一类时间分数阶传输线模型及仿真分析

A Time-Fractional Transmission Line Model and Its Simulation

针对传输线电压、电流波的传播特点,采用推广的时间分数阶传输线方程来描述传输线上电压、电流波的反常扩散过程;并应用分数阶Adomian分解方法对时间分数阶传输线方程进行瞬态分析,最后给出了无损传输线传输过程的仿真实例.仿真结果表明,引入时间分数阶导数的无损传输线模型能很好地描述无损传输线上电压、电流波的传播和扩散过程的瞬态特点,对于传输线的瞬态分析具有一定的实际意义,与常用的分数阶Laplace算法等相比,提出的求解算法具有仿真时间短、数据量较少和计算简单等特点.

In view of the fluctuating propagation of voltage/current wave in transmission line, a generalized time-fractional equation is used for transmission line to express the abnormal diffusion process of the voltage/current wave. Introducing the Adomian decomposition method, transient analysis is made to the generalized equation with a simulation done as instance for lossless transmission line. Simulation results showed that introducing the derivative of the time-fractional equation into the lossless transmission line model is available to express well the transient characteristics of the propagation/diffusion process of voltage/current wave in such a line, and it is of practical importance to the transient analysis of transmission line. In comparison with the conventional fractional Laplace algorithm, the method proposed is shorter in simulating time, and simpler in computation with less data required.