A Probabilistic Study of Common-Mode and Differential-Mode Responses of a Plane-Wave Excited Twisted-Wire Pair Above a Perfect Ground Plane

This article presents a probabilistic approach for the immunity/susceptibility assessment of a twisted-wire transmission line in the presence of a perfect ground plane. A random electromagnetic field is assumed to excite the transmission line, which is essentially modeled as a plane wave with certain parameters (magnitude, polarization angle, direction-of-arrival angles) treated as independent random variables. Closed-form expressions are provided for the probability density function of the induced common-mode and differential-mode terminal voltages in certain cases. New formulas for the pertinent first and second moments (mean values and mean square values) are also obtained. A general Monte Carlo technique is employed to verify the aforementioned closed-form expressions, but also for treating excitation scenarios that are not analytically tractable.