n阶网络任意2节点间的等效电阻公式

Formula of equivalent resistance between any two nodes of n step network

研究了一类n阶电阻网络任意2节点间的等效电阻问题,解决了一个之前一直没有解决的电阻网络难题.首先给出了一个任意2节点间等效电阻的普适公式,然后采用网络分析方法构建了差分方程模型以及边界条件约束方程模型,由此证明了所给出的等效电阻公式.最后给出了无穷网络的等效电阻公式,并且将特殊情形下的结论与其他结论进行了对比与讨论,验证了本文所得结论的正确性.

Considering the equivalent resistance between any two nodes of n step resistor network,which is a difficult problem that has not been solved before.First of all,we present a general formula of equivalent resistance between any two nodes of n step resistor network. Second,we model the differential equation by the method of network analysis,and model the constraint equation by the currents of input and output,thus the formula of equivalent resistance is proved by using the above equations.Finally,the formula of equivalent resistance of infinite network is given,and the conclusions in special cases are compared and discussed with other conclusions,and thus the correctness of the conclusions obtained is validated.