Experimental Exposure Evaluation From the Very Close Near- to the Far-Field Using a Multiple-Multipole Source Reconstruction Algorithm

Abstract

Exposure assessment of wireless devices operating at ≥6 GHz requires measurement of power density (PD) from a distance of 2 mm ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\geq \lambda $ </tex-math></inline-formula> /25) from the surface of the device (reactive near field) to the far field with minimal uncertainties. The challenges are field distortion and backscattering by the probe, spatial resolution, sensitivity, isotropy, and phase accuracy. In addition, the surfaces of the device may not be planar. Today, methods based on phaseless amplitude measurements are widely applied using plane-to-plane phase reconstruction (PR) to obtain the field phasors. The obtained phasors in conjunction with Maxwell’s equations allow to evaluate the fields in the whole volume of interest. Although these methods meet the PD compliance criteria for flat surfaces at distances as close as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda /5$ </tex-math></inline-formula> , they are unsuited for curved surfaces and closer distances. To overcome these limitations, we present a method based on a multiple-multipole expansion for accurate PD evaluation in all field regions using sparse phaseless electric field measurements. We construct a physically relevant vectorial basis in terms of elementary electric or magnetic dipoles and optimize their amplitudes such that the measured fields are reproduced with minimal error. The proposed procedure yields current distributions that resemble the physical radiation source and accurately reconstruct the electromagnetic field from the (reactive) near-field to the far-field regions with an uncertainty of <0.6 dB. Our approach does not pose any geometric requirements to the measurement or evaluation surfaces and thus supports conformal assessments, providing a potential solution for accurate PD evaluation of 5G devices and beyond.