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.Index Terms-Absorption cross section (ACS), printed circuit board (PCB) trace, stochastic electromagnetic fields, transmissionline coupling.

The ability of an enclosure to protect its contents from electromagnetic interference is quantified by its shielding effectiveness. Previous research has proved that the contents of an enclosure may greatly change the internal field and thus the shielding effectiveness. The power balance method is an efficient approach to analyze shielding problems of populated enclosures. One assumption of the power balance method is that in the steady state, the electromagnetic field in an enclosure is homogeneous. In actual circumstances, however, the presence of losses in an enclosure often compromises the field homogeneity and the power balance method may become inaccurate. A diffusion equation approach has been previously proposed to overcome this problem. In this paper, we predict the internal electromagnetic field of a populated enclosure by using the diffusion model, and compare them with the fields obtained by the power balance method, a fullwave electromagnetic solver and measurements, to demonstrate its efficacy. Comparisons between the diffusion model and the power balance method show that for populated enclosures, the internal electromagnetic field varies with position and that the diffusion model allows this to be observed.

The power balance technique for the prediction of shielding effectiveness of reverberant enclosures is fast and simple to use. However, it assumes a uniform field in the enclosure, which has been shown to be incorrect in the presence of dissipative contents. The diffusion model is a generalization of the power balance method that can account for the field inhomogeneity due to the presence of losses with much lower computational effort than a full wave solver. Evaluation of a 2D diffusion model produced promising results compared to physical measurements. Here we present a 3D diffusion model applied to an enclosure with an aperture and dissipative contents. Comparisons between the 3D diffusion model, measurements and a full wave solver suggest that it is able to account for the variation of the electromagnetic field due to dissipative contents with far less computational effort than full wave solvers. The diffusion model allows rapid solution of the shielding effectiveness of enclosures with dissipative contents and arbitrary geometries. and reduces the time to model equipment enclosures from hours to minutes, whilst still determining the variation of field strength due to contents. In addition, the method may help predict field inhomogeneity in reverberation chambers.

Knowledge of the shielding effectiveness of an enclosure is important for the electromagnetic compatibility of electronic systems. The shielding effectiveness of an enclosure depends on the absorption cross section of its contents. It might be expected that the energy absorption in an electronic circuit changes according to the operating state of the semiconductor devices which compose the active components. In most published research, the absorption cross section measurements were performed when the contents were unpowered. In this paper we compare the measured absorption cross sections of the components of a personal computer in powered and unpowered states. Comparisons indicate that power and the particular operating configuration do not have a significant influence on the absorption cross section. This means that the process of determining absorption cross sections of circuit boards and other components can be easily achieved without the need to provide power and define a particular operating state.