Theory on resistance of <i>m</i> × <i>n</i> cobweb network and its application

Tan, Zhi‐Zhong

doi:10.1002/cta.2035

Cited by 43 publications

(25 citation statements)

References 16 publications

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“…At the end of this paper, we propose a profound problem based on the previous research in the article : how to derive the resistance of an m × n network of cross resistors as shown in Figure . We look forward to the solution of the problem.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…As is well known, the research of complex impedance network is more difficult than that of the resistor network because the equivalent impedance has many different properties from equivalent resistance. From previous studies of the equivalent impedance, we find that the results of the equivalent complex impedance are always curious and nonlinear . Thus, complex impedance is an important problem worthy of study.…”

Section: Introductionmentioning

confidence: 96%

“…The computation of the two‐point resistance in networks is a classical problem in circuit theory and graph theory, which has been researched for more than 170 years . The computation of resistances is relevant to a wide range of problems ranging from science and technology to engineering . However, it is usually very difficult to obtain the exact resistance in complex resistor networks ; the construction of and research on the models of complex networks therefore make sense for theories and applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Over the past few decades, the rectangular network topology has been published in some papers with the superposition current distribution, the random walks, the lattice Green function,() the Laplacian matrix,() the analytical solution obtained by recursion or equivalent transform methods,() and so on.…”

Section: Introductionmentioning

confidence: 99%

The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

Ammar¹,

Baudrand

2019

Circuit Theory & Apps

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Summary This paper deals with an RLC circuit network with triangular or hexagonal grid. It is about a planar equilateral triangular grid where the passive (resistor, capacitor, and inductor) or active (voltage source for example) components are located at the sides or/and at nodes attached to the ground. The planar graph is oriented by three main direction vectors phase shifted to 60° degrees. The wave concept iterative process (WCIP) method was employed to the theoretical formulation of the problem. In the formulation, the potential difference across each circuit component is represented by an auxiliary source defined in the spectral domain. The proposed theory is developed into two definition domains: a spectral domain in which periodicity and coupling between the circuit components are defined and a spatial domain describing the network topology and imposing the continuities conditions (Kirchhoff laws). The transition between the spectral and spatial domain is ensured by the so‐called fast hexagonal Fourier transform. Numerical applications demonstrate the ability of the method for solving the inhomogeneous triangular lattices. Various conceptions have been proposed including an RL, RC, and RLC triangular network circuit, a perturbed triangular RLC circuit, and a triangular circuit excited by many lumped sources.

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“… 24 studied the resistance of globe network, ref. 25 computed the resistance of the fan and cobweb networks, refs 26 , 27 calculated the resistance of the fan network with arbitrary boundaries, refs 28 – 30 calculated the resistance of the cobweb network under different conditions, ref. 31 studied the resistance of a hammock network by two different methods, ref.…”

Section: Introductionmentioning

confidence: 99%

Potential formula of the nonregular m × n fan network and its application

Tan

Chen

2018

Sci Rep

Self Cite

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Potential formula of an arbitrary resistor network has been an unsolved problem for hundreds of years, which is an interdisciplinary problem that involves many areas of natural science. A new progress has been made in this paper, which discovered the potential formula of a nonregular m × n fan network with two arbitrary boundaries by the Recursion-Transform method with potential parameters (simply call RT-V). The nonregular m × n fan network is a multipurpose network contains several different types of network model such as the interesting snail network and hart network. In the meantime, we discussed the semi-infinite fan network and a series of novel and special conclusions are produced, the effective resistance is educed naturally. The discovery of potential formulae of resistor network provides new theoretical tools and techniques for related scientific research.

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Theory on resistance of m × n cobweb network and its application

Cited by 43 publications

References 16 publications

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

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

The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

Potential formula of the nonregular m × n fan network and its application

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