基于矩阵束方法的传输线系统瞬态响应分析

Transient response analysis on the transmission line system based on matrix pencil method

摘要:

带有频变负载的传输线系统的瞬态响应分析是电磁兼容领域的一个重要内容，特别是对于频变负载网络较为复杂或内部结构不清晰的情况，其瞬态响应的分析较为困难。本文首先在采样频率点处对频变负载端口导纳进行测量或计算得到相应的采样导纳，并采用有理函数逼近的方式对端口导纳进行等效；之后采用矩阵束(MPM)方法求解出有理逼近函数所需的极点和留数，并将其代入到分段线性递归卷积(PLRC)技术中，实现传输线和频变负载连接点处电压的分段线性递归卷积表达；最后，结合传输线方程实现带有频变负载的传输线系统的瞬态响应分析，并通过2个算例对所提方法的性能进行验证。结果表明，所提方法在计算精确度上具有明显的优势。

Abstract:

Transient response analysis of Transmission Line(TL) systems with frequency-dependent load is an important topic in the field of electromagnetic compatibility, especially for the situation where the frequency-dependent network is more complicated or the internal structure is not clear, the corresponding analysis of its transient response is more difficult. In this paper, firstly, the corresponding sampling values are obtained by measuring or calculating the admittances of the frequency-dependent loads at the sampling frequencies, and the equivalence of the admittances is performed by adopting the rational function approximation; then, the Piecewise Linear Recursive Convolution(PLRC) expression of the voltage at the connection point between the TL and frequency-dependent loads is obtained by bringing the poles and residues solved by Matrix Pencil Method(MPM) into the PLRC technique; finally, the transient response analysis of the TL system with frequency-dependent loads is obtained by combining the MPM, PLRC and TL equation, and the performance of the proposed method is verified by two numerical examples. The results illustrate that the proposed method has obvious advantages in calculation accuracy.