5×n阶网络等效电阻的两个普适公式  

Two General Formulas of Equivalent Resistance of 5 × n Step Network

作　　者：谭剑[1] 谭志中[2] 

机构地区：[1]扬州大学信息工程学院,江苏扬州225009 [2]南通大学理学院,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2012年第2期88-94,共7页Journal of Nantong University(Natural Science Edition)　

基　　金：江苏省教育科学"十一五"规划2009年度立项课题(D/2009/01/127)

摘　　要：针对5×n阶电阻网络的等效电阻计算尚未解决的问题,通过网络分析构建差分方程组模型.利用矩阵变换方法,给出5×n阶电阻网络节点间的电流通用规律,并且根据边界电流条件,获得了5×n阶电阻网络等效电阻的2个普适公式,给出了n→∞的结果.在n=0,1,2三种特例情形下的计算结果与实际相一致,验证了该公式的正确性.As to the problem that the calculation of the equivalent resistance of 5 × n step network hasn′t worked out,the basic structure of 5 × n step network is studied and the equivalent resistance of the network is analyzed and calculated.A set of difference equation is solved by using the matrix transform method and two general formulas for the inlet resistance of 5 × n step network are proposed.Meanwhile,the infinite 5 × n-network is taken into account,and two equivalent resistances in this case are also obtained.Finally,effectiveness and correctness of the methods used in this paper are verified in special cases of n = 0,1,2.The results revealed have certain guidance value in the actual application.

关 键 词：5×n阶网络 差分方程 矩阵变换 等效电阻 普适规律 

分 类 号：O441[理学—电磁学]