任意2×n阶Fan网络的电特性研究  

Study of electric properties of an 2×n Fan network

作　　者：谭志中[1] 余清怡 王一骁 TAN Zhi-zhong;YU Qing-yi;WANG Yi-xiao(Department of Physics, Nantong University, Nantong, Jiangsu 226019, China)

机构地区：[1]南通大学物理系,江苏南通226019

出　　处：《大学物理》2019年第3期14-19,31,共7页College Physics

基　　金：国家级大学生创新创业训练计划项目(201710304006);江苏省自然科学资金面上项目(BK20161278)资助

摘　　要：采用递推-变换(RT)方法研究了一类2×n阶Fan(扇形)电阻网络的电特性(包括支路电流,任意节点的电压,等效电阻),取得了理论和方法上的创新.文章以支路电流为变量应用基尔霍夫定律建立矩阵方程模型以及边界条件方程模型,通过矩阵变换研究矩阵差分方程的通解与特解,获得了任意2×n阶Fan电阻网络的支路电流公式,导出了2×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.We achieve the innovation in theory and method on the research of the electrical properties(including the branch current,voltage of any node,and equivalent resistance)of an arbitrary 2×n Fan resistor network by the Recursion-Transform(RT)method.In this paper,the matrix equation model and the boundary condition equation model are established by using the branch current as the variable in terms of applying Kirchhoff's law.We study the general solution and special solution of the matrix equation by the matrix transform,thus the branch currents of the 2×n Fan network are obtained,and derived the voltage formula of arbitrary node,at the same time,the equivalent resistance formula between any two nodes is obtained as well.The special situation of the conclusion is analyzed and discussed.

关 键 词：电阻网络 递推-变换方法 矩阵方程 电特性. 

分 类 号：O441.1[理学—电磁学] TN711.3[理学—物理]