The basic principle of <i>m</i> × <i>n</i> resistor networks

Here the problem of equivalent resistance of general 2 × n‐order resistor networks with four different resistor parameters is investigated, and innovations in theory and method are made. Here, the second‐order matrix equation model and boundary condition equation model are established by the RT‐I technique (recursion–transform theory based on current parameters), and the general solution and the special solution of the matrix equation are given by using the matrix transformation method. The current distribution law in the circuit is obtained, and three equivalent resistance formulas of general 2×n‐order resistor networks are obtained. Finally, by analyzing and discussing the special case of the conclusion, the relationship between different resistances is obtained, and the results are compared with those of other literatures.

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“…According to the system of Equations (19) and (20), a quadratic equation with one variable on can be obtained…”

Section: Matrix Transformation and General Solutionmentioning

confidence: 99%

Resistance Theory of General 2 × n Resistor Networks

Zhang

Huang

Chen

et al. 2021

Advcd Theory and Sims

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“…The second technique used is called the recursion transform method; it is based on the solution of a recurrence relation given by a matrix transformation of the equations involving the electrical currents. It was developed by Tan in 2011 21 to compute the equivalent resistance of a finite resistor lattice with diverse architecture such as a square grid, 22,23 complex networks, [24][25][26] circuits with different boundaries, 27,28 a cobweb networks, 29,30 and cylindrical topologies. 31,32 In spite of the fact that the method is applied to many complex topologies, it is limited to the homogeneous circuit without a localized feeding source.…”

Section: Introductionmentioning

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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“…The tolerance of the resistor is an important parameter of the resistor, which tells us about the amount by which the resistance of the resistor may vary from its specified value during the operation. The variation may go down or up in the percentage specified tolerance, and in some cases, these variations can significantly impact the performance of the overall circuit system significantly 7–10 …”

Section: Introductionmentioning

confidence: 99%

“…The variation may go down or up in the percentage specified tolerance, and in some cases, these variations can significantly impact the performance of the overall circuit system significantly. [7][8][9][10] In general, for a particular application, the following parameters of a resistor used in an electronic circuit are considered carefully, namely, the required resistance value, maximum power dissipation, maximum current capacity, and maximum breakdown voltage across the resistor. Unfortunately, the tolerance of resistor is seldom considered.…”

Section: Introductionmentioning

confidence: 99%

Effect of resistor tolerance on the performance of resistor network—An application of the statistical design of experiment

Pandey

Tan

2021

Circuit Theory & Apps

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Resistors come with different tolerances, but they are generally not seriously considered in circuit simulation as only the exact resistances are used. In actual implementation of a resistor network, the tolerance of the resistors used can affect the performances of the network, especially when the network consists of large number of resistors. This work demonstrates the use of the statistical design of experiment methods combined with circuit simulator to obtain the optimum value of the tolerances for different resistors in a resistor network for an application used in proton therapy. The discretized positioning circuit consisting of 86 resistors of four different values (R1 = 1KΩ, R2 = 600 Ω, R3 = 300 Ω, and R4 = 100 Ω) is analyzed for three tolerances of 0.05%, 0.1%, and 0.5%, respectively, and maximum variation in the output signal is observed for 0.5% tolerance. Resistors with values of R1 and R4 are dominant in numbers (56 with R1 and 22 with R4 out of 86 resistors) in the network, and hence, their effect is observed to be significant on the output as expected. Significant interactions between resistors are also observed.

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The basic principle of m × n resistor networks

Cited by 28 publications

References 39 publications

Resistance Theory of General 2 × n Resistor Networks

Resistance Theory of General 2 × n Resistor Networks

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

Effect of resistor tolerance on the performance of resistor network—An application of the statistical design of experiment

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