基于对称性研究2×n阶梯形电阻网络等效电阻

Research on the equivalent resistance of 2×n order ladder resistance network based on the symmetry

在分析2×n阶梯形电阻网络对称性的基础上,对任意负载电阻的n阶梯形电阻网络构建等效电阻的递推关系,经过简单的等效变换得出n阶梯形电阻网络等效电阻的通项公式,并将该公式和图2电路用于分段计算n阶和2×n阶梯形电阻网络的等效电阻,以及直接用于计算2×n阶梯形电阻网络等效电阻的通项公式.这项研究揭示了n阶、2×n阶梯形电阻网络的内部以及它们之间存在的紧密联系.采用这种方法能使研究过程大为简化.

On the basis of analyzing the symmetry of 2 × n order ladder resistance network and by using the recurrence relation in constructing equivalence resistance for n order ladder resistance network for arbitrary resistance load,the general term formula of n order ladder resistance network is obtained through simple equivalent transformation. The formula is applied to the piecewise calculation of equivalent resistance of n order and 2 × n order ladder resistance network and also applied to the calculation of the general formula for 2 × n order ladder resistance network. The present study reveals the close relation between the n order ladder resistance network and the 2 × n order ladder resistance network and the inner rules of them. The complexity of the research is eliminated by using this method.