Electrical characterization of the 2 × 6 × n cobweb cascaded resistor network model by the improved recursion-transform method

Abstract

Since the cobweb model combines the properties of several network topologies, the cobweb resistor network based on the cobweb model has aroused the interest of scholars. However, owing to the complicated structure of the cobweb cascaded resistor network, it is very challenging to solve with conventional approaches. To address this issue, an improved recursion-transform approach was employed. The electrical characterization of the 2 × 6 × n cobweb cascade resistor network model was studied in this paper. Firstly, the equivalent circuit of the resistor network to be solved was found. Secondly, the recursive equation of the equivalent circuit was constructed. Then, the recursive equation was linearized. Finally, the equivalent resistance of the resistor network was obtained by solving the linear recursive equation. This approach significantly reduces the computation procedure because it adopts the scheme of simplifying the circuit first, then establishing the equation and solving it. The findings indicate that the equivalent resistances between the two nodes of this resistor network change with the change of the order n. When n tends to infinity, these equivalent resistances will have definite convergence values. The calculation results show that these equivalent resistances are already very close to their convergence values, respectively, when n takes 7 or 8.