内嵌交叉电阻的N阶多功能电阻网络的等效电阻研究  

Study on Resistance Formulae of a Multipurpose N-Step Network with Cross Resistors

作　　者：谭志中[1] 

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《南通大学学报（自然科学版）》2016年第1期49-57,共9页Journal of Nantong University(Natural Science Edition)　

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(2015B01)

摘　　要：研究了一类内嵌交叉电阻的N阶多功能电阻网络模型,这是一个之前一直没有解决的问题.该网络模型含有8个任意参数使得该网络包含了多个不同的网络类型.解决该问题包括以下4个步骤:首先建立一个简化的等效模型;其次应用基尔霍夫定律建立一个非线性差分方程模型;再次采用变换的方法给出非线性差分方程的解;最后建立了一个负电阻元素概念,得到了理想的研究结果,并给出数个有趣的特殊结论.该研究方法和得到的结论也适用于复阻抗网络的研究.A multipurpose N-step network with cross resistors was studied. The network model contains eight arbitrary parameters which make the network contain a number of different types. This problem was resolved by four steps：First of all, a complex graphics was simplified into a simple equivalent model;Then Kirchhoff′s laws were employed to analyse the network and establish a nonlinear difference equation;Next, the method of equivalent transformation was constructed to obtain the general solution of the nonlinear difference equation. Finally, a new concept of negative resistance for the needs of the equivalent conversion was constructed, and two general resistance formulae of a multipurpose ladder network of cross resistors were obtained. Base on these four steps several interesting and specific results are gained. The proposed method and the results were suitable for the research of complex impedance network as well.

关 键 词：内嵌交叉电阻 多功能网络 等效变换 非线性差分方程 基尔霍夫定律 负电阻 

分 类 号：O441.1[理学—电磁学] TN711.3[理学—物理]