基于递推-变换方法计算圆柱面网络的等效电阻及复阻抗

发布时间：2018-04-14 00:14

本文选题：圆柱面网络 + 递推-变换方法　；参考：《物理学报》2017年07期

【摘要】：获得任意电阻网络等效电阻的解析解一直是科学和数学上的难题.本文采用递推-变换方法研究了一类任意m×n阶圆柱面网络的等效电阻及复阻抗问题.首先采用网络分析建立递推矩阵方程模型;其次构造对角化矩阵变换方法以便获得矩阵的特征值和特征向量,从而获得矩阵方程的通解;再次采用网络分析建立边界条件约束方程模型,进而获得矩阵方程的特解;最后利用矩阵逆变换给出支路电流的解析解,从而获得任意m×n阶圆柱面网络轴线上等效电阻的解析解,所得结果由特征根构成及单求和表达.作为公式的应用,给出了任意半无限和无限情形时的数个新的等效电阻公式,在与其他文献结论的对比研究中得到了一个有趣的新的三角函数恒等式.研究了圆柱面RLC网络的等效复阻抗问题,给出了精确的等效复阻抗公式.
[Abstract]:The analysis of arbitrary equivalent resistance network solutions is a difficult problem in science and mathematics. In this paper, the recursive equivalent resistance of push - transform method is studied for a class of arbitrary m * n order cylindrical network and complex impedance. First, using network analysis to establish a recursive matrix equation model; the structural diagonalization matrix transform method in order to obtain the eigenvalues and eigenvectors of matrices, so as to obtain the general solution of the equation; again using network analysis to establish the boundary condition equation model, and then get the solution of the matrix equation; finally, using matrix inverse analytic solution of the given branch current, thus obtained any m * n step network on the axis of the cylindrical surface of the equivalent resistance the solution results composed of eigenvalue and single summation expression. As the application of the formulas, given arbitrary semi infinite and infinite case when the number of new formulas of equivalent resistance, and in An interesting new trigonometric function identities is obtained in the comparative study of other literatures. The equivalent complex impedance problem of cylindrical RLC network is studied, and the exact equivalent complex impedance formula is given.

【作者单位】：南通大学物理系;南通大学数学系;
【基金】：江苏省基础研究计划(自然科学基金)面上项目(批准号:BK20161278)资助的课题~~
【分类号】：O441.1

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