Quantitative Comparison of Power Densities Related to Electromagnetic Near-Field Exposures With Safety Guidelines From 6 to 100 GHz
Kun Li, Kensuke Sasaki, Kanako Wake, Teruo Onishi, Soichi Watanabe
Abstract
This paper presents a quantitative analysis of the differences between the various definitions of spatially averaged power densities ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> ) for localized exposure to electromagnetic near-fields at frequencies from 6 to 100 GHz. The spatially averaged modulus of the complex Poynting vector ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula> ) and spatially averaged norm of the real part of the complex Poynting vector ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula> ) were compared using numerical approaches, where their relationships with the spatially averaged absorbed power density ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sAPD</i> ) and the local peak temperature elevation on skin tissue were analyzed. Our results demonstrated that outside the typical boundary of the reactive near-field, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$> \lambda $ </tex-math></inline-formula> /( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi$ </tex-math></inline-formula> ), which is used as a rough guide of the applicable condition for reference levels in the RF safety guidelines, but at most 10 mm from the radiation source, the maximum difference between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula> is smaller than 0.7 dB from 6 to 100 GHz. For the appropriate conditions recommended in the RF safety guidelines, the differences between the ratios of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sAPD</i> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> and those for the plane-wave normal incidence, are at most 1.4 dB and 0.9 dB for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{norm}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{mod}$ </tex-math></inline-formula> , respectively. Under the same condition, the ratios of the temperature rise to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> for the relatively small antennas (total dimension less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\lambda$ </tex-math></inline-formula> ) do not significantly exceed that for the plane-wave normal incidence, which means that the expected maximum temperature rise is lower than the temperature rise that is derived from the operational health effect threshold in terms of the temperature rise divided with the reduction factors employed in the RF safety guidelines. The above results provide suggestive evidence that the effect of the definition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$sIPD_{s}$ </tex-math></inline-formula> on the human exposure characteristics is not significant compared with those of the other factors, i.e., the antenna type (size), frequency, distance from the source, and averaging area.