E-Field Distribution modeling in a Homogeneous Phantom for a rapid SAR measurement Olivier Merckel and Jean-Charles Bolomey Supélec/DRE 3 rue Joliot-Curie Gif-sur-Yvette, FRANCE e-mail: Olivier.Merckel@supelec.fr Gilles Fleury Supélec/Me 3 rue Joliot-Curie Gif-sur-Yvette, FRANCE e-mail: Gilles.Fleury@supelec.f r Abstract: Specific Absorption Rate (SAR) designates the electromagnetic power density deposited per unit mass of biological tissue. SAR measurements are required to assess the compliance of mobile phones with existing standards and recommendations. The use of homogeneous phantoms leads to a relatively simple distribution of the electric field. Several ways of determining the decrease of the electric field in function of depth are here explored. The choice of a pseudo propagation constant allows to drastically reduce the number of E-field measurement points needed for the SAR calculation. The measurement time is then reduced to less than a minute, while the standard way takes about 10 minutes for a complete measurement of almost thousand E-field data points. Keywords : SAR, fast, propagation, parametric, ellipsoid. Introduction The experimental electromagnetic dosimetry of mobile phones has much developed since the beginning. Most of the existing dosimetric facilities utilize automatic positioning systems to move an E-Field measuring probe, with the help of robotized arms [1], or three axes displacement systems in order to achieve SAR (Specific Absorption Rate) measurements. The European Standard prEN50361 [2] details the ways to measure the SAR in a head-like phantom, and the maximum value of the SAR averaged in 10 g allowed. The electromagnetic properties of the liquid filling the phantom are similar to those of the brain. According to the new European standard, a complete phone test lasts about half a day, pointing out a new concern: the rapidity of SAR measurement. A rapid (less than 1 minute) and non-invasive SAR measurement solution, based on a probe integrated in a spherical phantom around which the phone under test turns, has been still developed [3]. The rapid SAR measurement method that we propose here is fully compatible with popular instrumentation and, hence, can be directly implemented on most existing SAR measurement facilities using mechanical scanning of an E-field probe [4]. The number of electric field data is reduced by a factor 30 that allows dividing the measurement time by a factor 10 approximately. The physical quantity that we measure, the maximum SAR (1) averaged in 1 g and 10 g of contiguous tissues, is the volumetric integration of the quadratic electric field, weighted by the conductivity σ and the density ρ of the media: ρ E σ SAR 2 = (1) with E (V/m) the E-field norm, σ (S/m) the conductivity of the medium, and ρ (kg/m 3 ) its density. The simplicity of the E-field distribution in the phantom, the more often in a long spot perpendicularly to the direction of propagation, its reproducibility between the different mobile phones, allows to consider generic parametric models of the E-field able to fit the principal electromagnetic characteristics of the phones. The number of parameters of those models (between 5 and 11) is sufficiently low to reconstruct the electric field in the whole data volume, from a small number of data, in a very reasonable computation time (on the order of one second). The acquisition time is then drastically reduced. The results presented in the last section show SAR reconstructions of commercial phones from three models involving a strict ellipsoidal approach, and two hybrid ellipsoidal-plane wave or mean propagation constant approach, those one trying to reduce the number of data points needed to a few ones distributed in a plane. These approaches are based on a long experience in SAR measurements, and in parametric methods applied to physical measurements. Their development has been possible with the help of the hundreds SAR tests of commercial phones, and are a result of the research effort conducted to improve the accuracy and the rapidity of the Supélec dosimetric facility. Physical characteristics of the E-field Decrease of the E-Field in function of depth The construction of the mathematical models representing the electric field is issued from the conclusions of systematic SAR tests on a hundred of real mobile phones (at 2 frequencies - 900 MHz and 1800 MHz). The analysis of the E-field in function of depth in the head-like phantom shows an exponential decay (see Fig. 1) for more than 90 % of the tested phones. The curves corresponding to each tested phone are distributed around the line corresponding to the theoretical propagation constant α of the plane wave (2). ( ) ( ) ( ) d z α e d y x E z y x E - - = , , , , (2) For the standard materials used, and for a plane wave, α = -29.4 Np/m at 900 MHz, and α = 41.4 Np/m at 1800 MHz. . Figure 1. Depth decrease of the maximum normalized E-Field, for 64 phones at 900 MHz.