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

Abstract

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.

Research on the equivalent complex impedance of multiparameter 2 × n LC network

“…28 Progress has also been made in the study of multiparameter resistor network problems, such as the equivalent resistance problem of a 2 Â n pure resistor network with three parameters. 24 In the research on complex impedance networks, the study of a complex impedance network with few parameters has made some progress, 32 but there is little research on complex impedance networks with multiple parameters. This study takes a 2 Â n LC network with four parameters as an example to study the equivalent complex impedance problem of the multiparameter complex impedance network model.…”

“…The construction and research of resistor network models are now considered as the basic methods to investigate many scientific problems. With the advancements in resistor network research, researchers have established several main methods for researching resistor networks, such as Kirchhoff's law analysis method, 9 Green's function technique, 1,2 Laplacian matrix method, 3–8 equivalent transformation method, 9 recursion‐transform method, 9–32 and so forth. Among them, the recursion‐transform method was proposed by Zhi‐Zhong Tan (Nantong University) in 2011.…”

“…Among them, the recursion‐transform method was proposed by Zhi‐Zhong Tan (Nantong University) in 2011. Compared to the previous methods, this method has wider applicability and can be applied to the study of finite and infinite resistor network problems with arbitrary boundaries, which makes up for the shortcomings of the previous methods 19–32 . In addition to the research methods, the problems of researchers' concerns continue to expand and deepen.…”

“…In recent years, significant progress has been achieved in this field, 24,25,28,31,32 in particular, in solving the problem of a resistor network with few parameters (one or two), such as the equivalent resistance of an m × n ‐order rectangular resistor network with two parameters 28 . Progress has also been made in the study of multiparameter resistor network problems, such as the equivalent resistance problem of a 2 × n pure resistor network with three parameters 24 . In the research on complex impedance networks, the study of a complex impedance network with few parameters has made some progress, 32 but there is little research on complex impedance networks with multiple parameters.…”

“…Compared to the previous methods, this method has wider applicability and can be applied to the study of finite and infinite resistor network problems with arbitrary boundaries, which makes up for the shortcomings of the previous methods. [19][20][21][22][23][24][25][26][27][28][29][30][31][32] In addition to the research methods, the problems of researchers' concerns continue to expand and deepen. For example, several studies investigate the equivalent impedance between any two nodes in a three-dimensional cubic network and a three-dimensional hexagonal prism network consisting of resistors or capacitors.…”