Study on the electrical characteristics of 6 × n cobweb cascaded circuit network model

Abstract

Given the excellent topological properties of the cobweb model, the cobweb circuit network based on the cobweb model has attracted researchers' attention. The equivalent resistance of the cobweb cascaded resistor network is one of the difficult problems of the resistor network. In order to solve this problem, a 6 × n cobweb cascade resistor network model was taken as an example, and an improved recursion-transform method was adopted in this study. Firstly, an equivalent circuit model of the circuit network to be studied was constructed. Secondly, according to Kirchhoff's circuit law, a nonlinear difference equation model of the equivalent circuit model was established. Then, the nonlinear difference equation model was transformed into a linear one by introducing a new sequence. Finally, the equivalent resistance of the circuit network to be studied was obtained by solving the linear difference equation model. It was also discussed that the 6 × n cobweb cascade resistor network model could be transformed into four other types of network models under different conditions. A 6 × n cobweb cascaded LC complex impedance network was further studied based on the above research results. The equivalent complex impedance of this network was obtained by using the method of variable substitution under the quasi-stable condition. It was found that the equivalent complex impedance varied monotonously or quiveringly in different parameter ranges. This study provides a new theoretical basis for the research of cobweb networks.