Formulae of resistance between two corner nodes on a common edge of the <i>m</i> × <i>n</i> rectangular network

Tan, Zhi‐Zhong; Zhang, Qinghua

doi:10.1002/cta.1988

Cited by 34 publications

(25 citation statements)

References 20 publications

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“…Early discussions along this line are due to Tan et al [6,[8][9][10]. A similar analysis for a fan network has been given recently in [11].…”

Section: B Matrix Equation For Longitudinal Currentsmentioning

confidence: 95%

“…An alternative direct approach of computing resistances had been developed by Tan et al [6,[8][9][10] that, when applied to the cobweb and globe networks, gives the result in terms of a single summation. This offers a direct and somewhat simpler approach.…”

Section: F Special Casesmentioning

confidence: 99%

“…Studies of the resistance problem have also been carried out independently by Tan et al along a route that we shall refer to as the method of direct evaluation [6,[8][9][10]. The direct method is useful in cases when there exists a special node such as a pole of the globe or the center of the cobweb, with all other nodes connected to it equally along longitudes of a globe or the radii of a cobweb.…”

Section: Introductionmentioning

confidence: 99%

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Two-point resistance of a resistor network embedded on a globe

Tan

Essam

2014

Phys. Rev. E

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We consider the problem of two-point resistance in an (m-1) × n resistor network embedded on a globe, a geometry topologically equivalent to an m × n cobweb with its boundary collapsed into one single point. We deduce a concise formula for the resistance between any two nodes on the globe using a method of direct summation pioneered by one of us [Z.-Z. Tan, L. Zhou, and J. H. Yang, J. Phys. A: Math. Theor. 46, 195202 (2013)]. This method is contrasted with the Laplacian matrix approach formulated also by one of us [F. Y. Wu, J. Phys. A: Math. Gen. 37, 6653 (2004)], which is difficult to apply to the geometry of a globe. Our analysis gives the result in the form of a single summation.

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“…Early discussions along this line are due to Tan et al [6,[8][9][10]. A similar analysis for a fan network has been given recently in [11].…”

Section: B Matrix Equation For Longitudinal Currentsmentioning

confidence: 95%

Section: F Special Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-point resistance of a resistor network embedded on a globe

Tan

Essam

2014

Phys. Rev. E

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“…Ref. investigates the equivalent resistance of M × N resistor network, presents the analytical expressions for even and odd M , and applies to calculate the equivalent impedance of the network containing capacitor and inductor.…”

Section: Resultsmentioning

confidence: 99%

“…Thus, in Figure 3, N + 1 meshes through line m along the horizontal direction form a supernode; it must yield Based on Equations (19) and (20), Equation (22) gives clear and simple relations, which are shown in Appendix.…”

Section: Mesh Currentsmentioning

confidence: 99%

Application of the recursion‐transform method in calculating the equivalent resistance of two‐dimensional finite resistor network

2016

Circuit Theory & Apps

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Summary Looking for a handy and exact calculation for the equivalent resistance of an M × N resistor network is important but difficult, even for the rectangular resistor network. In this paper, we calculate the equivalent resistance of an M × N rectangular resistor network by means of the recursion‐transform method, where the idea of multiple external current sources based on the typical mesh current is used, and find a new formula of equivalent resistance which is different from the result of the other paper. In our scheme, recalculations are not required to obtain the equivalent resistance between different terminals. We further investigate how the order of resistor network and the ratio between two unit resistances affect the equivalent resistance. We find that the equivalent resistance between arbitrary terminals tends to a constant as the order and ratio increase when M is given. Copyright © 2016 John Wiley & Sons, Ltd.

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Resistance formulae of a multipurpose n‐step network and its application in LC network

Tan

Asad

Owaidat

2017

Circuit Theory & Apps

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We consider a multipurpose n-step network with cross resistors that is a profound problem that has not been resolved before. This network contains a number of different types of resistor network model. This problem is resolved by three steps: First of all, we simplify a complex graphics into a simple equivalent model; next, we use Kirchhoff's laws to analyse the network and establish a nonlinear difference equation; and finally, we construct the method of equivalent transformation to obtain the general solution of the nonlinear difference equation. In this paper, we created a new concept of negative resistance for the needs of the equivalent conversion and obtain two general resistance formulae of a multipurpose ladder network of cross resistors. As applications, several interesting specific results are produced. In particular, an n-step impedance LC network is discussed. Our method and the results are suitable for the research of complex impedance network as well.

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Formulae of resistance between two corner nodes on a common edge of the m × n rectangular network

Cited by 34 publications

References 20 publications

Two-point resistance of a resistor network embedded on a globe

Two-point resistance of a resistor network embedded on a globe

Application of the recursion‐transform method in calculating the equivalent resistance of two‐dimensional finite resistor network

Resistance formulae of a multipurpose n‐step network and its application in LC network

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