Electrical properties of an m × n rectangular network

Abstract

Electrical properties of an m × n rectangular network with two arbitrary boundaries is investigated, which is an unsolved problem before. Here a new theoretical advance has been made, which sets up two new formulae on evaluating the exact electrical characteristics (potential and resistance) of the nonregular m × n rectangular networks by the recursion-transform method with potential parameters (RT-V), and many interesting new results are derived when making different boundary conditions. It should be emphasized that nonregular rectangular network with two arbitrary boundaries is a kind of multi-function network contains several different types of network model such as the regular rectangular network, Fan network and hammock network. Therefore, our research results provide the new theoretical basis for the study of complex network models.