Circuit network theory of n-horizontal bridge structure

Abstract

This research investigates a complex n order cascading circuit network with embedded horizontal bridge circuits with the N-RT method. The contents of the study include equivalent resistance analytical formula and complex impedance characteristics of the circuit network. The research idea is as follows. Firstly the equivalent model of n-order resistance network is established, and a fractional difference equation model is derived using Kirchhoff’s law. Secondly, the equivalent transformation method is employed to transform the fractional equation into a simple linear difference equation, and its particular solution is computed. Then the solution to the difference equation is used to derive the effective resistance of the resistance network of the embedded horizontal bridge circuit, and various special cases of equivalent resistance formula are analyzed and the correctness of the analysis model gets verified. Finally, as an expanded application, the equivalent complex impedance of LC network is studied, and Matlab drawing tool is employed to offer the equivalent impedance with various variables of the graph. Our results provide new research ideas and theoretical basis for relevant scientific researches and practical applications.

Two-point resistances in symmetric bracelet resistor networks: accurate estimates and exact expressions

“…Looking more closely at the relative difference ΔR/R between the estimate given by equation (15) and the numerical result (figure 5), the accuracy of the estimate increases rapidly as a function of n, reaching the numerical accuracy for n 10. The correction terms depending on n, beyond the dominant 1/n term, therefore quickly become negligible as n increases.…”

“…In the case of the n-bracelet, we can easily do better than the estimates in equation (15), because with equation (11) we have the exact expression of R 0n as a function of n and b. For n = 3, we simply have R 03 = (1 + 2b)/(3 + 2b), which we could see directly as a resistor 1 twice in parallel with a resistor 1 + 2b.…”

“…Dedicated methods have subsequently been developed to study extended RNs, such as Laplacian matrix methods [8], electrical images [9] or the transfer matrix approach [10]. In addition to numerical methods, three-dimensional RNs of increasing complexity are now routinely analysed using powerful exact methods based on lattice green functions [11,12] or the rapidly developing Recursive Transform method of Tan and co-workers [13][14][15]. In parallel with these achievements, physicists returned to neglected basic networks.…”

Analytical formulas for calculating the electrical characteristics of multiparameter arbitrary configurational homogenous ladder networks

“…In this area, some attempts have been made to derive analytical expressions to compute a few electrical characteristics. Tan et al 25,26 used the variable substitution method to calculate the equivalent impedance of an LC network. Using a nonlinear differential equation, Chen et al 27 calculated the equivalent impedance for a two‐terminal trapezoidal complex impedance network with few parameters.…”

Electrical properties of a generalized 2 × n resistor network

“…For example, in the literature [39,40], equivalent circuits can be used to study the reflection and refraction of electromagnetic waves of the superstructure grating, while reference [41] uses complex impedance circuits to study water transport in plants. At present, researchers have accomplished many achievements in research by using the N-RT method [42][43][44][45][46][47][48][49]. This paper intends to study a class of a generalized 2 × n circuit network model, which is different from previous models in that the resistance on the middle axis is independent of the resistance on the upper and lower boundaries as shown in figure 1.…”