# Cấu trúc sóng chức năng trong điện lý thuyết P7

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## Cấu trúc sóng chức năng trong điện lý thuyết P7

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SAR Distributions in a Head Model The development of cellular telephones and mobile communication systems has led to a growing awareness of the vital role that wireless systems play in communication networks and the biological effects of EM fields on users. Since cellular hand phones are operated in close proximity to human heads while in use, there has been increasing public concern about the health effects of the human head exposed to EM energy emitted from mobile handset antennas.

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## Nội dung Text: Cấu trúc sóng chức năng trong điện lý thuyết P7

4. 194 SAR DISTRIBUTIONS IN A SPHEROIDAL HEAD MODEL 7.3 FORMULATION OF THE PROBLEM 7.3.1 Expansions of EM Fields Using Spheroidal Wave Functions The EM waves excited by the wire antenna can be expressed in terms of the spheroidal vector wave functions by means of the formulated dyadic Green’s functions for spheroidal structures introduced in Chapter 3. The electric fields inside (El N I&) and outside (ET) the multilayered spheroidal model are expressed as El(r) = F 2 2 { [AlfM M;$$cl,J) +dlZN N”(‘> emn ,mn e omn n=m m=O X 2-6”“@),(k7, c’)I&‘) dV’ JJJ V’ Nmn emn(cj9t)+ ‘fHEnNZO + t3zn Mzt3) Ornlz (cf9c)] X v, JJJ$$%$;Jh,dv’ 5’)&(f) mn f = 2,3,4,5, and 6, (7.lb) 5. FORMULATION OF THE PROBLEM 195 (7.lc) where the prime symbol denotes the source point location, Nm, is the nor- malization factor of the angular function, and ci = 4 kid (i = 1,2). 6mo is the Kronecker delta function, Ia = I(t’) .s (where 6 = 2, s), and I( 6. 196 SAR DISTRMJTIONS IN A SPHEROIDAL HEAD MODEL Thus, the localized SAR is related directly to the internal field, and all the numerical procedures involve determination of the electric field distribution within the biological human head. The ANSI/IEEE C95.1-1992 RF Safety Guidelines proposes a detailed procedure to satisfy the safety guidelines for uncontrolled environments, which are defined as situations where there exists exposure of persons who have no control of exposure [1571. The SAR in each layer of the multilayered prolate spheroid is defined as aj JE12/2pj, where aj and pj represent the average conductivity and density of the j th layer, respectively. Values of aj and pj are presented in Table 7.1. 7.4 NUMERICAL COMPUTATION On the basis of the EM fields calculated inside the multilayered prolate spher- oidal model, the SAR in each layer of the spheroidal head model can be ob- tained. To simplify the calculation, the transmitted power of the dipole or monopole is assumedto be 1 W at both the GSM and PCN frequencies. The convergence of the matrix equation system for the determination of un- known scattering and transmission coefficients is discussed in Chapter 3. For the multilayered spheroidal structure presented in this chapter, the truncation number is generally chosen to be the maximum number of Integer( lkal + 4). Four Mathematics packages were developed on the basis of the previously verified software package to calculate the multilayered dielectric spheroidal structure. l The first is Source.nb, which is used for calculation of the integral about the wire antenna in Eq. (7.1). l The second is Itemexpansion.nb, which is used for calculation of the intermediates Ittyln(c) described in Appendix B. l The third package is Matrixequation.nb, which is applied to deter- mine the unknown scattering coefficients using the matrix equation sys- tem. In practical computation, the truncation number is chosen to be 48. l The last package, Efield.nb, is designed for computation of the electric field inside the multilayered dielectric spheroid. For convenience in the investigation of a multilayered spheroidal head model, the results of spheroidal wave functions and intermediate items used in the functional expansion for each layer are first calculated using packages introduced in Chapter 2 and saved as numerical tables. EM fields due to different antennas and their positions are then obtained using those equation packages. 7. RESULTS AND DlSCUSSION 197 7.5 RESULTS AND DISCUSSION The various SAR distributions inside the multilayered spheroidal model of the human head for a quarter-wavelength GSM dipole, PCN dipole, GSM mono- pole, and PCN monopole have been calculated and the results are presented in Figs. 7.2 to 7.4, 7.6 to 7.8, 7.10 to 7.12 and 7.14 to 7.16, respectively. The inner SAR distributions of the multilayered spherical head model for these various antennas are presented for comparison in Figs. 7.5, 7.9, 7.13, and 7.17, respectively. Here the spherical head is modeled as a six-layer sphere with the maximum radi us r = +(a+ b), and the thicknesses of the second through fifth layers are the same-asthose of the prolate spheroidal model. In all these figur ‘es,the antenna is placed on the right of the multilayered model, and the SAR values in each figure are normalized to the peak value in the model. The peak SAR values in the multilayered spheroidal head model vary with the inclination angle of the antenna at both the GSM and PCN frequencies. The SAR value increaseswhen the inclination angle /? increases, as illustrated in Figs. 7.2 to 7.4, 7.6 to 7.8, 7.10 to 7.12, and 7.14 to 7.16 (at inclination angles of p = O”, 30’) and 60° for different antennas), respectively. In all cases,the SAR values decreaserapidly inside the multilayered spheroidal head model 7 from the right of the head model to the left of the head model. It is also found that the peak SAR values for monopole antennas are higher than their dipole counterparts at the same frequency (e.g., compare Fig. 7.2 with Fig. 7.10, or Fig. 7.6 with Fig. 7.14). This conclusion agrees with those from FDTD calculations [144,158). From the rear view of the SAR distribution, it is found that the SAR values inside the spheroidal head model decrease faster when the inclination angle p of the dipole becomes smaller [e.g., Figs. 7.2(a), 7.3(a), and 7.4(a)]; while for GSM and PCN monopoles, there is no such obvious phenomenon for inner EM fields and the SAR values show an asymmetric distribution for the upper and lower parts of the spheroid, as shown in Figs. 7.10 to 7.12 and 7.14 to 7.16. From the figures presented, it can be seenthat the SAR distribution inside the multilayered spheroidal head model for a GSM dipole or monopole differs from that for its PCN counterpart, especially for the SAR distribution from the rear view (e.g., the comparison of Fig. 7.2 with Fig. 7.6, or Fig. 7.10 with Fig. 7.14). For dipole antennas, the peak SAR value at the GSM frequency (shown in Figs. 7.2 to 7.4) occurs at the CSF layer and is smaller than its counterpart at the PCN frequency (shown in Figs. 7.6 to 7.8), where the peak value occurs at the surface of the model. For monopole antennas, the peak SAR value also increases with the operating frequency of the antenna, and the peak value occurs at the surface. For GSM dipoles, although the EM fields inside the head model decrease from the right of the model to the left, the SAR value inside the head model shows a peak value at the right part of the CSF layer, of which the electric conductivity is much higher than those 8. 198 SAR DISTRIBUTIONS IN A SPHEROIDAL HEAD MODEL 1 1 1 L I 1 L a t lO.O- 8.0- CO- 4.0- 2.0- o.o- -2.o- -4.o- -6.O- -8.O- -1 o.o- I I 1 1 1 1 I I I 1 -10.0 -6.0 -2.0 2.0 6.0 (a) C/I= 0 and x (rear view) 10.0 8.0 6.0 -4.o- -CO- -8.O- -1 o.o- I 1 I I 1 1 ’ I I 1 -10.0 -6.0 -2.0 2.0 6.0 1 (b) 4 = ~12 and 3x12 (side view) Fig. 7.2 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (GSM dipole), normalized to 1.86 W/kg. s = 1.5 cm, p = O”, and the unit of the coordinate is centimeters. 9. RESULTS AND OKUSSION 199 lO.O- 8.0- 6.0- 4.0- 2.0- o.o- -2.o- -4.o- -6.O- -8.O- -lO.O- -10.0 -6.0 -2.0 2.0 6.0 10.0 (a) 4 = 0 and 7~ (rear view) 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 I I 1 I 1 1 1 I I -1 I.0 -6.0 -2.0 2.0 6.0 l( (b) 4 = ~~12 and 3~ /2 (side view) Fig. 7.3 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (GSM dipole), normalized to 2.11 W/kg. s = 1.5 cm, p = 30’) and the unit of the coordinate is centimeters. 10. 200 SAR DISTUlBUTlONS IN A SPHEROlDAL HEAD MODEL 10.0. 8.0, 6.0, 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 -6.0 -2.0 2.0 6.0 11 (a) 4 = 0 and T (rear view) 1 1 I 1 I 1 ’ ’ L 1o.o- 8.0- 6.0- 4.0- 2.0- o.o- -2.o- -4.o- -6.O- -8.O- -1 o.o- t I 1 1 1 I 1 I I I -10.0 -6.0 -2.0 2.0 6.0 I (b) 4 = r/2 and 3x12 (side view) Fig. 7.4 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (GSM dipole), normalized to 2.60 W/kg. s = 1.5 cm, p = 60”, and the unit of the coordinate is centimeters. 11. RESULTS AND DISCUSSION 201 8.0- 6.0- 4.0- 2.0- o.o- -2.o- -4.o- -6.O- -8.O- -1 o-o- I I 1 t t I 8 I I I -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 (a) 4 = 0 and T (rear view) 8.0- 6.0- 4.0- 2.0- o.o- -2.o- -4. o- -6. O- -8. O- 1 I I r I 1 I I 1 I -lO.O! -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 (b) 4 = 42 and 3~12 (side view) Fig. 7.5 SAR distributions (in dB) inside the multilayered spherical head model (GSM dipole), normalized to 2.23 W/kg. s = 1.5 cm, p = 30”) and the unit of the coordinate is centimeters. 12. 202 SAR DISTRIBUTIONS IN A SPHEROIDAL HEAD MODEL 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 1 1 1 I 1 1 1 1 1 -1 .O -6.0 -2.0 2.0 6.0 l( (a) 4 = 0 and x (rear view) 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 1 1 I I 1 1 1 I 1 -1 .O -6.0 -2.0 2.0 6.0 10.0 (b) 4 = 7~12 and 3x12 (side view) Fig. 7.6 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (PCN dipole), normalized to 2.37 W/kg. s = 1.5 cm, p = O”, and the unit of the coordinate is centimeters. 13. RESULTS AND DISCUSSION 203 1 o.o- 8.0- 6.0- 4.0- 2.0- O.O- -2.o- -4.o- -6.O- -8.O- -lO.O- , 1 -10.0 -6.0 -2.0 2.0 6.0 10.0 (a) 4 = 0 and T (rear view) lO.O- 8.0- 6.0- 4.0- -4.o- -6.O- -8.O- -lO.O- t I 1 I 1 I I 1 I 1 t -10.0 -6.0 -2.0 2.0 6.0 10.0 (b) 4 = ~12 and 3x12 (side view) Fig. 7.7 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (PCN dipole), normalized to 2.83 W/kg. s = 1.5 cm, 0 = 30”, and the unit of the coordinate is centimeters. 14. 204 SAR DISTRIBUTIONS IN A SPHEROIDAL HEAD MODEL 10.0 8.0 6.0 4.0 2.0 0.0 -2.0 -4.0 -6.0 -8.0 -10.0 1 I I 1 I I I I 1 -1 .O -6.0 -2.0 2.0 6.0 10.0 (a)$ = 0 and T (rear view) 10.0 8.0 6.0 4.0 2.0 o.o- -2.o- -4.o- -6.O- -8.O- -10.0 -6.0 -2.0 2.0 6.0 10.0 (b) 4 = x/2 and 3x12 (side view) Fig. 7.8 SAR distributions (in dB) inside the multilayered prolate spheroidal head model (PCN dipole), normalized to 3.41 W/kg. s = 1.5 cm, p = 60”, and the unit of the coordinate is centimeters.