Theoretical and Numerical Assessment of Maximally Allowable Power-Density Averaging Area for Conservative Electromagnetic Exposure Assessment Above 6 GHz

Esra Neufeld, Eduardo Carrasco, Manuel Murbach, Quirino Balzano, Andreas Christ, and Niels Kuster, Bioelectromagnetics December 2018, Volume 39, Issue 8, pp. 617–630; online 01 November 2018; doi: https://doi.org/10.1002/bem.22147

The objective of this paper is to determine a maximum averaging area for power density (PD) that limits the maximum temperature increase to a given threshold for frequencies >6 GHz. This maximum area should be conservative for any transmitter at any distance >2 mm from the primary transmitting antennas or secondary field-generating sources. To derive a generically valid maximum averaging area, an analytical approximation for the peak temperature increase caused by localized exposure has been developed. The results for a threshold value for the temperature increase of 1 K have been validated against simulations of a series of sources composed of electrical and magnetic elements (dipoles, slots, patches, and arrays) that represent the spectrum of relevant transmitters. The validation was successful for frequencies at which power deposition occurs superficially, i.e., at >10 GHz. In conclusion, the averaging area for a PD limit of 10 W/m² that conservatively limits the temperature increase in the skin to less than 1 K at any distance >2 mm from the transmitters is frequency dependent, increases with distance, and ranges from 3 cm² at <10 GHz to 1.9 cm² at 100 GHz. In the far-field, the area depends additionally on distance and the antenna array aperture. The correlation was found to be worse at frequencies <10 GHz and very close to the source, the systematic evaluation of which is part of another study on the ratio of temperature increase to incident power density to investigate the effect of different coupling mechanisms in the reactive near-field. The model presented herein can be applied directly to all other PD and temperature thresholds.

The scientific and technical impact of the study can be summarized as:

• Analytical relationships for localized exposure in the 5G frequency range that permit estimation of temperature increase and conservative limits on the acceptable PD averaging area have been established for devices positioned as close to the body as 2 mm
• The predictions have been validated against simulations performed with conservative models of layered skin configurations exposed to a range of single antennas and antenna arrays in the frequency range of 10 – 100 GHz
• For frequencies >30 GHz, the analytical predictions of temperature increase generally deviate from the simulation results by <25%
• The results demonstrate that a conservative averaging area can be expressed as function of frequency, distance from the transmitter, and – in the far-field – antenna aperture