Relationship between the impedance matrix and the transfer matrix with specific reference to symmetrical, reciprocal and conservative systems
Relationship between the impedance matrix and the transfer matrix with specific reference to symmetrical, reciprocal and conservative systems
复制标题
阻抗矩阵和传递矩阵之间的关系，具体参考对称、互易和保守系统
DOI：
10.1006/jsvi.1993.1089
复制
发表时间：
1993
影响因子：
4.7
通讯作者：
M. Munjal
中科院分区：
文献类型：
--
作者：
V. Easwaran;Vh Gupta;M. Munjal
阻抗矩阵法和传递矩阵法是线性动力系统分析中常用的方法。本文推导了这些矩阵之间的一般关系。研究了对称系统、互易系统和保守系统的阻抗矩阵和传递矩阵的性质。在此过程中，得出以下结论：(a)对称系统不是常被误解的互反系统的子集；(b)互反系统的级联再次产生互反系统，而对称系统的级联不一定产生对称系统；(c)传递矩阵的行列式为±1，是对称系统和互易系统的一个性质，但这个条件不足以建立系统的互易性或对称性；(d)保守系统的阻抗矩阵是斜厄米矩阵。
Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.