用FDTD法求解传输线方程

传输线的电路模型—电报方程(一阶双曲型偏微分方程组)是分析传输线暂态过程的出发点。借助电路理论、计算数学、程序设计等知识推导出一种简单、快速、有效的时域数值解法。利用有限时域差分理论对偏微分方程组进行离散,得到一种全新的差分计算格式,并根据电压、电流在始端、终端上的约束关系,运用传输线集中参数的等效模型确定边界条件;最后仿真计算得到响应波形。并对传输线在不同边界条件、传输线耦合等情况下的暂态过程进行MATLAB编程计算得到仿真波形。并将其仿真波形与EMTP-ATP软件仿真得到的波形进行对比,验证了此方法的可行性。

Using the finite-difference time-domain (FDTD) method to solve transmission-line equations

We Transmission line circuit model,telegraph equations(a hyperbolic partial differential equations),is the starting point of analyzing transmission lines transient process.A simple and quick and effective numerical solution in time domain has been deduced by the aid of circuit theory and computational mathematics and program design.The partial differential equation group has been discretized with the theory of FDTD solution,therefore a bran-new differential computation formation has been obtained.Furthermore,boundary conditions of the basic lumped equivalent circuit mode have been found according to constraints between voltage and current at the ends of lines.Finally voltage and current waveforms has been obtained by simulation.Matlab is used for the simulation of the transient of transmission line under various boundary conditions,various coupling conditions.Simulation results from Matlab are compared with waveforms by the EMTP-ATP simulation software,the efficient of the method is proved.