The basic principle of <i>m</i> × <i>n</i> resistor networks*

Abstract

Abstract The unified processing and research of multiple network models are implemented, and a new theoretical advance has been made, which sets up two new theorems on evaluating the exact electrical characteristics (potential and resistance) of the complex m × n resistor networks by the recursion-transform method with potential parameters, and applies to a variety of different types of lattice structure with arbitrary boundaries such as the nonregular m × n rectangular networks and the nonregular m × n cylindrical networks. Our research gives the analytical solutions of electrical characteristics of the complex networks (finite, semi-infinite and infinite), which has not been solved before. As applications of the theorems, a series of analytical solutions of potential and resistance of the complex resistor networks are discovered.