摘要
研究了一类非对称的n阶网络任意两个节点间的等效电阻及LC复阻抗网络问题.首先给出n阶网络的两个等效电阻公式,然后采用网络分析构建差分方程模型,以及边界条件方程和电流在输入与输出点的约束方程,证明所给出的两个等效电阻公式的正确性.同时给出无穷网络的等效电阻公式,并将特殊情形下的结论与其他结论进行了对比与讨论.将文章所提出的方法和得到的结论应用于复阻抗网络的研究中,分析了一类LC网络的等效复阻抗问题,绘制出相应的复阻抗随频率变化的图形,发现了LC网络在特定条件下的振荡特性和共鸣特性.
The problem of the equivalent resistance between any two nodes of an asymmetric n-step resistor network and its LC network was investigated. First of all, two general formulae of equivalent resistance between any two nodes of an n-step resistor network were proposed;Second, the differential equation by the method of network analy- sis was modeled, and the constraint equation by the currents of input and output was also modeled, thus the formula of equivalent resistance was proved by using the above equations;In the meantime, the formula of equivalent resis- tance in the infinite network is given, and the conclusions in special cases were compared and discussed with other conclusions, and validate the correctness of the conclusions obtained in this paper. As applications, the proposed method and results were suitable for the research of complex impedance network as well, an n-step LC impedance network was further explored in detail, and the corresponding graphics of the complex impedance changes with the change of parameters was drawn, and the characteristics of oscillation and resonance in the LC network under certain conditions was found.
作者
王一骁
余清怡
谭志中
WANG Yixiao YU Qingyi TAN Zhizhong(School of Sciences, Nantong University, Nantong 226019, China)
出处
《南通大学学报（自然科学版）》
CAS
2017年第2期46-55,共10页
Journal of Nantong University(Natural Science Edition)
基金
江苏省自然科学基金面上项目(BK20161278)
南通大学教学改革研究项目(2015B01)
关键词
电路网络
差分方程
等效电阻
基尔霍夫定律
共鸣
circuit network
difference equation
equivalent resistance
Kirchhoff＇s law
resonance
