一类n阶三脚架电阻网络的等效电阻研究  

A study of the equivalent resistance of an n-step network with tripod structure

作　　者：谭志中[1] 陆建隆[2] 

机构地区：[1]南通大学物理系,江苏南通226019 [2]南京师范大学教师教育学院,江苏南京210097

出　　处：《大学物理》2016年第12期13-18,共6页College Physics

基　　金：南通大学自然科学类科研基金前期预研项目(15ZY16);南通大学教学改革研究项目"大学物理教学与科研相长模式研究"(2015B01)资助

摘　　要：研究了一类n阶三脚架网络的等效电阻模型,该模型含有7个不同的电阻元素,因而包含了多个网络模型.文章采用构建等效模型的方法导出了一个非线性差分方程模型,采用变量代换的方法间接地给出了非线性差分方程的通解.本文进一步创造了一个负电阻的概念,获得了电阻网络任意节点间的等效电阻公式.利用特殊条件下的数个特殊例子与相关结果进行了比较.本文的结论也适用于复阻抗网络的等效复阻抗研究.We study the equivalent resistance of an n-step network with tripod structure,which is a profound problem, has not been resolved before. The network model contains seven arbitrary parameters which make the network contain a number of different types. First of all, we establish a nonlinear difference equation by means of simplifying a complex graphics into a simple equivalent model; next, we construct the method of equivalent transformation to obtain the general solution of the nonlinear difference equation. Finally, we create a new concept of negative resistance for the needs of the equivalent conversion, and obtain two general resistance formulae of an n-step network with tripod structure. We compare several results by making use of a number of specific examples in the special conditions. Our method and the results are suitable for the research of complex impedance network as well.

关 键 词：三脚架网络 等效模型 非线性差分方程 等效变换 负电阻 

分 类 号：O441.1[理学—电磁学] TN711.3[理学—物理]