Study on the equivalent resistance of a class of n-ring network

This article considers a class of periodic network models with n-order rectangular structures, which contain any n unit cells. The equivalent resistance analytical formula of this network model is investigated using the recursion-transform method based on voltage parameters (RT-V). Two new analytical expressions for equivalent resistance are obtained by establishing the principal difference equations and the boundary condition difference equations, followed by theoretical calculations and derivations. At the end of the article, the correctness of the theoretical formulas is verified through simple circuits, and the conclusions under special cases and infinite networks are discussed. This research result can provide a new theoretical basis for relevant interdisciplinary research and simulation studies.