加强型多边形电阻或电容网络的等效值研究  

Research on equivalent resistance or capacitor of enhanced polygon network

作　　者：谭志中[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《大学物理》2011年第12期29-32,37,共5页College Physics

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)资助

摘　　要：规则联接的多边形电阻或电容网络等效值的统一研究已经取得了一些结果,但对于多边形网络中的参数值为任意情形下的等效值问题尚缺乏研究.本文采用网络分析研究方法,实现了加强型多边形电阻或电容网络等效电阻或电容的统一建构,获得了简洁的等效电阻或电容的通用公式,所得结论也适用于多边形概念拓展到非平直空间的二边形(二角形)情形.最后将所得结果与相关结果进行了比较,说明了所得结论也适用于多边形复阻抗网络.Some results for the study of equivalent resistance of regularly connected polygon resistance network have already obtained, however, the study of unitive equivalent is still lacked if the parameter value （resistance or capacitor） in the polygon network is arbitrary constant. We analyze the network, construct a model based on difference equation and study unifying of equivalent resistance or capacitor of enhanced polygon network. We get a laconic general formula of equivalent resistance or capacitor of enhanced polygon network by analyzing the network, and obtain a simple expression of Fibonacci sequence in the meantime. We also expand the polygon concept arrives to two sides structure of the non-Euclid space. The results are compared with connected argument. The conclusion is also suitable to some regularly connected polygon impedance networks.

关 键 词：规则多边形 网络分析 等效电阻或电容 统一建构 非平直空间 费波那契数列 

分 类 号：O441.1[理学—电磁学]