研究了一类n 阶Fan 电阻网络的电特性(任意节点的电压，等效电阻)，取得了理论和方法上的创新. 文章以节点电压为变量应用基尔霍夫定律建立二阶差分方程模型以及边界条件方程模型，通过研究差分方程的通解与特解，获得了n阶Fan 网络任意节点的电压公式，同时获得了任意2 节点间的等效电阻公式，并分析与讨论了结论的特殊情形. 本课题的研究工作实现了教学与科研的协同相长.

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.