Equivalent complex impedance between the arbitrary-stage nodes in the 3 × 6 × m cascaded cobweb LC network

Abstract The calculation of the equivalent complex impedance between arbitrary-stage nodes in cascaded cobweb complex impedance networks represents a challenging issue in the field of circuit network analysis. To address this challenge, this study proposes a systematic approach composed of the following steps: (1) Replace the cascaded cobweb complex impedance network with a cascaded cobweb pure resistive network that maintains the same connection topology; (2) Introduce the concept of ‘negative resistance’ to decompose the cascaded cobweb resistive network into three equivalent sub-networks—referred to as the left, middle, and right sub-networks; (3) Employ an improved recursion-transformation method to calculate the equivalent resistance between the final-stage nodes of the left and right sub-networks; (4) Based on the parallel relationship among the three sub-networks, determine the equivalent resistance between arbitrary-stage nodes of the cascaded cobweb pure resistive network; (5) Substitute the resistance parameters in the derived resistance expression with their corresponding complex impedance parameters to obtain the expression for the equivalent complex impedance between arbitrary-stage nodes of the original cascaded cobweb complex impedance network. Using this method, the equivalent complex impedance between the arbitrary-stage nodes in a 3 × 6 × m cascaded cobweb LC network was successfully calculated. This approach offers an effective and generalizable solution for determining the equivalent complex impedance or resistance between arbitrary-stage nodes in cascaded circuit networks.