关键词: Fan 网络, 电位公式, 等效电阻, 差分方程, 教学科研相长

Abstract: The electrical properties (including the voltage of any node，and equivalent resistance) of a class of n-step Fan resistor network are studied，and innovation in theory and method has been achieved. In this paper，the second-order difference equation model and the boundary condition equation model are established by using the node potential as the variable in terms of applying Kirchhoff's law. By studying the general solution and special solution of difference equation，the voltage formula of arbitrary node of n-order Fan network is obtained，at the same time，the equivalent resistance formula between any two nodes is obtained as well，and the special situation of the conclusion is analyzed and discussed. Our research work realizes the cooperation and mutual benefit between teaching and scientific research.

Key words: Fan network, voltage formula, difference equation, equivalent resistance, mutual benefit between teaching and research