Electrical characteristics of the 3 × 6 × n cobweb cascaded LC complex impedance network

Abstract

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.