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The multiparameter 2 Â 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 Â 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.

For the cobweb circuit network, the previous research focuses on the single-stage cobweb. In this paper, we studied a kind of multi-stage cobweb composed of n single-stage cobwebs, namely a 3 × 6 × n cobweb cascade LC network (CCLCN). To calculate the equivalent impedance of such large-scale complex circuit networks, we used a method that combines the replacement method with the modified recursive-transformation method (referred to as the R-MRT method). The CCLCN circuit was first replaced by a purely resistive circuit with identical connections, then the purely resistive circuit was calculated by the modified recursive-transformation method, and finally, the equivalent impedance of the CCLCN circuit was obtained by parameter replacement. Utilizing the above method, we obtained the exact analytical expression of the equivalent impedance of the 3 × 6 × n CCLCN. This result shows that the equivalent impedance problem of large-scale complex circuit networks such as the multi-stage cobweb has been solved.

SummaryIn this paper, a kind of multi‐stage cobweb resistance network consisting of n single‐stage cobwebs, namely, a 3 × 6 × n cobweb cascade resistance network (CCRN), was studied. To calculate the equivalent resistance of such a large‐scale complex network, we used a modified recursion‐transform (MRT) method. Firstly, the resistance network to be solved was simplified to a simple equivalent network. Thereafter, the recursive relation of the equivalent network was established according to the basic law of circuit. Then, the nonlinear recursive relation was transformed into the linear recursive relation by variable transformation technique. Finally, the equivalent resistance was gained by resolving the linear recursive relation. By this method, we obtained the exact analytical expression of the equivalent resistance of the 3 × 6 × n CCRN. The computation results show that the 3 × 6 × n CCRN's equivalent resistance is decided by the number of circuit stages n, and as n goes to infinity, these equivalent resistances all tend to a definite limit value.