Resistance Theory of General 2 × n Resistor Networks

Abstract

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.

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

“…In the field of scientific research and engineering technology, many practical problems can be simulated and studied by building resistor network models 1–36 . The construction and research of resistor network models are now considered as the basic methods to investigate many scientific problems.…”

“…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.…”

“…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.…”

“…36 The rectangular resistor network model problem has always been one of the hotspots of resistor network research. 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.…”