2×n阶网络对角等效电阻的另一种公式

Another General Formula on the Diagonal Equivalent Resistance of 2×n-Rank Network

通过网络分析构建差分方程组模型,构建巧妙的矩阵变换方法,得到了差分方程组模型的通解。根据通解并结合2×n阶电阻网络的边界条件,给出2×n阶电阻网络对角等效电阻的另外一种形式的普适规律,研究表明,2×n阶网络对角节点间的等效电阻可以有不同的表达形式,但彼此具有等价性。在与其它相关结果比较时得到了一个有意义的公式,对探求其它节点间的等效电阻之间是否也存在关系很有启发意义。

A general solution of a difference equation model was obtained after the construction of the difference equation model and matrix transform through network analysis. Based on the general solution and different marginal conditions of 2×n-rank network, we propose another form of general formula for the diagonal equivalent resistance of 2×n-rank network. It is proved that the diagonal equivalent resistance of 2×n-rank network can have different forms but they have equal value. Furthermore a significant formula was achieved in comparison with another relative result.