Nonuniform lossy transmission lines with fractional-order elements using NILT method

The paper introduces a generalization of non-uniform lossy transmission line modeling approach in the fractional-order domain. The concept is based on proposing fractional-order elements rather than the classic integer orders in the transmission line (TL) model. In recent years higher attention is being paid to fractional-order calculus due to its potential field of applications, especially in electrical engineering. As for TLs, it is shown that fractional-order modeling provides a higher degree of freedom for optimization and compensates for power losses along the transmission line, especially in high frequency applications. Moreover, due to the rapid evolution of operating frequencies and transmission speeds, the frequency dependent parameters, such as a skin effect, are considered in the presented model. Through this work, we will be showing the impact of fractional-order primary elements and skin effect on the TL model. The paper further describes the utilization of the numerical inverse Laplace transform (NILT) method to provide a feasible time-domain solution of the model. In recent work, the NILT method was introduced, and was further enhanced by adapting the quotient-difference infinite series convergence acceleration technique. Besides, it is shown that by utilizing this NILT method, it is possible to effectively incorporate fractional orders and frequency dependence of the TL in the frequency domain, hence competently simplifying the solution. The TL is simulated in the MATLAB environment. The results are compared for several cases, namely, for uniform and non-uniform TL, for cases with frequency dependent parameters and for those without.