Non-local telegrapher’s equation as a transmission line model

Abstract

Transmission line displaying non-locality effects is modelled by considering the magnetic coupling of inductors in the series branch of Heaviside's elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given non-local magnetic flux through the cross-inductivity kernel. Non-local telegrapher's equations are derived as the continuum limit of corresponding Kirchhoff's laws and solved for prescribed external excitation analytically by the means of integral transforms method and also numerically. Numerical examples of the mollified impulse responses illustrate the non-local behavior of signal propagation in case of power, exponential, and Gauss type cross-inductivity kernels.