Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

Abstract

The electrical properties of conducting meshes are investigated numerically by solving the related Kirchhoff equations with the Lanczos algorithm. The method is directly inspired by the recursion technique widely used to study the electronic and vibrational spectra of solids. The method is demonstrated to be very efficient and fast when applied to resistor networks. It is used to calculate equivalent resistances between arbitrary pairs of nodes in simple resistive lattices. When the resistance fluctuates statistically from bond to bond, the method makes it possible to evaluate the fluctuations of the electrical properties of the network. It is also employed to assign an effective bulk resistivity to a discrete conducting three-dimensional mesh.