On the perturbation of a uniform tiling with resistors

Owaidat, M. Q.; Asad, Jihad; Tan, Zhongfu

doi:10.1142/s0217979216501666

Cited by 15 publications

(11 citation statements)

References 43 publications

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“…For example, Cserti [2] studied the equivalent resistance of infinite network without considering the boundary for the first time using the Lattice Green's function (LGF) technique, and then the equivalent resistance formula of infinite network was obtained. After that, LGF function technique was further developed and applied [3][4][5][6][7][8][9][10]. In applications, equivalent resistance and capacitance problems of three-dimensional cubic networks were studied by Asad [5,6].…”

Section: Introductionmentioning

confidence: 99%

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Electrical properties of an arbitrary 2 × n order fan network

Wang¹,

Ding²,

Tan³

2019

Phys. Scr.

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This paper deals with the electrical properties (branch current, node voltage, and equivalent resistance) of arbitrary 2 × n order Fan resistor network by means of the recursion-transform method. Taking the branch current as a variable, the matrix equation model and the boundary condition equation model are firstly established by applying Kirchhoff’s laws. Then the general solution and special solution of the matrix difference equation are studied by the matrix transformation. After that, the branch current formula of 2 × n order Fan network, the voltage formula of arbitrary node, and the equivalent resistance formula between any two nodes are all derived. Finally, special cases in the conclusions are analyzed and discussed.

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Section: Introductionmentioning

confidence: 99%

“…In applications, equivalent resistance and capacitance problems of three-dimensional cubic networks were studied by Asad [5,6]. For Owaidat et al studied several complex infinite networks by using LGF technique [7][8][9][10]. So the LGF function technique plays an important role in studying infinite networks.…”

Section: Introductionmentioning

confidence: 99%

Electrical properties of an arbitrary 2 × n order fan network

Wang¹,

Ding²,

Tan³

2019

Phys. Scr.

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“…In the literature, a perturbed lattice is defined as an electrical circuit wherein we remove one or two bonds. 46,47 With WCIP formalism, by using the auxiliary source concept, a perturbed lattice is defined as a heterogeneous lattice in which we replace one or many auxiliary sources with an open or shorted circuits. As an example, we carry out a slight perturbation to the circuit of Figure 9 by eliminating, in the bottom layer, a band of branches ( substituting the auxiliaries sources by open circuits) (M/2 + 1) ≤ p ≤ (M/2 + 1) + 5 and (N/2 + 1) ≤ q ≤ (N/2 + 1) + 5.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the following case, we propose to study an example of a perturbed circuit. In the literature, a perturbed lattice is defined as an electrical circuit wherein we remove one or two bonds 46,47 . With WCIP formalism, by using the auxiliary source concept, a perturbed lattice is defined as a heterogeneous lattice in which we replace one or many auxiliary sources with an open or shorted circuits.…”

Section: Numerical Examplesmentioning

confidence: 99%

Electrical characteristics for triangular resistors–capacitors–inductors network designed on two coats

Ammar¹,

Asad

Jarrar

2021

Circuit Theory & Apps

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This work deals with a theoretical study of a triangular electrical lattice built on two layers. First, the auxiliary source notion is introduced for characterizing the potential difference over each electrical element, then the mathematical formalism of the Wave Concept Iterative Process (WCIP) method is developed and adapted to the studied circuit. The method is based on the concept of the incident and reflected waves which are defined from the current and voltage at each branch of the circuit. Two relations connecting the waves are established into two definition domains: a spectral domain using the Kirchhoff laws and the auxiliary source connections and another spatial domain defining the boundary conditions and the circuit design. Hence, a system of two equations is obtained, and it is resolved by an iterative process; the transition between the two domains is ensured by the fast Fourier transform and its inverse. Moreover, the equivalent impedance between the feeding source and the nodes of the bottom layer has been calculated.Among the numerical simulation methods, this method has demonstrated its performance for analyzing various designs of the networks including resistors-inductors (RL), resistors-capacitors (RC), and resistors-capacitorsinductors (RLC) circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.

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“…Infinite networks consisting of either identical resistors or identical capacitors have been the subject of much research effort for a long time. Three methods and techniques that have been developed are mainstream in investigating the infinite resistor networks, including the current distribution method [1], the lattice Green's function (LGF) method [3][4][5][6][7][8][9][10] and the random walk method [11,12]. The LGF method is important because it enables us to study infinite perfect networks in addition to perturbed infinite networks, as one can see in the previous works carried out.…”

Section: Introductionmentioning

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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On the perturbation of a uniform tiling with resistors

Cited by 15 publications

References 43 publications

Electrical properties of an arbitrary 2 × n order fan network

Electrical properties of an arbitrary 2 × n order fan network

Electrical characteristics for triangular resistors–capacitors–inductors network designed on two coats

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

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