Modeling and Simulating Transmission Lines Using Fractional Calculus

Transient analysis of transmission lines has recently been received more attention because operating speeds in high - speed digital electronics are increasing. This paper presents a new direction for transient analysis of the transmission lines. The laws of the voltage or current wave transmits in the transmission line obey to diffusion phenomenon. Transmission line equations are hyperbolic partial differential equations, firstly changing transmission line equations into diffusion equations. This paper discusses the transient responses of the voltage or current wave in the transmission line using fractional calculus. We present the analytic solution for the diffusion equations with the help of the boundary condition and the input-output behavior of the transmission line can be modeled by a fractional operator with a parameter of the value of the derivation order [0, 1]. Finally the paper computes transient response of transmission line with two typical input functions. Numerical result shows that this approach is an effective way.