linyi UniversityAbstract 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.https://doi.org/10.1038/s41598-024-80899-w |
| spellingShingle | Ru Wang Xiaoyu Jiang Yanpeng Zheng Zhaolin Jiang Deliang Xiang New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials Scientific Reports |
| title | New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials |
| title_full | New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials |
| title_fullStr | New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials |
| title_full_unstemmed | New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials |
| title_short | New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials |
| title_sort | new equivalent resistance formula of m times n rectangular resistor network represented by chebyshev polynomials |
| url | https://doi.org/10.1038/s41598-024-80899-w |
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