Research on the electrical properties of 2 × 6 × n cobweb cascaded LC network model

Abstract

Given that the cobweb model incorporates the properties of numerous network topologies, the cobweb circuit network based on the cobweb model has stimulated the interest of researchers. In this paper, the electrical properties of the 2 × 6 × n cobweb cascaded LC network (CCLCN) model, which is a kind of complex impedance network, was studied by using the substitutionmethod. Firstly, the complex impedance network to be studied was transformed into the pure resistance network with the same connection mode. Secondly, according to the method of improved recursion-transform, the equivalent resistance of this pure resistance network was determined. Finally, the equivalent complex impedance of the 2 × 6 × n CCLCN model was obtained by replacing the corresponding parameters between the two networks. The findings demonstrate that the equivalent complex impedance of this network model has disparate properties in different χ ranges. In the χ ranges where ρ″ and σ″ are real numbers, the equivalent complex impedance has the same or similar monotone variation as χ for most values of n. In the χ ranges where ρ″ and σ″ are complex numbers, the equivalent complex impedance has different oscillations variation as χ when n takes on different values. The substitutionmethod utilized in this study can be extended to solve all types of complex impedance problems of nonlinear network.