Fractional-Order lossy transmission line with skin effect using NILT method

Abstract

The paper describes a method of modelling lossy transmission lines with frequency dependent parameters in the fractional-order domain. It is shown that in high frequency systems the frequency dependence of the transmission line (TL) and other related losses are essential to be considered in the model. In this paper fractional-order domain is used to model the lossy transmission line, which compensates for losses and provides higher flexibility and more reality for the TL analysis and simulation. As for the frequency dependence of the TL skin effect is included in the model, due to its high impact in high frequency applications. Analysis of a TL is processed in the Laplace-domain which effectively simplifies the solution. Though, the difficult or even impossible part is to obtain the required original time-domain from the results by analytic means. In order to overcome this difficulty a numerical inverse Laplace transform (NILT) method is introduced in this paper. The NILT method is implemented successfully, and the voltage/current waveform distributions along the lossy fractional-order TL are simulated and the results are displayed. The model is effectively tested and realized in the Matlab language.