用波形迭代法分析非均匀多导体传输线的时域响应

本文从频域电报方程出发推出了一个描述传输线ABCD矩阵的微分方程,将传输线时域响应分析从微分方程的边值问题转化为数学上更易求解的初值问题。然后利用波形迭代法数值求解非均匀传输线的ABCD矩阵,证明了一个关于迭代收敛性的定理,并据此采取了旨在加快收敛速度的将传输线分割成许多相互级联的子网络的步骤。传输线的ABCD矩阵求得后,便可借用付里叶变换和卷积技术对具有线性、非线性负载的传输线时域响应进行分析。给出的应用实例表明,诙分析方法是有效而可靠的。

Time-Domain Respones Analysis of Nonuniform Multiconductor Transmission Lines by the Waveform Relaxation Method

In this paper a differential equation describing the ABCD matrices of transmission is derived from the Telegrapher's equation in the frequency-domain,thus the problem of time-domain re-spones analysis is transformed from a differential equation with boundary conditions to one with an initial condition which much easier to solve.Then the waveform relaxation method is used to numerically solve the ABCD matrices of nonuniform lines.A theorem about the convergence of the waveform relaxation method is proven.After obtaining the ABCD matrices,the time-domain respones of arbitrarily loaded transmission lines is easily analyzed with the FFT and convolution techniques.The given exem-ple demonstrates that this approach is reliable and efficient.