Equivalent resistance of n-step networks with △ structure

Abstract

The equivalent resistance of a class of n-step resistor networks with △ structure and multi-parameter is investigated and a breakthrough in methodology and theory is made. In this paper, a simple equivalent model is established, and a nonlinear difference equation is established by applying Kirchhoff's law. The solution of the nonlinear difference equation is given by the transformation method of variable substitution. Finally, a simple equivalent resistance formula is obtained. This paper also gives several interesting special conclusions, indicating that our network model contains a series of basic n-step resistor network models. Our method and the conclusions can also be applied to research on complex impedance networks. Keywords: n-step network, Equivalent resistance, Nonlinear difference equation, Equivalent transform, Variable substitution