Attenuation Characteristics of the SAR in a COST244 Phantom with Different EM Source Locations and Sizes

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1 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE PAPER Special Section on 2004 International Symposium on Antennas and Propagation Attenuation Characteristics of the SAR in a COST244 Phantom with Different EM Source Locations and Sizes Shoichi KAJIWARA a), Atsushi YAMAMOTO, Koichi OGAWA, Akihiro OZAKI, and Yoshio KOYANAGI, Members SUMMARY This paper addresses the variation of the attenuation characteristics of the Specific Absorption Rate (SAR) in a lossy medium as a function of the distance between an antenna and the medium with different EM-source sizes. Analysis and measurements were performed using a dipole antenna at 900 MHz and a COST244 cubic phantom. From this, an empirical equation has been derived, representing the attenuation characteristics of the SAR. The equation takes into consideration an energy loss due to the spatial spread of electromagnetic waves. In the case where an antenna is placed more than λ/2π away from the medium, the attenuation characteristics of the SAR are those obtained from plane waves in the lossy medium. In the case where a half-wavelength dipole antenna is located close to the medium, at a distance of less than λ/2π, the attenuation characteristics of the SAR are calculated from an equation that includes a loss caused by the spread of energy as a cylindrical wave. Moreover, when the length of antenna is short, it is found that a spatial attenuation factor appropriate to a spherical wave should be taken into account. key words: SAR, attenuation characteristic, COST244 phantom, lossy medium, spatial spread of energy 1. Introduction In recent years, a number of studies have been made on the Specific Absorption Rate (SAR) caused by a mobile phone antenna close to the head of an operator [1] [3]. The SAR is defined by the following equation: SAR= σe2 ρ [W/kg] (1) where E [V/m] is the effective value of the electric field amplitude, σ [S/m] and ρ [kg/m 3 ] are the electrical conductivity and the density of human tissue, respectively. In general, an approximation of a plane wave for the electromagnetic field has been applied to E in Eq. (1) in order to represent the SAR characteristics in the internal parts of the head [1], [4]. For example, attenuation characteristics of the SAR in a phantom are determined from an empirical formula in [1]. However, the electric field radiated from the antenna can be considered to be, not only a plane wave, but also as a spherical wave or a cylindrical wave, since a mobile phone is used closely adjacent to the human head. The authors have proposed a new measurement system for the SAR, which makes use of an ingenious algorithm that predicts the SAR from the measurement of the magnetic field distribution in the vicinity of a cellular radio in free space [5]. In this procedure, the average SAR is calculated from the 3-dimensional SAR distribution in a cubic shape, estimated from the SAR on a phantom surface using an attenuation constant of the liquid in the phantom. Thus, an accurate evaluation of the attenuation constant is essential for this measurement system. This paper presents a formula to provide more accurate attenuation characteristics of the SAR, taking a spatial attenuation factor of the electromagnetic field of a spherical or a cylindrical wave into consideration. Attenuation characteristics of the SAR in a COST244 phantom that simulates the human head are evaluatedwith different electromagnetic source locations and magnitudes using the FDTD technique. From this, physical pictures regarding the attenuation characteristics in the lossy medium of the COST244 phantom are clearly understood. The analysis shows that excellent agreement between predictions using the formula and the calculated values is obtained. 2. Theoretical Model Figure 1 shows the model used for calculation in this paper. The COST244 model [6] was used as a human phantom. This model of a head was homogeneous, with a relative permittivity ε r = 41.5, a conductivity σ = 0.95 S/m, and density ρ = 1000 kg/m 3, which are the electric constants simulating Manuscript received October 1, Manuscript revised January 14, The authors are with Matsushita Electric Industrial Co., Ltd., Kadoma-shi, Japan. a) kajiwara.shoichi@jp.panasonic.com DOI: /ietcom/e88 b Fig. 1 Theoretical model. Copyright c 2005 The Institute of Electronics, Information and Communication Engineers

2 2392 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE 2005 the brain tissue. A half-wavelength dipole at 900 MHz with a length of 160 mm was used as a radiation source. A continuous wave was radiated. The distance, d mm, between the antenna and the surface of the human head model was varied. The origin of the coordinates was set at the center of the surface of the human head model, directly under the feeding point of the antenna. The FDTD method was used for analytical calculation purposes. The minimum cell size in the analysis area was x = y = z = 0.75 mm; the absorbing boundary condition was an eight-layer PML (perfect matched layer). The value of the SAR evaluated in this paper was normalized to that of the SAR(0), which was obtained at a depth of a half cell (y = 1.25 mm) for the FDTD analysis. 3. Attenuation Characteristics of the SAR Figure 2 shows the attenuation characteristic of the SAR in the human head model when the distance (d) between the antenna and the model was increased from 2.5 mm to 100 mm. The horizontal axis represents the distance y from the surface of the human head model to the observation point, which is normalized to the wavelength at 900 MHz (λ=333 mm in free space). The vertical axis represents the value of the SAR, normalized to the SAR(0) at the surface. Each bullet identifies the result of FDTD analysis as the distance d is changed. As seen in Fig. 2, the results when d 50 mm (shown as and ) agree well with those for the plane wave shown by the solid line calculated from Eq. (5), as will be explained in the next section. On the other hand, when d < 50 mm shown by,,,, and in Fig. 2, the attenuation is steeper than that with d 50 mm. This reveals that the distance between the antenna and the surface of the head model greatly influences the attenuation characteristics of the SAR in the medium. From this, the attenuation characteristics of the SAR cannot be expressed as that those associated with a plane wave incidence when the antenna is located close to the head. 4. Consideration of the Spatial Spread of Energy Electromagnetic plane waves propagating in a medium in the direction of y are given in the following equations [4]: E(y, t) = E 0 exp ( αy) cos (ωt βy + φ) (2) H(y, t) = H 0 exp ( αy) cos (ωt βy + φ θ) (3) where α [Np/m] is the attenuation constant and β [rad/m] is the phase constant. α is defined by the following equation: α = ω ε µ σ2 ω 2 ε 1 2 where ω [rad/m] is the angular frequency, µ [H/m] is the magnetic permeability, σ [S/m] is the electrical conductivity and ε [F/m] is the real part of permittivity. Since the SAR is proportional to E squared from Eq. (1), using the attenuation constant defined by Eq. (4), the value of the SAR in the y direction is generally given by [1], [7]: 1 2 (4) SAR(y) = SAR(0) exp( 2αy) (5) where the SAR(0) is the SAR value at the surface of the medium. However, the attenuation characteristic of Fig. 2, changing as it does with the distance from the source, cannot be explained clearly, when the attenuation constant α of the plane wave is applied only as in Eq. (5). Figure 3 shows physical pictures representing the electromagnetic waves traveling in a medium. Here, the energy of the electromagnetic wave propagating along the y axis is considered to be attenuated proportionally to (1/y) n in accordance with the law of energy conservation. As seen in Fig. 3, in the case of loss-less medium, n is determined as 0, 1, or 2 for a plane wave, cylindrical wave, or spherical wave, respectively, because the extension of the area along the y axis corresponds to the spatial spread of energy. Fig. 2 Attenuation characteristics of the SAR in a lossy medium at 900 MHz. Fig. 3 Physical pictures representing the spread of electromagnetic waves in a medium.

3 KAJIWARA et al.: ATTENUATION CHARACTERISTICS OF THE SAR IN A COST244 PHANTOM 2393 Fig. 4 Energy spread in the 2-dimensional plane for two different EMsources. Consequently, an empirical equation that represents the attenuation characteristics of the SAR can be derived by multiplying Eq. (5) by a term expressing the spatial spread of energy: SAR(y) = SAR(0) exp( 2αy) (y/d + 1) n (6) In Eq. (6), the denominator on the right hand side represents a spatial attenuation factor, obtained from a ratio of cross sections of energy flux at d and at the distance from the wave source to the point of interest (y + d). With regard to n in Eq. (6), which expresses the degree of spatial spread of energy, let n in the xy plane be nxy and n in the yz plane be nyz,thenn = nxy + nyz. Accordingly, n = nxy + nyz = = 0 for the plane wave in the case where the point of observation is far from the antenna (Fig. 3(a)), n = nxy + nyz = = 1 for the cylindrical wave when a line source is arranged parallel to the z axis (Fig. 3(b)), and n = nxy + nyz = = 2 for the spherical wave radiated from a point source (Fig. 3(c)). Furthermore, observing the energy spread in the 2- dimensional plane, when energy spreads in a plane shown in Fig. 4(a), n(z) is constant at a point on the line parallel to z axis. When energy spreads circularly as shown in Fig. 4(b), the value of n(θ) is constant on the arc of the circle whose center is a point of a wave source. 4.1 Line Source Far from the Medium Figure 5 shows the attenuation characteristics of the SAR for a half-wavelength dipole antenna when d is 0.15λ (50 mm). The solid line represents the attenuation characteristic when n = 0 in Eq. (6). The circle marks show the calculated results using the FDTD. The triangle marks are the measured data achieved using the electric field probe method [8] under the same condition as in the analysis. From Fig. 5, the agreement between the calculated and measured results is quite good, confirming the validity of the calculation using the FDTD. Moreover, the calculated and measured results agree well with the value when n = 0 in Eq. (6) which simulates the attenuation characteristic of the plane wave in Eq. (5). Fig. 5 Attenuation characteristics of the SAR in a lossy medium with a λ/2 dipole antenna when d = 0.15λ (50 mm). In this paper, the boundaries for separating the farfield and near-field region are defined as the radian sphere d 0 = λ/2π 0.16λ [9], where λ is the wavelength in free space. From this, the electromagnetic waves propagating in the medium can be considered as being in the far-field when d 0.15λ (50 mm) since d 0 is about 50 mm at 900 MHz. Therefore, it can be understood from this definition that when d is 0.15λ the electromagnetic waves impinging upon a medium have physical properties similar to a plane wave, and hence the attenuation characteristic of the SAR in a lossy medium, shown by the solid line in Fig. 5, approaches thatof the SAR whenn equals 0 in Eq. (6) which eventually agrees with Eq. (5). Figure 6 shows the distribution of the SAR in the xy and yx planes, calculated using the FDTD analysis when a half-wavelength dipole antenna is located 0.15λ from a lossy medium. The value of the SAR is normalized to the maximum value and shown in db. It can be observed from Fig. 6 that, in the xy plane, the wavefronts of waves traveling in the medium are lined up along the x axis in the vicinity of the feeding point of the antenna. On the other hand, in the yz plane, wavefronts in the shape of a cosine wave can be seen along the z axis, which is created by the cosine-shaped current distribution induced on a half-wavelength dipole antenna. In Fig. 6(a), SAR distribution pattern has been perturbed by the effect of a phantom edge. However, the distribution pattern of the SAR peak area, which is the most significant region for the SAR evaluation, is not influenced by a phantom edge. This fact has been carefully confirmed by other calculations using a semi-infinite phantom (see Appendix B). In order to investigate the spatial spread of energy in the medium in more detail, n in Eq. (6) was evaluated in the xy and yz planes. Figure 7(a) shows the attenuation factor of n in the y axis direction, normalized to the surface SAR value at any x(z = 0) in the xy plane. Similarly, Fig. 7(b) shows n(z) intheyz plane. As can be seen in Fig. 7, the attenuation rate for any point parallel to the surface of the medium is identical because n(x)andn(z) are constant along the x and z axis, with this fact suggesting that the spatial

4 2394 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE 2005 Fig. 6 Distribution of the SAR in a lossy medium with a λ/2 dipoleantenna when d = 0.15λ (50 mm). Fig. 10 Distribution of the SAR in a lossy medium with a λ/2 dipole antenna when d = 0.015λ (5 mm). spread of energy in the medium can be considered to be that of a plane wave. In this paper, the term plane wave is used to represent a wave with a spatial attenuation factor from Eq. (6) being equal to zero. As mentioned earlier, the shape of a cosine wave shown in Fig. 6(b) is created by the cosine-shaped current distribution induced on a half-wavelength dipole antenna. Thus, the SAR distribution does not necessarily rep- Fig. 8 Distributions of the Poynting vector in the (a) y-directed (b) z-directed (c) total component. resent the spatial spread of energy in the medium. This phenomenon can be well understood from the direction of energy stream in which the energy progresses, demonstrated by the Poyinting vector. Figure 8 shows the Poynting vector of the y-directed component, Fig. 8(a), z-directed component, Fig. 8(b), and the combination of all x-y-z components, Fig. 8(c). The x- directed component is not shown because of its very small value relative to the other components. The calculation was

5 KAJIWARA et al.: ATTENUATION CHARACTERISTICS OF THE SAR IN A COST244 PHANTOM 2395 Fig. 9 Attenuation characteristics of the SAR in a lossy medium with a λ/2 dipole antenna when d = 0.015λ (5 mm). Fig. 7 n with a λ/2 dipole antenna when d = 0.15λ (50 mm). made using a COST244 cubic phantom medium for the case of d = 0.15λ. As can be seen from Fig. 8, the distribution of the Poynting vector in the y-directed component is very similar to that of the total component, whilst the z-directed component has less effect. This fact suggests that the direction of the progression of energy stream shown by the Poynting vector is in alignment with a direction perpendicular to the antenna axis, indicating that the energy flow undergoes no extension of the area along the y axis. The above considerations strongly support the statement that the spatial spread of energy from a λ/2 dipole antenna when d = 0.15λ can fairly be considered to be that of a plane wave, as derived from the results of Fig Line Source Close to the Medium Fig. 11 n with a λ/2 dipole antenna when d = 0.015λ (5 mm). As in the case where the half-wavelength dipole antenna is close to the human head model, Fig. 9 shows the attenuation characteristic of the SAR when d = 0.015λ (5 mm). The circle marks are calculated results using the FDTD. The triangle marks are experimental data achieved by the electric field probe method [8] under the same condition as in the analysis. It is found from Fig. 9 that the analytical values concurred precisely with the measured values, proving the effectiveness of the FDTD analysis. In Fig. 9, each thin line is the attenuation characteristic when n = 0, 1, and 2 in Eq. (6). The bold line represents the attenuation characteristic when n = 0.8 in Eq. (6), obtained by best fitting the data calculated by the FDTD to Eq. (6) using the least mean squares method. Figure 9 indicates that attenuation characteristic obtained from Eq. (6) of n = 0.8 is in good agreement with the calculated results. Since the obtained value of n is close to 1, it is considered that the energy spreads as a cylindrical wave in the medium. Figure 10 shows the distribution of the SAR in the xy and yz planes, calculated using the FDTD analysis when the half-wavelength dipole is close to the medium. The figure shows that the distribution in the yz plane is almost the same as that in Fig. 6(b), whereas the distribution in the xy plane is quite different from that in Fig. 6(a), in which the waves traveling in the medium spread with circular wavefronts. Figures 11(a) and (b) show n values as a function of φ

6 2396 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE 2005 in the xy plane and as a function of z in the yz plane, obtained from Fig. 10. In Fig. 11(a), since n(φ) is constant on the arc of circle whose center is a point of a wave source, the energy spreads circularly in the medium. On the other hand, in Fig. 11(b), since n(z) from the surface of medium is constant for any point on the line parallel to z axis, the energy flow undergoes no extension of the area along the y axis. Therefore, the spatial spread of energy in the yz plane can be considered to be that of a plane wave, as discussed in Fig. 6(b). These phenomena indicate that the energy spreads circularly in the xy plane as emission from a point source and is maintained constant in the yz plane because of the nature of the line source. Based on the observations from Figs. 10 and 11, it can be concluded that, in this case, the spread of energy can be considered to be a cylindrical wave. Now, it should be pointed out that, although the SAR distributions shown in Fig. 6(b) and Fig. 10(b) are similar, the corresponding attenuation factors shown in Fig. 7(b) and Fig. 11(b) differ from each other. The reason for this phenomenon can be understood from the following explanation: the SAR distribution represents a characteristic in a certain single cut-plane, whereas the attenuation factor is a value whose property is influenced not only by the SAR distribution in the plane of observation of interest but also by distributions in other planes. In other words, the difference between the attenuation factor shown in Fig. 7(b) and that in Fig. 11(b) is caused by the difference between the SAR distribution shown in Fig. 6(a) and that in Fig. 10(a). Fig. 12 Attenuation characteristics of the SAR in a lossy medium with a λ/15 dipole antenna when d = 0.015λ (5 mm). 4.3 Point Source Close to the Medium It was revealed that the spatial spread of energy in a lossy medium is like a plane wave when the source is far from the medium as shown in Fig. 5 and a cylindrical wave when close to the medium as shown in Fig. 9. Based on this fact, it is estimated that the energy spreads with a spherical wave when the point source is located near the medium. Therefore, in order to examine this conjecture, the attenuation characteristic has been investigated when a short dipole antenna is located near the medium. Figure 12 shows the attenuation characteristic of the SAR when a short dipole antenna (λ/15 = 22 mm) is located at a distance d of 0.015λ (5 mm) rom the human head model. Figure 12 clearly shows that Eq. (6) is a good approximation when n = 1.6. The energy thus spreads as a spherical wave because the obtained value of n is close to 2. Figure 13 shows the distribution of the SAR calculated using the FDTD in the xy and yz planes when the dipole antenna with length of a λ/15 is close to the medium. From a comparison with Fig. 10(a) and Fig. 13(a), the distribution of the SAR of a short dipole is observed to be the same as that of the half-wavelength dipole since both the antennas function as point sources in the xy plane. On the other hand, in the yz plane, the distribution shown in Fig. 13(b) is found to be a little different from that shown in Fig. 10(b), in which the waves traveling in the medium spreads with Fig. 13 Distribution of the SAR in a lossy medium with a λ/15 dipole antenna when d = 0.015λ (5 mm). circular wavefronts. This is exactly the same situation as in Fig. 10(a) and Fig. 13(a). Figures 14(a) and (b) show n values as a function of φ in the xy plane and as a function of θ in the yz plane, obtained from Fig. 13. In Fig. 14, n(φ)inthexy plane and n(θ) in the yz plane are observed to be constant. In consequence, it can be stated that the spread of energy is spherical, since the antenna functions as a point source with regard to a wave in both the xy and yz planes. Note that although the SAR distributions shown in Fig. 10(a) and Fig. 13(a) are similar, the corresponding attenuation factors shown in Fig. 11(a) and Fig. 14(a) differ from each other. The reason for this phenomenon can be understood with the same explanation as mentioned in the previous section.

7 KAJIWARA et al.: ATTENUATION CHARACTERISTICS OF THE SAR IN A COST244 PHANTOM 2397 Fig. 15 n as a function of d for a λ/2 dipole antenna. Fig. 14 n with a λ/15 dipole antenna when d = 0.015λ (5 mm). 5. Source Geometries Dependency 5.1 Source Locations Fig. 16 n as a function of d for a λ/15 dipole antenna. As mentioned in the previous Sects. 4.1 and 4.2, when a half-wavelength dipole antenna is located more than λ/2π from the COST244 phantom, n approaches zero, whereas the antenna is placed at less than λ/2π, n approaches one. This fact suggests that n is expected to take a value of 0 < n < 1 in the case of the middle distance. Furthermore, it is shown in Sect. 4.2 that the value n does not correspond to 1 since the source is arranged at a distance of 0.015λ (5 mm) from the medium. This fact also suggests that n is expected to approach 1 if the source is located less than 0.015λ from the medium. To confirm this hypothesis, an investigation has been conducted into the value n as a function of the distance d from λ (2.5 mm) to 0.3λ (100 mm). Figure 15 shows the relationship between n and d at z = 0foraλ/2 dipole antenna. It is seen from Fig. 15 that n remains almost unchanged when d is increased from 0.15λ to 0.3λ, indicating that the electromagnetic waves in this region, which represents beyond the radian sphere, can be considered to be substantially a plane wave as explained in Sect On the other hand, n is 0.99 with d = λ, which is larger than n = 0.8 with d = 0.015λ and is very close to 1. It is considered from this result that the electromagnetic waves have a property of a cylindrical wave when d = λ. Further consideration shows that n has values of 0.58 and 0.28 with d = 0.030λ and 0.075λ respectively, both of which being values between 0 and 1 as expected. In a similar manner to that for a λ/2-dipole antenna case, an investigation has been made of the relationship between n and d at z = 0foraλ/15 dipole antenna, as illustrated in Fig. 16. It is confirmed from Fig. 16 that when the distance d is greater than 0.15λ the value n converges to 0, which is the same phenomenon as seen in. Figure 15 On the other hand, when the source is adjacent to the medium, the value n approaches 2, proving clearly that the waves exhibit a spherical energy spread as described in Sect Source Sizes Figure 17 shows n as a function of z, with the length of a dipole antenna L, as a parameter. The lateral axis is normalized to the wavelength of 900 MHz. L is set at λ/15, λ/10, λ/4 andλ/2. These lengths were chosen to simulate the size of practical antennas for cellular phones commercially available in the market. For example, λ/15 (22 mm) corresponds to a small built-in antenna, or λ/2 (165 mm) corresponds to an antenna with which the whole chassis is excited. The antenna is located 0.015λ (5 mm) from the COST244 phantom. The feeding point of the antenna is placed at z = 0.

8 2398 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE 2005 The attenuation characteristic of the SAR in a lossy medium was examined. As a result, it was revealed that when an antenna is placed close to a lossy medium, the loss caused by the spatial spread of energy must be considered in addition to the loss due to the medium itself. Furthermore, the formula, which takes the spatial attenuation factor into consideration, is effectiveinestimatingtheattenuationcharacteristic of the SAR in the lossy medium. References Fig. 17 n as a function of z with the length of a dipole antenna, L, asa parameter. Table 1 Relationship between L, d and n at x = z = 0. The constant n was determined as that along y(z), in parallel with the y axis as shown in Fig. 4(a). It is found from Fig. 17 that, when L is more than λ/10, abrupt changes in n can be seen in the region of about 0.05λ from the tip of the antenna. In addition, n maintains an almost a constant value of n = 0.8 in the remaining portion of the antenna, L 0.1λ around the feeding point. It is understood from this that the electromagnetic waves in the medium change abruptly from cylindrical to spherical waves as the observation point moves towards the tip of the antenna. On the other hand, when L = λ/15, n equals 1.6 at the feeding point and approaches 2 at the tip of the antenna. This fact shows that, in this case, waves propagate with a spherical nature, even near the feeding point, because of the small size of the antenna. Here, the relationship between L and n regarding the values of d = 0.015λ and 0.15λ is shown in Table 1. As described in this chapter, Figs. 15, 16 and 17 strongly support the validity of the physical mechanism responsible for the attenuation characteristics of the SAR in a lossy medium as discussed in this paper. 6. Conclusion [1] N. Kuster and Q. Balzano, Energy absorption mechanism by biological bodies in the near field of dipole antennas above 300 MHz, IEEE Trans. Veh. Technol., vol.41, no.1, pp.17 23, Feb [2] N. Kuster, Q. Balzano, and J. Lin, Mobile Communications Safety, Chapman & Hall, London, U.K., [3] R.Y.-S. Tay, Q. Balzano, and N. Kuster, Dipole configurations with strongly improved radiation efficiency for hand-held transceivers, IEEE Trans. Antennas Propag., vol.46, no.6, pp , June [4] W.H. Hayt, Jr. and J.A. Buck, Engineering Electromagnetics, sixth edition, McGraw-Hill, [5] K. Ogawa, A. Ozaki, S. Kajiwara, A. Yamamoto, Y. Koyanagi, and Y. Saito, High-speed SAR prediction for mass production stages in a factory by H-field measurements, IEEE Antennas and Propagation Society International Symposium Digest, vol.2, pp , June [6] COST244 WG3, Proposal for numerical canonical models in mobile communications, Proc. COST244, pp.1 7, Roma, Nov [7] M.Y. Kanda, M.G. Douglas, E.D. Mendivil, A.V. Gessner, and C.K. Chou, Faster determination of mass-averaged SAR from 2-D area scans, IEEE Trans. Microw. Theory Tech., vol.52, no.8, pp , Aug [8] T. Schmid, O. Egger, and N. Kuster, Automated E-field scanning system for dosimetric assessment, IEEE Trans. Microw. Theory Tech., vol.44, no.1, pp , Jan [9] C.A. Balanis, Antenna Theory: Analysis and Design, John Wiley & Sons, Appendix A: Investigation Using the SAM Phantom In order to investigate the generality of Eq. (6) in this paper, the FDTD analysis was performed using a SAM phantom and a half-wavelength dipole antenna at 900 MHz. Figure A 1 shows the model used for calculation. The origin of the coordinates was set at the boundary of liquid and shell in left ear region of the SAM phantom model, directly under the feeding point of the antenna. The distance, d mm, between the feeding point of antenna and the surface of the (a) 3D. (b) yz plane. Fig. A 1 Calculation model using a SAM phantom. IEEE Standards Coordinating Committee 34 on Product Performance Standards Relative to the Safe Use of Electromagnetic Energy, Draft recommended practice for determining the spatialpeak specific absorption rate (SAR) in the human body due to wireless communication devices: Experimental techniques, P1528, 2003.

9 KAJIWARA et al.: ATTENUATION CHARACTERISTICS OF THE SAR IN A COST244 PHANTOM 2399 Fig. A MHz. Attenuation characteristic of SAR in a SAM phantom at liquid was varied. The electrical constant of the phantom, the frequency, the input power, and the conditions of the analysis are the same as those of Sect. 2. Figure A 2 shows the attenuation characteristic of the SAR in the phantom when d is 0.15λ (50 mm) and 0.015λ (5 mm). The triangle marks are the calculated results using the FDTD when d is 0.15λ (50 mm), the marks indicate the results when d is 0.015λ (5 mm). The solid lines represent the attenuation characteristics using Eq. (6). In Fig. A 2, n has values of 0.1 and 0.8 with d = 0.15λ and d = 0.015λ respectively, both of the values correspond to L = λ/2 of Table 1. The attenuation characteristic of the SAM phantom is substantially the same as the COST244 phantom along the y axis. These results demonstrate the generality of Eq. (6). Fig. A 3 Distribution of SAR in a semi-infinite phantom with a λ/2 dipole antenna when d = 0.15λ (50 mm). Appendix B: Consideration on the Edge Effect Using a Semi-Infinite Phantom In order to examine the edge effect of a COST244 cubic phantom, the SAR distribution of a semi-infinite phantom is calculated when d = 0.15λ (50 mm). Figure A 3shows that the SAR distribution of a semi-infinite phantom undergoes no perturbation that can be observed in the COST244 phantom due to the edge effect, as shown in Fig. 6. Figure A 4 shows the SAR distributions along the x axis on the surface of the COST244 and semi-infinite phantom. In Fig. A 4, the solid and dotted lines represent the SAR distribution of the two phantoms. As can be seen in Fig. A 4, the two curves agree well in the region of about 0.35λ (120 mm) around the feeding point. The results show that the influence of the edge effect is insignificant in most important area for the SAR evaluation. Fig. A 4 Distributions of SAR along the x axis on the surface of the cube and semi-infinite phantom. Shoichi Kajiwara was born in Fukuoka, Japan, on July 5, He received the B.S. degree from Kyushu Institute of Technology in In 1992, he joined Matsushita Electric Industrial Co., Ltd., Osaka, Japan. His research interests include mobile handset antennas, their biological effects, and electromagnetic near-field measurements. He is currently pursuing a Ph.D. degree at the Graduate School of Science and Technology, Chiba University, Chiba, Japan.

10 2400 IEICE TRANS. COMMUN., VOL.E88 B, NO.6 JUNE 2005 Atsushi Yamamoto was born in Okayama, Japan, on Feb. 16, He received the B.S. and M.S. degrees from Okayama University in 1995 and 1997, respectively. In 1997, he joined Matsushita Electric Industrial Co., Ltd., Osaka, Japan, where he has been engaged in research and development on antennas for cellular radio communications. His research interests also include millimeter-wave propagation, scattering and diffraction. He received the YRP (Yokosuka Research Park) Young Scientist Award from the YRP in 2002, based on accomplishments and contributions to millimeterwave technologies. Koichi Ogawa was born in Kyoto on May 28, He received the B.S. and M.S. degrees in electrical engineering from Shizuoka University in 1979 and 1981, respectively. He received a Ph.D. degree in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan, in He joined the Matsushita Electric Industrial Co., Ltd., Osaka in 1981, where he was engaged in research and development work on a 23-GHz quasi-millimeter-wave and a 50-GHz millimeter-wave integrated circuit and a12/14-ghz very small aperture terminal (VSAT) satellite communication system. He is currently a research group leader of Mobile Communication RF-Devices, which include antennas, filters, amplifiers and oscillators, etc. His research interests include compact antennas, diversity antennas for mobile communication systems, electromagnetic interaction between antennas and the human body, and other related areas of radio propagation. His research also includes millimeter-wave circuitry and radio propagation. He received the OHM Technology Award from the Promotion Foundation for Electrical Science and Engineering in 1990, based on accomplishments and contributions to millimeter-wave technologies. He also received the TELECOM System Technology Award from the Telecommunications Advancement Foundation (TAF) in 2001, based on accomplishments and contributions to portable handset antenna technologies. Dr. Ogawa is the chief director of a technical committee for the Next Generation Wireless Communications in the Kansai Electronic Industry Development Center (KEC), Osaka, Japan. From 1999 he has been engaged in a special lecture regarding wireless communications engineering in Chiba University, Chiba, Japan. From 2003 he has also been engaged as a Guest Professor of the Center for Frontier Medical Engineering, Chiba University, Chiba, Japan. He is a member of the IEEE. He is listed in Who s Who in the World. Akihiro Ozaki was born in Aichi, Japan, on June 5, He received the B.S. degree in electrical engineering from Doshisha University in Since 2001 he has been with Matsushita Electric Industrial Co., Ltd. where he has been engaged in a study and development work on electromagnetic near-field measurement systems. He is currently concerned with research and development of electronic components, especially thin film devices. Yoshio Koyanagi See this issue, p.2275.