RESONANCE FIELDS AND SHIELDING OF A LIVING ROOM EXPOSED TO RADIATIONS FROM A TRANSMITTER BY VECTORIAL FINITE ELEMENT- NEURAL NETWORK METHOD

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1 RESONANCE FIELDS AND SHIELDING OF A LIVING ROOM EXPOSED TO RADIATIONS FROM A TRANSMITTER BY VECTORIAL FINITE ELEMENT- NEURAL NETWORK METHOD M. S. H. Al Salameh and R. S. M. Daaghmeh 2 Depatment of Electical Engineeing, Jodan Univesity of Science and Technology, Ibid, Jodan 2 College of Engineeing and Technology, Palestine Technical Univesity, Kadooi-Tulkam, Tulkam, Palestine salameh@just.edu.jo ABSTRACT This pape pesents the application of vectoial finite element-neual netwok method along with automatic ectangula mesh geneation fo the pediction of the esonance fields in two dimensional model of a concete living oom. These fields may come fom an electomagnetic tansmitte such as two-way adio tansmitte, amateu adio tansmittes, o paging tansmittes. The influence of placing a conductive window sceen is studied with the aim of educing the inteaction of tansmitte stations with humans inside the living oom. The electic field is calculated inside the oom with vaious situations: oom with doo and window, with two windows and funitue, with doo and window in addition to funitue, and with a fine metallic window sceen. The shielding effectiveness of the window sceen is evaluated fo diffeent incident angles of the wave. It is found that window sceen can povide about 3 db shielding effectiveness. Keywods: esonance fields, shielding effectiveness, adiations, tansmitte, concete oom, vectoial finite element-neual netwok method.. INTRODUCTION The demand fo wieless communications is apidly gowing. The pesence of electomagnetic fields in the envionment and its biological effects has also been the topic of ecent eseach. Besides themal effects, the electomagnetic (EM) fields have the potential to influence the neuon function net and chemical eactions in the cells, especially in peiod when cell gows and divides []. Theefoe, it is impotant to measue the electomagnetic fields (EM) in ooms. A numeical study of the esonance enhancement of the electomagnetic (EM) fields inside living oom nea the basic antenna stations was pesented in [], whee a mathematical appoach based on the method of auxiliay souces (MAS) was used to solve fo the electomagnetic (EM) fields inside the living oom. In the analysis of shielding effectiveness of monolaye and double laye cement shield ooms to HEMP (high electomagnetic potection) [2], the ooms wee simulated using finite diffeence time domain method. The pape [3] discussed indoo wave popagation chaacteistics of a einfoced concete building at 2 MHz band fo a potable adio telephone o othe indoo adio communication system design. Wave popagation losses though the windows ae measued in tems of effective adiation patten. In [4], the esults showed that the concete thickness and conductivity ae the main factos that affect the shielding effectiveness. At low fequencies, the magnetic field shielding effectiveness is not obvious fo the pue concete, but fo fequency moe than MHz, the wie gid buied in the concete is effective. Shielding is one of effective methods which can be used to educe electomagnetic fields in ooms. Finite element method (FEM) technique can be used in calculating shielding effectiveness. In this pape, we investigate the usability of the vectoial finite elementneual netwok technique along with automatic mesh geneation fo evaluating the esonance fields and shielding effectiveness of concete ooms. The oom model used is 2-dimensional. Details of FEM mesh numbeing ae given. The influence of the shield is studied, and calculated electic field is obtained fo a oom with vaious situations such as: oom with doo and window, with two windows and funitue, with doo and window in addition to funitue, and with a fine metallic window sceen. The electic field distibution in the shielded (with window sceen) oom is calculated. Using the shielding in the ooms clealy shows impovement in educing penetated EM field values. 2. VECTOR FINITE ELEMENT- NEURAL NETWORK FORMULATION Finite element method is one of the most poweful and efficient numeical algoithms used to solve geneal patial diffeential equations [5, 6]. This is due to the fact that it can handle abitay boundaies with extemely iegula shapes and the domain of the poblem can include media with vaying mateial chaacteistics. The basic steps of the finite element method ae: domain discetization, fomulation of the system of equations, and solution of the system equations. The size of each element in the mesh esticts the maximum fequency which the mesh can accept. If the longest side of the tiangula element is, then: λ., λ = λ ε µ Whee, λ is wavelength (in metes), λ is wavelength in fee space, and ε, µ ae elative pemittivity and pemeability, espectively. The electomagnetic fields within the poblem domain satisfy the vecto wave equation: () 58

2 uu E uu 2 = k ε, ε = ε σ c E c j µ ω ε (2) In which, uu E is the electic field vecto, k o the fee space wave numbe, ω adian fequency, ε fee space pemittivity, and σ electic conductivity in S/m. Since the natual systems seek the state of minimum enegy, the uu uu ( E ) ( E ) uu uu 2 uu uu F = k εc E E dω+ jωµ ( E H ) nds µ Ω s fields ae equivalently the solution of the vaiational equation: * δ F( E ) = (3) Whee, denotes the complex conjugate, and E * is chosen as the vaiation paamete in ode that the final system of equations will be in tems of the physical quantity E. Vecto Finite Element method (VFEM) functional fo unbounded poblems can be epesented as [7]: (4) whee E uu, H uu ae electic and magnetic field vectos, espectively, Ω is the solution egion, µ is fee space pemeability, n is unit outwad nomal vecto to contou S enclosing the solution egion Ω, j =. When solving open egion poblems using the finite element method (FEM), the infinite egion exteio to the scattee must be tuncated by an atificial oute bounday in ode to pemit pactical implementation on a digital compute. In this pape, the suface S is chosen to confom to the ectangula oom as shown in Figue-. minimizing the functional in VFEM is equivalent to the solution obtained fom the HNN by minimizing the netwok s enegy. The adiation bounday condition fo tansvese electic illumination is [7]: uu S s E φ 2 jη k ρ H z =, Z = Z 2jk ρ, µ η =, ε = ω µ ε k (6) Supescipt s efes to scatteed field, ρ, φ, Z ae ^ cylindical coodinates, indicates unit vecto, and subscipt efes to unbounded medium. In ode to solve (4) and (5) numeically, the poblem domain must be descitized into finite elements. A typical tiangula finite edge element is shown in Figue-2. The edges ae denoted by the numbes, 2 and 3. Also, the tangential components of the electic field vecto evaluated at the centes of the edges ae denoted by E t, E t 2 and E t 3. Figue-. Poblem geomety and solution egion. On the othe hand, the total enegy of the Hopfield Neual Netwok (HNN) is given by [7]: P = w ij Si S j + SiT i (5) 2 Whee w ij ae the neual weights epesented by the element matices of the edge element method, S i, S j ae the neuons' states epesented by the tangential components of the electic field vecto in the mesh, and T i is the neual theshold epesented by the incident wave on the oom. It is easy to ecognize the similaities between equations (4) and (5). In othe wods, the solution obtained by Figue-2. Tiangula edge element; edge vaiables epesent neuons' states. Fom simple geometical consideations, each tangential component can be expessed as: E = E cosϕ + E sinϕ, i ti xi i yi i ϕ < π (7) 59

3 Whee E xi and E yi ae the x and y components of the electic field evaluated at the cente of edge i ( i=, 2 o 3), and φ is the azimuthal angle of edge i measued i fom positive x-axis. Futhe, the x and y components, within each element, ae expessed by a linea intepolating function (othe highe ode intepolating functions can also be used) of y and x, espectively: E = a + cy, E = b + cx (8) x y Whee a, b and c ae constants. Combining equations (4)- (8) and using the edge elements discetization, yield the following linea system of equations: [ A ] E = [ B ] t (9) In which, [ A ] is a squae matix that involves the shape functions of the tiangula edge elements epesenting the neual netwok weights, [ Et ] is global vecto containing the edge vaiables (the tangential components of the field along the tiangles edges) epesenting the neuons' states, and [ B ] is the excitation vecto epesenting the thesholds of the neual netwok. The system of equations (8) can be solved fo the electic field vecto[ E t ]. 3. FEM MESH AND SOLUTION ALGORITHM Finite element models equie a definition of the physical aea by ceating elements that fom a finite element mesh. Ceating the mesh is one of the most tedious pats of woking with finite element models. Fo this eason, automatic mesh geneation methods have been employed to ceate lage goups of elements inside defined polygonal boundaies. One application of the finite element method is the analysis of shielding effectiveness of ooms with the aim of educing inteaction of tansmitte stations with humans. The total numbe of equations being solved depends on the numbe of elements in the mesh. As element size deceases, the total numbe of elements inceases. Smalle elements give moe accuate esults because the diffeential equations ae solved at moe points, yielding a bette distibution of solution values. Howeve, the inceased numbe of computations also inceases the time equied to poduce a solution. Thee ae tadeoffs between solution accuacy and computation speed. In this pape, the ectangula mesh is divided into layes of tiangula elements. The layout of the fist laye (3 elements, 5 nodes, 7 edges) is shown in Figue-3, and two layes (2 elements, 2 nodes, 23 edges) ae shown in Figue-4. Note that elements numbes ae enclosed in small ectangles, edges numbes ae witten nea the aows, and the emaining ae the nodes numbes. The numbeing is pefomed in a counteclockwise manne. Figue-3. Numbeing of nodes, edges and elements in the fist laye in the mesh. Figue-4. Numbeing of two layes in a mesh. MATLAB was used to wite the compute codes. Mesh data can be saved o loaded fom ASCII disk file, and this is a convenient way to ceate an initial mesh. The saved file includes: numbe of layes, total numbe of elements, and nodes and edges numbeings. The following is a simple saved file which holds the basic infomation fo initialization of ectangula mesh fo the fist laye shown in Figue-3. Element numbe node numbeing edges numbeing

4 Pogams fo mesh efinement wee also witten. Afte that we used the following pocedue (shown in Figue-5) to solve the poblem: a) Descitize the domain of the ectangula FEM mesh. b) Pedetemine convegence citeion (theshold eo ε s ) (chosen to be -4 ). c) Specify mateial paametes ( ε, µ, σ ) fo all elements. d) Define the adiation bounday condition. e) Geneate the vecto finite element mesh. f) Stat iteations to compute the electic field at the edges of each element accoding to the Finite Element Neual Netwok method [7]. g) When the eo is below the theshold eo value in step, stop and give esults. The eo is defined as the diffeence between the two sides of equation (9). Note that when electic field iteation values ae substituted fo [E t ] in equation (9), the equality will not hold unless we each the exact solution fo [E t ]. Stat Descitize the domain of the FEM mesh Pedetemine the theshold eo, ε s = 4 Specify mateial paametes (,, ) ε µ σ fo all elements Define adiation bounday condition Geneate the mesh Iteate to compute electic field at edges of each element No Eo < theshold Yes End and show esults Figue-5. Flowchat that descibes the solution algoithm. RESULTS Some examples ae solved to show the applicability of the finite edge element- neual netwok method. Towads that end, a oom with diffeent configuations is consideed: A. oom with doo and window, B. oom with two windows and funitue, C. oom with window and doo and funitue, and D. Room with shielded window. MATLAB codes wee witten to solve these poblems. Howeve, befoe poceeding with the oom solutions, and in ode to validate the witten compute pogams, a metallic shielding enclosue was solved and the esults compaed vey well with the solutions pesented in [8]. A. Room with doo and window The coss-section of the oom (6m 3m) is shown in Figue-6. A wave fom a tansmitte impinges on the oom. The oom is in the fa zone of the tansmitte and 6

5 thus the wave is assumed plane wave. The oom is consideed to be made of concete. The concete paametes chosen ae: elative pemittivityε = j 2.8, conductivity σ =.389 S/m, elative pemeability µ = [9]. The tansmitting fequency of 25 MHz is chosen to coespond to the fist esonance of the oom, i.e., when the oom length is half wavelength. In ode to calculate the electomagnetic fields in the oom, the mesh is divided into 452 tiangula elements with numbe of edges = In this case, the size of the tuncating bounday (24m 22m) was adjusted until stable esults wee obtained. The field distibution is shown in Figue-7 fo zeo incidence angle. Due to esonance, the field inside the oom is highe than outside. The esonance patten is eadily obseved in the oom whee the field is lagest in the middle of the oom and deceases steadily towads the ends of the oom. In addition, note that the field magnitude is highest along the window opening, since the lossy and conductive walls of the oom block the incident wave. Fo othe incidence angles, the esults ae summaized in Figue-8. In this poblem high esonance fields aise especially at gazing incidence. It is noticed fom Figue-8 that the electic field deceases with inceasing the incidence angle. The maximum esonance field at θ = was (.6 V/m) and only.357 V/m at θ = 85. B. Room with funitue and two windows The oom geomety is illustated in Figue-9. The funitue was abitaily chosen to have the following paametes: µ =, ε = 3 j 2, σ =.27 s/m; the algoithm is valid fo any values of mateial paametes. The piece of funitue dimensions wee chosen as: width of.2 m and height of.6 m. The fequency of the incident wave is 25 MHz. We see fom the electic field distibution shown in Figue- that high field values appea in the middle of the oom when the angle of the incident wave is zeo. Howeve, the field is lowe than that of the oom without the piece of funitue. It seems that the funitue has the effect of shifting the esonance fequency. So, we expect that the field would be highe at a lowe esonant fequency as will be seen in the examples below. Again the field values decease with inceasing the angle of the incident wave (Figue-). Note that the ate of decease of the field is petubed aound the 45 incidence angle. This may be explained as follows: it is evident fom Figue-9 that at 45 incidence, the incident wave diectly stikes the funitue inside the oom causing additional eflection of the wave which may locally enhance the field stength. The tuncation bounday was 24m 24m, numbe of elements = 728, edges = C. Room with funitue, opened doo and window The oom geomety is shown in Figue-2. The piece of funitue has the same size and mateial paametes as that descibed in the pevious example. Figues 3 and 4 eveal that the high field values occu in the middle of the oom when the angle of incidence is zeo. The FEM mesh has numbe of elements= 728 and edges = The maximum esonance field at θ = was (. V/m) and only.22 V/m at θ = 85. As in the othe examples, the maximum field at esonance deceases with inceasing the angle of incidence as shown in Figue-4. In Figue-5, we display the elation between the electic field and fequency whee it is evident that the field is a stong function of fequency. Figue-5 shows that although the field at 25 MHz is loweed in the pesence of the funitue, it is significantly highe at lowe and highe fequencies. In othe wods, the funitue has the effect of shifting the esonance fequency of an empty oom. D. Shielded window with a fine metallic sceen Conside the oom with the window shielded by a fine metallic sceen as shown in Figue-6. Since the metallic sceen is vey fine (i.e., distance between adjacent filaments of the sceen is much smalle than the wavelength), it can be epesented by a continuous metallic sheet. Fom Figue-7, the maximum electic field at θ= is only.2 V/m, wheeas the maximum field fo this oom with unshielded window is 7.6 V/m (the field distibution fo the case of a oom with only a window is not shown in ode to limit the numbe of pages of the pape). The shielding effectiveness (SE) of this sceen is defined as [], []: EO SE = 2 log, in db E Whee E is the maximum electic field at esonance without shielding, and E is the maximum electic field at esonance with shielding. Table- shows that the window metallic sceen is a viable tool to inhibit field penetation. SE fo the window sceen is about 3 db fo diffeent incidence angles of the wave. Note that in all the pesented examples, the field mainly entes the oom fom the window (on the side of the incident wave). On the contay, the field mainly entes fom the oom walls in the case of sceened window as can be seen in Figue-7. The penetating field deceases almost linealy with the incidence angle as shown in Figue-8. 62

6 Max field without shielding in V/m Table-. Shielding effectiveness of the oom with shielded window. Max field with shielding in V/m Shielding effectiveness in db Incidence angle in degees µ, ε.3 m µ ε, σ, Incident wave m µ,ε Room floo 2 m Doo 3m 6 m Figue-6. Wave incident on a oom with doo and window Tuncation bounday y(m) x(m).4.2 Figue-7. Electic field amplitude at esonance inside and nea a oom (6m 3m) with doo and window. The colo ba indicates electic field amplitude in V/m. Incidence angle θ =. White lines ae oom boundaies. 63

7 .6 maximum field at esonance (V/m) Angle(degees) Figue-8. Maximum field in oom (with doo and window) at esonance vs. incidence angle. Figue-9. The oom with funitue and two windows. y(m) x(m) Figue-. Electic field amplitude at esonance inside and nea the oom with funitue and two windows (θ = )

8 .6 Maximum field at esonance (V/m) Angle (degees) Figue-. Maximum field in oom (with funitue and two windows) at esonance vs. incidence angle. Figue-2. The oom with funitue, opened doo and window y(m) x(m) Figue-3. Electic field amplitude at esonance inside and nea the oom with funitue, opened doo and window (θ = )

9 Maximum field at esonance (V/m) Angle (degees) Figue-4. Maximum field in oom (with opened doo, funitue and window) at esonance vs. incidence angle. Electic field amplitude Ex (V/m) Fequency (MHz) Figue-5. Effect of changing fequency: Maximum electic field amplitude inside the oom (with opened doo, funitue and window) as a function of fequency, at θ =. Figue-6. The window is shielded by a fine metal sceen. 66

10 y(m) x(m).2 Figue-7. Electic field amplitude at esonance inside and nea the oom with window metallic sceen, θ =. maximum electic field (v/m) Angle Figue-8. Maximum field in the oom with sceened window at esonance as a function of incidence angle. CONCLUSIONS The finite element neual netwok method can be used to undestand the field behavio inside the oom fo a numbe of paametes like fequency, angle of incidence, and location inside the oom. The field was solved fo diffeent oom configuations: oom with doo and window, with two windows and funitue, with doo and window in addition to funitue, and with a fine metallic window sceen. The shielding effectiveness (SE) of the window sceen was about 3 db fo diffeent angles of the incident wave. Thus, the fine metallic window sceen is efficient in educing the field penetation into the oom. It was obseved that the electic field inside the oom deceases as the incident angle of the incident plane wave inceases. The pesence of objects inside the oom such as the funitue affects the field distibution in the oom. As expected, the maximum field at esonance inside the oom is lage than the incident field due to multiple eflections fom the inne sufaces in the oom. The vaious exposue guidelines such as the ICNIRP (Intenational Commission on Non-Ionizing Radiation Potection) efeence levels of human exposue to electic and magnetic fields ae usually based on the field values in the egion outside the ooms. The esults hee show that these limits ae not adequate as the field inside the oom may become lage than outside the oom at esonance. REFERENCES [] D. K. akulia, K. Tavzaashvili, V. Tabatadze and R. Zaidze. 23. Investigation of the field distibution inside ooms located nea the basic antenna stations. Poceedings of 8 th intenational semina on diect and invese poblems of electomagnetic and acoustic wave theoy. Lviv, Ukaine. pp [2] Gue Fei and Zhou Bihua. 28. Analysis of shielding effectiveness of monolaye and double laye cement shield ooms to HEMP. China-Japan joint Micowave Confeence, Shanghai. pp

11 [3] J. Hoikishi, K. Tanaka and T. Moinaga GHz Band Wave Popagation Measuements in Concete Building fo Indoo Radio Communications. IEEE Tansactions on Magnetics. 35(4): [4] Zhibin Zhao, Xiang Cui, Lin li. 28. Analysis of Shielding Pefomance of Reinfoced Concete Stuctues Using the Method of Moments. IEEE Tansactions on Magnetics. 44(6): [5] Saeed Moaveni. 27. Finite Element Analysis: Theoy and Application with Ansys. 3 d Edition. Mankato, Pentice Hall. [6] J. Jin. 22. The Finite Element Method in Electomagnetic. John Wiley and Sons, Inc., New Yok. [7] M. S. Al Salameh and E. T. Al Zuaiqi. 28. Solutions to Electomagnetic Compatibility Poblems using Atificial Neual Netwoks Repesentation of Vecto Finite Element Method. IET Micowaves, Antennas and Popagation. 4: [8] M. S. Thaf Al Salameh and G. I. Costache Edge Element- Scatteing Amplitude Solution to Electomagnetic Leakage into Shielding Enclosues. IEEE Confeence on EMC. Dallas, TX, USA. pp. 9-3, [9] R. A. Dalk, C. L. Holloway. 2. Effects of Reinfoced Concete Stuctues on RF communications. IEEE Tans. EMC. 4(4): [] H. W. Ott Noise Reduction Techniques in Electonic Systems. 2 nd Ed. Wiley-Intescience, New Yok. [] Ooi Tian Hock and Foo Chew Houw Automated Shielding Effectiveness Test System fo Shielded Enclosues. 999 Intenational Symposium on Electomagnetic Compatibility, Tokyo, Japan. pp