Numerical and Analytical Analysis of Stochastic Electromagnetic Fields Coupling to a Printed Circuit Board Trace

Abstract

Stochastic electromagnetic fields coupling to printed circuit board (PCB) traces are important to the understanding of electromagnetic compatibility at high frequencies when the circuits or systems are electrically large. In this article, it is studied both numerically and analytically, and the factors affecting the absorbed power are investigated. We present new methods to determine the level of coupling on PCB traces or other transmission lines on a dielectric substrate. A Monte Carlo method is applied to generate random uniform fields, and the quasi-TEM transmission line model is employed to compute the response of the trace for each plane wave numerically. In the analytical method, the closed-form expressions of the zero-order and the first-order approximations are established for the PCB trace. Based on the first-order approximation method and the numerical results, a computationally efficient empirical method is developed to estimate the power received. The absorbed power increases with frequency in the electrically short case after which multiple resonances can be seen. The absorbed power in the matched case is neither the largest nor the smallest among all the cases. It increases with the square of the substrate height but decreases with the permittivity of the substrate.