Whole-body average SAR measurement using flat phantoms for radio base station antennas and its applicability to adult and child human models

Abstract

The specific absorption rate (SAR) measurement procedure for radio base station antennas using flat phantoms has been investigated and standardized by the International Electrotechnical Commission (IEC). This paper discusses the effectiveness of this procedure for considering Japanese human models based on numerical simulations with validation of whole-body average SAR (WBSAR) measurement. The WBSAR in two Japanese anatomical human models (adult male and 3-year-old child) and two box-shaped phantoms (large and small) using a standardized SAR measurement procedure are compared at 788 MHz and 3.5 GHz. Computational results show that the SAR measurement procedure in the IEC leads to overestimated WBSAR compared to those in Japanese anatomical human models. These results imply that the SAR measurement procedure above is applicable to not only some commonly used but Japanese human models. The WBSAR obtained using SAR estimation formulae in the IEC is also overestimated compared to those in Japanese anatomical human models. In addition, to reduce the measurement time and simplify the post-processing, this paper introduces a SAR measurement procedure based on the two-dimensional SAR distribution around the surface of the bottom of the phantom and the one-dimensional exponential decay of the SAR distribution in the direction of the phantom depth. SAR measurement examples of antennas for small radio base stations are also presented.

Appendix

The SAR estimation formulae for the WBSAR that are applicable to the main beam direction of radio base station antennas are given below [11].

$$ {SAR}_{wb}^{a, ch}(d)=C(f)\bullet \frac{H_{eff}}{{\overset{\sim }{A}}^{a, ch}\bullet {\overset{\sim }{B}}^{a, ch}}\bullet \frac{{\overline{P}}_{avg}}{\varnothing_{3 dB}\bullet L\bullet d}\bullet {\left[1+{\left(\frac{4\bullet \pi \bullet d}{\varnothing_{3 dB}\bullet D\bullet L}\right)}^2\right]}^{-1/2}\dots $$

(5)

where ${SAR}_{wb}^{a, ch}(d)$ is in W/kg and the superscripts “a” and “ch” denote “adults” and “children,” respectively. Moreover, ${\overset{\sim }{A}}^a$ = 0.089 m, ${\overset{\sim }{A}}^{ch}$ = 0.06 m, ${\overset{\sim }{B}}^a$ = 1.54 m, and ${\overset{\sim }{B}}^{ch}$ = 0.96 m. Terms L, ${\overline{P}}_{avg}$, ∅_3dB, and D are the physical antenna array length [m], average transmitted power [W], azimuth half power beamwidth [rad], and directivity [−], respectively. Term H_eff is defined as

$$ {H}_{eff}=\left\{\begin{array}{l}L\kern2.75em {H}_{beam}<L\ \mathrm{and}\ {H}_{beam}<\overset{\sim }{B}\\ {}\begin{array}{l}{H}_{beam}\kern0.5em L\le {H}_{beam}<\overset{\sim }{B}\\ {}\begin{array}{l}\begin{array}{cc}\begin{array}{c}\overset{\sim }{B}\end{array}& \kern2em \overset{\sim }{B}\le {H}_{beam}\end{array}\\ {}\begin{array}{cc}\begin{array}{c}\overset{\sim }{B}\end{array}& \kern2em \overset{\sim }{B}\le L\end{array}\end{array}\end{array}\end{array}\dots \right. $$

(6)

where H_beam = 2 ∙ d ∙ tan(θ_3dB/2) and θ_3dB is the vertical half power beamwidth [rad]. Term C(f) [10⁻⁴ m³/kg] is

$$ C(f)=\left\{\begin{array}{l}\begin{array}{l}\begin{array}{l}\begin{array}{l}\begin{array}{l}\left(3.5+\frac{f-300}{600}\right)\left(1+\frac{0.8d}{400}\right)\\ {}\kern6.75em 300\le f\le 900\ \mathrm{and}\ 200\le d\le 400\end{array}\\ {}6.3+\left(\frac{f-300}{600}\right)\bullet 1.8\end{array}\\ {}\kern6.75em 300\le f\le 900\ \mathrm{and}\ d>400\end{array}\\ {}4.5\bullet \left(1+\frac{0.8d}{400}\right)\\ {}\kern6.75em 900\le f\le 5000\ \mathrm{and}\ d\le 400\end{array}\\ {}8.1\\ {}\kern6.75em 900\le f\le 5000\ \mathrm{and}\ d>400\end{array}\right.\dots $$

(7)

where d is the distance in millimeters and f is the frequency in megahertz.