Exploration of the effect of fractional elements in nonlinear transmission lines
Purpose
The purpose of this paper is to explore how fractional derivatives affect the transient and steady-state behaviour of nonlinear transmission lines. This problem is of significance for high-frequency design of systems such as high-speed sampling systems and radar systems.
Design/methodology/approach
This paper shall consider the transient and steady-state responses of nonlinear transmission lines when fractional derivatives are considered. A lumped-parameter model is considered and the product-integration implicit trapezoidal rule shall be used for simulations.
Findings
The important observation is that small deviations of the order of the derivative from an integer order can have a significant effect on the transient and steady-state behaviour. This includes a change in the speed of the wave on the transmission line and on its damping.
Originality/value
The work is novel as it uses a lumped-parameter model with nonlinear capacitors and explores the effect on the dynamical behaviour when fractional derivatives are present. This is in contrast to the typical approach of using a partial differential equation derived under certain assumptions such as the nature of the nonlinear capacitor.
