Calculating Resistance in an Infinite Triangular Lattice Network

Abstract

Abstract: The lattice Green's function method is employed to analyze the resistance of a triangular network consisting of identical resistors in both perfect and perturbed scenarios, where a single interstitial resistance is added. In the perfect lattice scenario, all resistors are assumed to have equal resistance, and the network is considered ideal with no imperfections. To calculate the lattice Green's function and resistance of the perturbed lattice, Dyson's equation is utilized. This equation relates the perturbed and unperturbed Green's function and the interstitial resistance value. To validate the dependability of the lattice Green's function method in predicting the behavior of intricate networks, the accuracy of the computed values is evaluated by comparing them with the measured values for an infinite triangular network.

Keywords: Resistors, Lattice Green’s function, Perturbation.