A novel formula for representing the equivalent resistance of the $$m\times n$$ cylindrical resistor network

Meng, Xin; Jiang, Xiaoyu; Zheng, Yanpeng; Jiang, Zhaolin

doi:10.1038/s41598-024-72196-3

Sci Rep

2024

DOI: 10.1038/s41598-024-72196-3

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A novel formula for representing the equivalent resistance of the $$m\times n$$ cylindrical resistor network

Xin Meng,

Xiaoyu Jiang,

Yanpeng Zheng

et al.

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2024

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Cited by 2 publications

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

Wang,

Jiang,

Zheng

et al. 2024

Sci Rep

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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 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.

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

Wang,

Jiang,

Zheng

et al. 2024

Sci Rep

View full text Add to dashboard Cite

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An application of potential function in robot path planning and three optimized formulas for equivalent resistance

Dai,

Jiang,

Zheng

et al. 2024

era

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<p>The study proposed an innovative path planning algorithm based on the potential function of a special case of the cobweb resistor network, addressing the path planning problem in globe environments with obstacles. For the non-regular $ m \times n $ cobweb resistor network with arbitrary longitude, we found that by introducing Chebyshev polynomial of the second class, the precise equivalent resistance formulas could be optimized effectively. Compared with the original formula, optimized equivalent resistance formulas significantly reduced the time cost in large-scale data calculations. Furthermore, we have plotted 3D views of the equivalent resistance formulas for several special cases and conducted simulation experiments on the computational efficiency of the original and optimized formulas at different data scales, verifying the superiority of the optimized formulas. These findings provided new perspectives and tools for the computation of resistor networks and the design of path planning algorithms.</p>

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A novel formula for representing the equivalent resistance of the $$m\times n$$ cylindrical resistor network

Cited by 2 publications

References 68 publications

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

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

An application of potential function in robot path planning and three optimized formulas for equivalent resistance

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