一种计算有损均匀传输线正弦稳态解的方法

Method of Computing Sinusoidal Steady-state Solutions of Lossy Uniform Transmission Lines

由偏微分方程描述的均匀传输线至今还未有一种通用的求解方法,因此众多学者对传输线的理论问题仍在不断的探索和研究,其中均匀传输线稳态解的计算也是所研究的内容之一.提出了另一种计算有损均匀传输线正弦稳态解的方法.首先建立有损均匀传输线的复频域模型,解得线上电压电流在任意激励下的复频域解,随即得到关于线上电压电流的网络函数.然后根据网络函数与系统频率特性的关系,得出线上电压电流在正弦激励下的稳态解,最后通过计算实例验证了该结果的正确性.

There is no universal method of finding the analytic solutions to transmission lines discribed by partial differential equations, so many researchers are studying and developing transmission line theories. Computing steady-state solutions of uniform transmission lines is one part of the study. The paper introduces another method of computing sinsoidal steady-state solutions of lossy uniform transmission lines. First, the complex expressions of voltage and current with zero initial state are obtained from the complex frequency-domain model of lossy uniform tansmission lines. The network functions, which are the ratios of voltage and current＇ s image functions to the excitation＇ s image function, can be found from tile complex expressions. Sinusoidal steady-state solutions can be obtained by using the relation between network function and system＇s frequency characteristic. Finally, the method is demonstrated to be effective by an example.