Simulation of Signal Propagation Along Fractional-Order Transmission Lines

In this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the frequency domain, multiplications with phase factors are executed, and finally the result is transformed back to the time domain. This algorithm involves elementary functions only and the fast Fourier transformation, hence, computations are numerically efficient and accurate. However, applicability of the method is limited by the sampling theorem. Numerical results are presented allowing for the evaluation of the method.