Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

doi:10.1088/1674-1056/25/5/050504

中国物理B ›› 2016, Vol. 25 ›› Issue (5): 50504-050504.doi: 10.1088/1674-1056/25/5/050504

Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

Zhi-Zhong Tan(谭志中)

Department of Physics, Nantong University, Nantong 226019, China

收稿日期:2015-11-18 修回日期:2015-12-17 出版日期:2016-05-05 发布日期:2016-05-05
通讯作者: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn,tanzzh@163.com
基金资助:
Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University, China (Grant No. 15ZY16).

Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

Zhi-Zhong Tan(谭志中)

Department of Physics, Nantong University, Nantong 226019, China

Received:2015-11-18 Revised:2015-12-17 Online:2016-05-05 Published:2016-05-05
Contact: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn,tanzzh@163.com
Supported by:
Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University, China (Grant No. 15ZY16).

摘要/Abstract

摘要：

A rectangular m×n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform (RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h₁ = 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.

关键词: rectangular network, exact solution, RT method, complex impedance

Abstract:

Key words: rectangular network, exact solution, RT method, complex impedance

中图分类号: (Lattice theory and statistics)

05.50.+q

84.30.Bv (Circuit theory) 89.20.Ff (Computer science and technology) 02.10.Yn (Matrix theory)

谭志中. Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network[J]. 中国物理B, 2016, 25(5): 50504-050504.

Zhi-Zhong Tan(谭志中). Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network[J]. Chin. Phys. B, 2016, 25(5): 50504-050504.

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Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

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