大学物理 ›› 2018, Vol. 37 ›› Issue (8): 24-28.doi: 10.16854 /j.cnki.1000-0712.170560

• 教学讨论 • 上一篇    下一篇

一类任意n 阶Fan 网络的电特性研究

谭志中,吴鹏,罗小廉,孔泽霖   

  1. 南通大学物理系,江苏南通,226019
  • 收稿日期:2017-10-12 修回日期:2018-03-09 出版日期:2018-08-20 发布日期:2018-08-20
  • 作者简介:谭志中(1965—),男,南通大学物理系教授,硕导,主要从事理论物理研究与物理教学研究工作.
  • 基金资助:
    国家级大学生创新创业训练计划项目(20171304006);江苏省自然科学资金面上项目(BK20161278)资助

Research on electric properties of an n-step Fan network

TAN Zhi-zhong,WU Peng,LUO Xiao-lian,KONG Ze-lin   

  1. Department of physics,Nantong University,Nantong,Jiangsu 226019,China
  • Received:2017-10-12 Revised:2018-03-09 Online:2018-08-20 Published:2018-08-20

摘要: 研究了一类n 阶Fan 电阻网络的电特性(任意节点的电压,等效电阻),取得了理论和方法上的创新. 文章以节点电压为变量应用基尔霍夫定律建立二阶差分方程模型以及边界条件方程模型,通过研究差分方程的通解与特解,获得了n阶Fan 网络任意节点的电压公式,同时获得了任意2 节点间的等效电阻公式,并分析与讨论了结论的特殊情形. 本课题的研究工作实现了教学与科研的协同相长.

关键词: Fan 网络, 电位公式, 等效电阻, 差分方程, 教学科研相长

Abstract: The electrical properties (including the voltage of any node,and equivalent resistance) of a class of n-step Fan resistor network are studied,and innovation in theory and method has been achieved. In this paper,the second-order difference equation model and the boundary condition equation model are established by using the node potential as the variable in terms of applying Kirchhoff's law. By studying the general solution and special solution of difference equation,the voltage formula of arbitrary node of n-order Fan network is obtained,at the same time,the equivalent resistance formula between any two nodes is obtained as well,and the special situation of the conclusion is analyzed and discussed. Our research work realizes the cooperation and mutual benefit between teaching and scientific research.

Key words: Fan network, voltage formula, difference equation, equivalent resistance, mutual benefit between teaching and research