非规则3×n阶Hammock电阻网络的等效电阻  

Equivalent resistance of irregular 3 × n Hammock resistor network

作　　者：谭志中[1] TAN Zhizhong(School of Sciences,Nantong University,Nantong 226019,China)

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）》2022年第3期71-77,共7页Journal of Nantong University(Natural Science Edition)　

基　　金：江苏省自然科学基金项目(BK20161278)。

摘　　要：采用RT-I理论研究一类非规则3×n阶Hammock电阻网络的等效电阻,其中以支路电流为变量,并且应用基尔霍夫定律建立三阶矩阵方程及三阶边界条件方程,采用对角化矩阵变换获得矩阵差分方程的通解与特解。研究发现了非规则3×n阶Hammock电阻网络的3个系列的等效电阻解析式。该网络模型包含p和q两个任意参数,使得该网络代表了多种功能的网络模型,取不同的p和q参数可以用于研究一系列不同结构网络的电特性。该研究工作为未来相关的科学研究与应用提供了新的理论基础,也为相关的复杂网络研究提供新的思路。The equivalent resistance of a kind of irregular 3 × n Hammock resistor network is studied by the RT-I theory,in which the third order matrix equation and the third order boundary condition equation are established by Kirchhoff′s law and the branch current is taken as the variable.The general and specific solutions of the matrix difference equation are obtained by using the diagonal matrix transformation.In this paper,three series of equivalent resistance solutions for irregular 3 × n Hammock resistor networks are identified.The network model contains two arbitrary parameters p and q,so that the network represents a multi-functional network model.Taking different p and q parameters can be used to study the electrical characteristics of a series of networks with different structures.The result can provide a new theoretical basis for future research and application,and a new dimension for the related complex network research.

关 键 词：3×n阶Hammock网络 递推-变换理论 矩阵方程 电学性质 

分 类 号：O441.1[理学—电磁学]