Recursion-Transform method to a non-regular m×n cobweb with an arbitrary longitude

Tan, Zhongfu

doi:10.1038/srep11266

Cited by 46 publications

(58 citation statements)

References 21 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%

“…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%

“…The main progress of research methods in resistor networks basically has several different approaches, such as Kirchhoff's laws , the lattice Green's function technique , the Laplacian approach , the recursion‐transform method , the equivalent transformation methods and a method of nodal potentials . Thus, many resistor networks have been resolved by these methods.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Please note that formulae (1), (2), and (6)- (8) are discovered for the first time in this paper. In the following section, we are going to derive the above formulae by the RT-I method [ [36][37][38] including to model differential equations and matrix transformation.…”

Section: Resistance Of the 2×n Plane Networkmentioning

confidence: 99%

Electrical characteristics of the 2 × n and □ × n circuit network

2019

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This paper presents two new fundamentals of the 2×n and ,×n circuit network. The results of a plane 2×n resistor network can be applied to a ,×n circuit network, which has not been studied before. We first study the 2×n resistor network by modeling a differential equation and obtain two equivalent resistances between two arbitrary nodes of the 2×n network. Next, the ,×n cube network is transformed to the 2×n plane network equivalently to achieve two resistance formulae between two arbitrary nodes of the ,×n cube network. By applying the resistance results to the ,×n LC cube network, the complex impedance characteristics of the LC network, which includes oscillation characteristics and resonance properties, are discovered.

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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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Recursion-Transform method to a non-regular m×n cobweb with an arbitrary longitude

Cited by 46 publications

References 21 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

Electrical characteristics of the 2 × n and □ × n circuit network

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

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