Research on the equivalent complex impedance of multiparameter 2 × <i>n LC</i> network
Luo Li-jin, Fenghua Luo
Abstract
Abstract The multiparameter 2 × n LC complex impedance network is one of the difficult problems of the resistor network problem. In this study, the equivalent complex impedance problem of the four‐parameter 2 × n LC network model has been considered, where the network model contains four arbitrary L and C parameters. Our study involves four main steps: Firstly, a general difference equation model with current parameters has been established by utilizing Kirchhoff's law. Secondly, the general solution of the difference equation model has been obtained by matrix transformation. Thirdly, a matrix equation with boundary current parameters has been established, and the special solution of the boundary current has been obtained by substituting the general solution in the previous step. Finally, based on Ohm's law, the equivalent complex impedance formula has been obtained by using the special solution of the boundary current. The analysis of the derived equivalent complex impedances, Z ab ( n ) and Z ac ( n ), shows that they have different characteristics in different frequency ranges, and their variation is related to the mesh number n . The results of this study offer a theoretical basis for the related applied research.