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• An effective method to solve the equivalent complex impedance of the complex impedance circuits: the substitution method. • The expression for the equivalent complex impedance of the 2 × 6 × n cobweb cascaded LC complex impedance network. • Finding some interesting results of the 2 × 6 × n cobweb cascaded LC complex impedance network model. 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 substitution method. 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 substitution method utilized in this study can be extended to solve all types of complex impedance problems of nonlinear network. [ABSTRACT FROM AUTHOR]

• An improved recursion-transform method. • The expression for the equivalent resistance of 6 × n cobweb cascaded resistor network. • The 6 × n cobweb cascade resistor network could be transformed into four other types. • The expression for the equivalent impedance of 6 × n cobweb cascaded LC network. • Finding some interesting results of the 6 × n cobweb cascaded LC network. 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. [ABSTRACT FROM AUTHOR]