Electromagnetic coupling to transmission lines under complex illumination

Abstract

Introduction: Electromagnetic wave coupling to transmission lines has received much attention for many years. This classical EMC problem has recently evolved from deterministic models to statistical analysis [1]. This latter approach has been shown to be more suited to the modelling of realistic situations when transmission lines are immersed in diffused wireless communication systems. In the related works, the localisation and polarisation of the interference sources are considered as random variables, and closed form expressions or numerical approximations are derived concerning the statistical distribution of the induced voltage. A usual limitation of this approach is however the single interference source assumption leading to a single interference field impinging the lines. In confined situations, dense multipath environment, or when several transmitters are present, a better modelling might be obtained by considering a more complex excitation of the lines. In this Letter, a general formalism based on a plane wave spectrum illumination is proposed to study such a case. Formalism: Let a uniform and lossless bi-filar transmission line be located at the origin of a Cartesian co-ordinate system. The line is directed along the z axis, the spacing between the conductors is b ,t he conductor radius a, and the line length s. At z ¼0, the line is fed by a sinusoidal source V0 of impedance Z0. At the far-end, a load impedance Zs terminates the line. Using transmission line theory, the current flowing on the line is given by