MULTI-LAYERED LOSSY FINITE LENGTH DIELECTRIC CYLINDIRICAL MODEL OF MAN AT OBLIQUE INCIDENCE

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1 Proceeding 3rd Annual Conference IEEE/EMBS Oct.5-8, 1, Itanbul, TURKEY MULTI-LAYERED LOSSY FINITE LENGTH DIELECTRIC CYLINDIRICAL MODEL OF MAN AT OBLIQUE INCIDENCE S.S. Şeker, B. Yeldiren Boğaziçi Univerity, Dept. of Electrical- Electronic Engg Bebek, İtanbul-Turkey Abtract: Thi paper i intended to give a imple electromagnetic formulation of the EM power aborption propertie of multi layered cylindrical model of man at RF frequencie and above. The formulation, however, ha no limitation concerning frequency. Thu very low frequencie are alo conidered for comparion with the reult in literature. Both horizontal and vertical polarization are conidered. A ingle general expreion for model of man ha been derived. Aborbed power denity of man againt different value of incident power are illutrated at different frequencie and compared with tandard. 1 Introduction Recently, there ha been an increae in public interet about poible biological effect of electromagnetic EM energy emitted by variou electrical and electronic equipment. In repone to thi, experimental and modeling activitie are increae to obtain a wide and reliable etimation of the EM level. In particular, a coniderable amount of theoretical work ha been devoted to the invetigation of EM effect on human being uing variou hape. Coniderable dicrepancie exit in the difficulty of numerically evaluating of the different model.[1-5] The tudy of aborption propertie for ome threedimenional model of man i intereting in practice, but in mot of the real cae an exact calculation by analytical method i impoible. Generally, the real model are approached with numerical technique finite difference, moment method, finite element, etc. In mot of the cae the tarting point i the integral equation method. Though, where poible, analytic method allow a better phyical undertanding of the problem. Another advantage of the analytical approache i the poibility of teting the numerical method. In thi paper, the circular multi layered cylindrical model of man i tudied, which i ueful in threedimenional modeling of man. Thi way a comparion to ome numerical approache may be poible, for teting. Thu the preent invetigation deal with the circular multi layer finite-length /1$1. 1 IEEE cylinder at oblique incidence. An exact analyi i very difficult and laboriou to carry out. A in any other phyical problem it i neceary to introduce a implifying aumption. Namely thi analyi i baed on the approximation that the internal field induced within the finite-length cylinder are the ame a thoe induced within the infinite -length cylinder having the ame permittivity, orientation and diameter. Thee internal field are then ued to calculate the aborbed power denitie in term of the radar cro ection. To our knowledge thi the firt treatment of uch a problem. The reult apply when the minimum dimenion of the cylinder cro ection i mall compared with the cylinder length, although the length need not be mall compared with wavelength. The computed reult are obtained, and compared with the reult given in literature and good agreement wa obtained for TE and TM polarization. Numerical reult are alo obtained for low frequencie at normal incidence for comparion with previouly publihed work in the literature. [1] The methodology that i decribed in thi paper i quite general and powerful. It provide a tool for determining aborbed power denitie baed upon material propertie and geometric parameter. Becaue it i baed upon analytic decription of induced EM field mechanim within each layer of material it i computationally very efficient in comparion with numerical approximation. It doe not require the evere implifying aumption that are uually build into analytic decription. For model of man compoed of everal layer, thi work provide a trong alternative to brute force numerical calculation. It i particularly ueful for gaining inight into the material parameter and geometric contraint. Theoretical Formulation The magnitude of the cattering and incident power denitie are given by [] i E E S =, Si = η η (1) and η i the characteritic impedance of the free o pace. Aborbed power flux denity by human model i S = S S A i

2 Report Documentation Page Report Date 5 Oct 1 Report Type N/A Date Covered (from... to) - Title and Subtitle Multi-Layered Loy Finite Length Dielectric Cylindirical Model of Man at Oblique Incidence Contract Number Grant Number Program Element Number Author() Project Number Tak Number Work Unit Number Performing Organization Name() and Addre(e) Univerity, Dept of 8815 Bebek Y tanbul-turkey Sponoring/Monitoring Agency Name() and Addre(e) US Army Reearch, Development & Standardization Group (UK) PSC 8 Box 15 FPO AE Performing Organization Report Number Sponor/Monitor Acronym() Sponor/Monitor Report Number() Ditribution/Availability Statement Approved for public releae, ditribution unlimited Supplementary Note Paper from 3rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, October 5-8, 1, held in Itanbul, Turkey. See alo ADM1351 for entire conference on cd-rom. Abtract Subject Term Report Claification unclaified Claification of Abtract unclaified Claification of thi page unclaified Limitation of Abtract UU Number of Page 4

3 Proceeding 3rd Annual Conference IEEE/EMBS Oct.5-8, 1, Itanbul, TURKEY or S A = Si aσ () vector, ρ i the radiu of the outermot cylinder M and M i the total number of layer beginning from where σ = 4π f, p, q {v,h} i radar m=1. I 1 to I 1 are integral of Beel function. cro ection (RCS), f i the cattering amplitude Alo ψ = arctan ( β / β ), φ = φ φ where 1 and a = [ η ] 1 4πR i a contant. Thu from the lat β1 = coφ inθ two equation one can ee that radar cro ection i β = inθ coθ inφ coθ inθ the only important parameter determining The expreion in eq. (3) electromagnetic power aborption propertie of k k k k human. For finite length dielectric cylinder at a,b,a,b,c,d,k { c, } are obtained by oblique incidence, cattering amplitude, f are applying the boundary condition an each layer boundary of the multi-layered cylinder. given a [1] In order to check the correctne of the cattering amplitude, the multi layer infinite length cylinder and the ingle layer cylinder are conidered a pecial cae. Both cae the reult are exactly the ame a that given of ref. [3] where the experimental validation i alo hown. 3 Reult and Dicuion In the application of a given theory to practical computation, pecial care wa exercied in acertaining the limit of validity of the theory. Eq. (3) give u how much power tranmit to human being in term of only one meaurable parameter which i RCS. It can be meaured eaily in any radar laboratory. In thi part, the aborption characteritic of multilayered cylindrical model of man expoed to electromagnetic (EM) plane wave with oblique incidence ha been invetigated. f Figure 1. The geometry and the cro ection of the cylinder. = AπI + M n jn( φ i ψ ) 1 j e χ m n= m= 1 { [ p.a.qi 1 + p.b.qi ] c c + [ p. ( a + ja ).qi 3 + p. ( b + jb ).qi 4 ] e c c + [ p. ( a ja ).qi 5 + p. ( b jb ).qi 6 ] e c c + [ p. ( c + jc ).qi7 + p. ( d + jd ).qi 8 ] e c c + [ p. ( c jc ).qi + p. ( d jd ).qi ] e } (3) 9 1 Where A = k / 4π, χ i the relative uceptibility m of the m th cylinder layer, q i the unit polarization The amount of electromagnetic energy aborbed by expoed peron depend on the phyical characteritic of the human body; it ize, hape and compoition (i.e. relative percentage of mucle fat, bone, blood and oft tiue). The frequency determine the mechanim of aborption within the body. The reult are obtained for 9MHz, 18MHz and 45MHz. Thee frequency value are choen becaue of practical uage of them in daily life. 9 and 18MHz are commonly ued frequencie by GSM (Global Sytem for Mobile Communication) network..45ghz i choen becaue it i widely ued for microwave oven in the market. Table 1. give the parameter ued for each tiue layer of man [4], conidered in imulation. For the five layer model of man the fourth layer i conidered to be air of thickne 6 mm. and the fifth layer i taken to be humid clothing with complex permittivity ε r = 1 j5 for all frequencie [5]. The length of human ha been taken a 1.7m.

4 Proceeding 3rd Annual Conference IEEE/EMBS Oct.5-8, 1, Itanbul, TURKEY ε r Thickne (m) σ (S/m) Skin Fat Mucle Table 1. Parameter of the different tiue layer. Next we conider power aborption of human body in term of international tandard. Public expoure limit are given in Table. determined by International Commiion on Non - Ionizing Radiation Protection,. Figure 3. Aborbed power denity v. different value of incident power for model of man. Figure how the TE wave at 9MHz. Microwave Mobile phone bae oven frequency frequency Frequency 9MHz 18MHz 45MHz Public Expoure Limit denity (W/m ) denity (W/m ) denity (W/m ) Table. tandard. Figure 4. Aborbed power denity v. different value of incident power for model of man. Figure how the TM wave at 18MHz. Figure. Aborbed power denity v. different value of incident power for model of man. Figure how the TM wave at 9MHz. Figure 5. Aborbed power denity v. different value of incident power for model of man. Figure how the TE wave at 18MHz.

5 Proceeding 3rd Annual Conference IEEE/EMBS Oct.5-8, 1, Itanbul, TURKEY aborbed energy; the incident power denity of the field i more appropriate doimetric quantity [6]. Thi tudy reflect thi concluion. Figure 6. Aborbed power denity v. different value of incident power for model of man. Figure how the TM wave at 45MHz. Figure 7. Aborbed power denity v. different value of incident power for model of man. Figure how the TE wave at 45MHz. In addition to the figure above, the ame graph wa alo plotted for three layered model of man for a comparion with graph of five layered model. A a reult of thi comparion, it can be aid that although graph of three layered model are moother and average power denitie of two different model are almot ame, five layered model of man give more realitic approache to the human modeling. Thi work can be conidered a a generalization of the previouly work done on cylindrical model of man with both vertical and horizontal polarization and oblique angle of incidence and with no retriction on the frequency conidered. It i generally acknowledged that everal tudie have reported increaed cancer rik, epecially for children living cloer to high power electrical and electronic equipment. The comparion of the given figure allow u for a determination of EM wave ource power according to tandard. 5 Reference 1. Seker, S., I. Akkaya and C. Utku, Differential Cro Section of Multi - layered Loy Cylinder of Finite Length Progre in Electromagnetic Reearch, PIER 18, , Ihimaru, A., Wave Propagation and Scattering in Random Media, Vol. 1, 9-41, Academic Pre, Buey, H. E. and Richmond, Scattering by a loy dielectric circular cylinder of finite length, IEEE Tran. Antenna and Prop., Vol. AP-36, No., 33-37, J.C. Lin, Handbook of Biological Effect of Electromagnetic Field, CRS Pre, H. Maoudi, C.H. Durney, W. Barber and M.F. Ikander, Electromagnetic Aborption in Multilayered Cylindirical Model of Man, IEEE Tran. Microwave Theory Tech., Vol. AP 3, Sept. 1975, pp Guideline, Health Phyic, Vol. 74 (4), 494 5, 1998 Acknowledgement: Thi work wa upported by B.U. Reearch Foundation Project No: A1. 4 Concluion At frequencie around and greater than 1 GHz, the depth of penetration of the field into tiue i mall and SAR i not good meaure for aeing