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Electromagnetic radiation from complex printed circuit boards can occur over a broad frequency bandwidth, ranging from hundreds of megahertz to tens of gigahertz. This is becoming a critical issue for assessment of EMC and interoperability as electronic components become more and more integrated. We use emissions from an enclosure with a single-slot aperture and equipped with operating electronics to exemplify and model such sources. Spatial correlation functions obtained from two-probe measurements are used both to characterize the source and to propagate the emissions. We examine emissions in the submicrowave frequency range, where evanescent decay dominates the measured correlation function at the distances measured. We find that an approximate, diffusion-like propagator describes the measured emissions well. A phase-space approach based on Wigner functions is exploited to develop this approximation and to provide enhanced understanding of the emissions.

The radiation from complex PCBs can be characterized through a statistical approach involving the field-field correlation. A two-probe measurement technique is developed to measure the stochastic electromagnetic (EM) emission from an Arduino Galileo board in an enclosure in the time domain at two different heights. The Wigner distribution function, which is a representation in phase space, is used to understand the mechanics of near field emissions. The evolution of the field-field correlation function and Wigner function is observed for both measurements. These results serve as a proof of principle for understanding that Wigner Function is a good candidate to understand whether the concept of radiation pattern can be extended to near field.

Emergent wireless telecommunications and 5G mobile networks will operate at very high frequencies, ranging from microwave (5GHz) to mmWave (28GHz and beyond) regimes. Indoor coverage is challenging at these frequencies, where environments are expected to be highly overmoded. We perform full-wave Transmission Line Matrix simulations of a test electromagnetic environment. For electrically large, multiply connected rooms with simple polygonal irregularities, e.g. blades, we show that different regimes occur in the spatial field pattern as the frequency increases. From 1 GHz to 5 GHz the pattern is speckled. At 8 and 12 GHz we observe the emergence of specular components existing on a noisy background. The statistics of fields in the background are important for small scale fading in non-line-of-sight conditions. We characterize the spatial statistics of the test environment. Because of coupling and partially regular boundary, fluctuations acquire non-generic features, and they result in non-Rayleigh distribution functions at the investigated frequencies. The resurgence of directionality in the high microwave regime has an effect in fading statistics in a similar way of shadowing, from which background field statistics are fitted by fat tail (Bessel K) distribution. However, since the transition from low to high microwave regimes has no defined separation between specular and noisy components, generated by reflection and diffraction, ray tracing algorithms — more appropriate to predict energy of specular components — need to be extended to cope with noisy fields. We envisage these methods to be fundamental in the description of mmWave propagation. The achieved results are useful to create channel models for the outdoor-to-indoor transition and to extend mobile signal coverage to indoor regions.