In this paper a three dimensional Finite Difference Time sphere ( FDTD ) method is used to analyse communicating nomadic French telephones at 900-1800MHz. In the first portion, the aerial input electric resistance and the contemplation coefficient ( | S11| ) and the electromotive force standing wave ratio ( VSWR ) are studied. In the 2nd portion we report the computation of the close and far irradiated electromagnetic Fieldss, the Specific Absorption Rate ( SAR ) distribution ( included in a simple computational theoretical account of the human caput ) and the consequence of altering the distance between the caput and the aerial. Finally we study the consequence of frequence on the radiation form.

## 1.Introduction:

Nowadays because of the rapid development of the wireless communicating engineering the widespread usage of nomadic phone and ready to hand computing machines and the recent demands for radio computing machine webs [ 1,2 ] , there have been increasing public concern about the influence on the human organic structure. Besides the SAR has been recognized as one of the most important parametric quantities that describes the electromagnetic field interaction with the human organic structure [ 3,6 ] . Since it is really hard to quantify the SAR straight in the life human organic structure, the dosimetry is compelled to trust chiefly on a computing machine simulation with high declaration numerical Human theoretical accounts. Many techniques have been developed to imitate all these state of affairss. The FDTD algorithm is presently the most widely suited agencies for numerical [ 5,6 ] because it descretizes infinite into a figure of cells and assigns each cell a Corresponding permittivity and conduction. This algorithm offers a great flexibleness in patterning the heterogenous constructions of anatomical tissues and organs. [ 7-8 ] . The purpose of this analysis is to analyze the influence of the undermentioned parametric quantities: the distance between caput and phone, the theoretical account of the caput ( homogenous and heterogenous ) , and the consequence of frequence on both the soaking up and the distribution of electromagnetic Fieldss by the human caput. The features of the theoretical account of the caput studied were obtained from [ 9 ] . We used in the first instance a homogenous spherical caput ; and in the 2nd instance we have studied a spherical multilayer caput. To pattern the radiofrequency, we use a dipole excited at its centre.

The balance of the paper is outlined as follows: Section ( 2 ) focal points on the method of computations FDTD. Section ( 3 ) discusses the mold of a dipole aerial in a free infinite. In Section ( 4 ) and Section ( 5 ) , the interaction between the nomadic French telephone and the human caput has been studied every bit good as Electric Field and Specific soaking up rate are evaluated. Section ( 6 ) Near to far field transmutation is discussed. Section ( 7 ) illustrates the consequence of frequence on the distribution of the SAR. Finally we present our decisions in Section ( 8 ) .

## 2. FDTD preparation

In the FDTD preparation both infinite and clip are divided in to distinct sections. infinite is segmented in to package molded cells which are little in comparing with the wavelength The electric Fieldss ( Ex ( I, J, K ) , Ey ( I, J, K ) and Ez ( I, J, K ) ) are located on the borders of the box, and the magnetic Fieldss ( Hx ( I, J, K ) , Hy ( I, J, K ) and Hz ( I, J, K ) ) are positioned on the faces every bit shown in Figure 1. This orientation of the Fieldss is known as the Yee cell [ 1 ] and is the footing for FDTD. The clip is divided into little oversights where each measure represents the clip required for the field to go from one cell to the following. Given an beginning in infinite of the magnetic Fieldss in relation to the electric Fieldss, the values of the field in regard to clip are besides offset. The electric and magnetic Fieldss are updated utilizing a leapfrog strategy where the electric Fieldss come foremost, so the magnetic 1s are computed at each measure in clip. When many FDTD cells are combined together to organize a 3-dimensional volume, the consequence is an FDTD grid or mesh. Each FDTD cell will overlap the borders and faces with their neighbours. Therefore each cell will hold three electric Fieldss that begin at a common node associated with it. The electric Fieldss at the other nine borders of the FDTD cell will belong to other next cells. Each cell will besides hold three magnetic Fieldss arising on the faces of the cell next to the common node of the electric field as shown in fig 1.

Fig 1. Positions of the electric and magnetic

Field constituents in a Yee cell

This cognition of field values associated with the features of the tissue aid to find the SAR in the tissues without necessitating an invasive step. Now we present the Maxwell ‘s equations in three dimensions. We suppose the absence of magnetic or electric current beginnings, and the being of absorbing stuffs in the infinite.

Where the supplanting vector is related to the electric field through the complex permittivity

## — ( 3 )

The assorted constituents of the Fieldss are evaluated on the footing of neighbouring constituents of each oversight of clip and each cell in the modeling country. This method works in the clip sphere and allows direct visual image of Electromagnetic Fieldss.

3. Modeling dipole aerial in free infinite:

A simple dipole is illustrated in Figure ( 2 ) , consists of two metal weaponries. A dipole aerial maps with a current flow through the weaponries, which consequences in radiation. FDTD simulates a dipole in the undermentioned manner. The metal of the Weaponries are specified by puting the Ez parametric quantities to zero in the cells matching to the metal ; except in topographic point where the beginning is placed. This insures that the corresponding Ez field at this point remains zero every bit good as it would if that point were inside the metal. The antenna length was held changeless at each simulation. Absolutely Matched Layer ( PML ) boundary conditions were employed. The beginning is specified by puting the Ez field in the spread to a certain value. For the FDTD simulation, dipole is fed at the centre ( ten = Intelligence Community I”x, y=jc I”y, z=kc I”z ) spread of length I”z with a Gaussian pulsation [ 11 ] . So, the electric field in the spread of the dipole is:

## — ( 7 )

Figure 2. Geometry of the dipole aerial theoretical account.

## Electric current:

The current in the aerial at the provender point is obtained by using Ampere ‘s jurisprudence to the surface S with the jumping contour C on the wire at ( Intelligence Community, jc, kc +3/2 ) :

– ( 8 & A ; 9 & A ; 10 )

Figure 3 shows the current flowing through the centre of the dipole in the clip sphere.

## The input electric resistance computation:

The input electric resistance of an aerial is a really of import parametric quantity. After the concluding clip sphere consequences are obtained, the current and electromotive force are transformed to those in the Fourier sphere. The input electric resistance was calculated in the Centre fed dipole over a scope of frequences. It is determined from the ratio of the Fourier transform of the electromotive force moving ridge and that of the input current moving ridge:

— – ( 11 )

It should be noted that the clip difference I”t/2 between electromotive force moving ridge and current moving ridge is ignored since its consequence is really little.

## Figure ( 3 ) .Input current in footings of clip I ( T )

## Figure4.Input electric resistance of the dipole aerial

The input electric resistance of the dipole aerial is shown in Figure4.

The input electric resistance is good matched at 75.48+j1.12 at the resonance frequence of 1800MHz.

## The input return loss ( S11 ) and the

## electromotive force standing wave ratio ( VSWR ) :

The consequences of input electric resistance are so used to obtain the return loss features of the aerial. So the contemplation coefficient S11 of the half-wavelength dipole aerial is:

— ( 12 )

From the deliberate contemplation coefficient, the electromotive force standing wave ratio ( VSWR ) can be calculated as follows:

— ( 13 )

The bandwidth of the aerial, which was determined by the electric resistance informations, is the frequences matching to a contemplation coefficient of the aerial ( less than or equal to

1/3 ) that corresponds to VSWRa‰¤2.

In Figure 4, the resonant frequence which is around 1.8 GHz. was chosen as a frequence through the whole survey.

## Interaction between the French telephone

## and the human caput:

In this subdivision, the interaction between the nomadic French telephone and the human caput has been studied. A simplified homogenous spherical caput theoretical account is used. The domain has a radius of R = 10 centimeter and the tissue it contains has a comparative permittivity of Iµr =43.5 and conduction of I? =1.15 S/m. These tissue equivalent dielectric = 10 centimeter and the tissue it contains has a comparative permittivity of Iµr =43.5 and conduction of I? =1.15 S/m. These tissue equivalent dielectric parametric quantities were chosen harmonizing to [ 9 ] to imitate the encephalon tissue at 1.8GHz. For the calculation of SAR, the caput tissue denseness is assumed to be 1030 kg/m3. The comparative place of the dipole aerial relation to human caput theoretical account is illustrated in Figure6. The interaction between the nomadic French telephone and the human caput is studied from two point of views: foremost the impact of the distance between caput and phone ; second the consequence of caput type ( homogenous, heterogenous ) on the soaking up and distribution of electromagnetic Fieldss in the human caput and on the radiation form.

The following tabular array summarizes the dielectric invariable, the conduction I? and the mass denseness of the tissues used for the computations at 900 & A ; 1800 MHz [ 12 ] .

## 4. Near-Fields

The near-fields have been simulated in the plane defined by z=0.0mm. The consequences are viewed in Figure 7 and Figure 8 for the simulations. The beginning of the plane moving ridge has been aligned in the xz-plane with the feeding point of the French telephone theoretical account.

## Homogeneous Head

The computations were made at a frequence of 1.8 GHz. for a homogenous spherical caput of dielectric permittivity of 51.8 and a conduction of 1.5 S/m. We calculated the distribution of the electric field in the close caput near the aerial. This latter is located at a distance of 5mm at the side of the spherical caput. To see the consequence of the place of the aerial on the radiation form we have traced the visual aspect of the contemplation coefficient S11 for several distances between the heading and the phone.

Figure 7. The transversed electromagnetic field distribution of the dipole aerial in the homogenous caput omega =00mm

Figure8. The wholly fake electromagnetic field distribution of the dipole aerial in the homogenous caput omega =00mm.

## Figure 9.Input return loss ( S11 ) of the aerial for different values of vitamin D.

From Figure9. we can state that the radiation of the aerial depends on the distance between the phone and the heading. Hence, we can reason that there is a matching between caput and the aerial. In table2, the consequences of the deliberate drive point input electric resistance Zin of the dipole aerial are presented for each place of the French telephone in forepart of the homogenous human caput apparition.

Table 2. Consequences pf the drive point input electric resistance, VSWR and the input return loss ( S11 ) at each distance vitamin D ( centimeter ) between axis of dipole aerial and the outer surface of the homogenous human caput apparition.

The VSWR for each instance is so determined in regard to the free infinite input electric resistance. In this instance the aerial input electric resistance alterations drastically and the input power to antenna lessenings well. In the presence of the human caput, the resonance frequence is detuned about 5 % at GSM frequences. The presence of the human caput besides increases the input electric resistance of the dipole. Hence the electric resistance behaviour of the GSM dipole shows rather a strong dependance on the milieus.

## Heterogeneous caput

A spherical heterogenous Human caput theoretical account was utilized. This apparition consisted of three beds with stuffs imitating the human caput construction whose outer diameter is indistinguishable to that of homogenous sphere antecedently used. In Tble1, the type of each bed and its corresponding comparative permittivity, conduction and denseness are depicted harmonizing to [ 9 ] . In Figures 7,8, and 10 we see that the highest values of the electric field occur near the aerial. The magnetic field reaches its maximal value above the start of the aerial wire, near the eating point, where the current reaches its maximal value.

Figure10.The simulated electromagnetic field distribution of the dipole aerial in the heterogeneous Head for z=00mm.

## 5.SAR rating

The radiation beginning of the cellular phone was modeled by an tantamount dipole aerial. After holding obtained the induced electric field by the FDTD method, the local SAR in W/Kg for

## — ( 14 )

Tocopherol is the electric field magnitude in V/m, I? is the material conduction in S/m and I? is the mass denseness in kg/cubic meters.

## Homogeneous caput

An half wave dipole of 77mm enlightening at 1800MHz is placed 10mm off from the outer surface of the spherical human caput. The values of SAR ( or electric Fieldss ) are the highest in tissues around the aerial. These SAR values decrease quickly when one gets off from radiotelephony aerial. As a consequence the tissues around the ear are most open to electromagnetic Fieldss.

## Heterogeneous caput

The distribution of the local SAR values can be calculated straight from the electric field distribution, which consequences from the computing machine tally. In figure 12 and 13 the soaking up is greater in the tegument of the caput and the surface of the encephalon. Perversely the skull absorbs radiation ill, due to its low conduction and the difference in the dielectric belongingss of the related tissues [ 18 ] .

## Figure11.The simulated SAR distribution of the dipole aerial in the homogenous Head for z=00mm.

## Figure12.The simulated SAR distribution of the dipole aerial in the heterogenous Head for z=00mm.

## Figure13. SAR fluctuation as map of the cross distance.

We can province that the maximal soaking up occurs at the point where the phone is closer to the caput. Using the dealingss

D =Iµ .E and, the ratio between the SAR values in these tissues under a unvarying field distribution is about 0.35. In add-on, the maximal SAR values are well higher for the heterogenous theoretical account of caput.

## 6. Near to far field transmutation

While utilizing FDTD method, the provided informations are close Fieldss. Therefore, these near Fieldss are transformed to far Fieldss. Then, the far Fieldss are used to cipher the radiation form. First, we work within the frequence sphere and presume that the analyzed aerial is surrounded by the enclosed surface S. Then, allow ‘s presume that this closed surface has the local unit outward normal vector N.

Therefore, the electric and magnetic current densenesss can be written as follows:

— — — — ( 15 )

R: the place of the observation point ( x, y, omega )

‘ R: the Position of the beginning point on S ( x ‘ , Y ‘ , z ‘ )

I? : the angle between R and ‘ R.

Figure 14. The practical surface used for the nearto-far field transmutation and the co-ordinate system used for its computation.

Tocopherol and H are electric and magnetic Fieldss that propagate on the surface. Subsequently, we can specify the clip harmonic vector potencies N and L [ 18-22 ] .

& A ; — ( 16 )

J = a?’1, K is the numerical moving ridge figure, R, is the unit vector to the far field point and R ‘ is the vector to the beginning point of integrating. To obtain the far-field information from the

tantamount currents, it is necessary to incorporate them over each of the six faces of the practical box, here labelled surface S. That integrating can be done by utilizing the undermentioned brace of vector

potencies. These vectors ‘ potencies are in the Cartesian co-ordinate system. Following, these vectors potencies are converted into the spherical co-ordinate system. The I? and I† constituents of

the vector potencies N and L are given by:

— ( 17 )

— ( 18 )

Finally the far electric field can be calculated by the undermentioned relation

the radiation form is given by

where Pe is the input power aerial, and =I·0 is the free infinite.

Figure 15a, I? =90deg, xy plane.

Figure 15b, I† =90deg, yz plane.

The radiating forms were simulated in the XY plane ( program E ) and in the YZ plane ( H plane ) for the dipole entirely at the halfway frequence of the set ( 1.8GHz ) .

Figure 16a, I? =90deg, xy plane.

Figure 16b, I† =90deg, yz plane.

Figure 16: Radiation forms for additive dipole aerial radiating in the presence of homogenous spherical caput theoretical account. Figures 15 and 16 show the consequence of the caput theoretical account in the XY plane ( plane E ) and in the YZ plane ( H plane ) . We can see that the caput blocks the radiation forms in the head way. In the YZ plane the radiation in halfspace where the caput is situated is affected earnestly. So in the XY plane the radiation more reduced towards the caput ‘s way.

7. The consequence of frequence

To see the consequence of the frequence on the distribution of the SAR, we have drawn the SAR ‘s profile for the two used frequences ( 900 MHz and 1800 MHz ) and a homogenous caput.

Figure17. SAR normalized profile through a homogenous spherical caput for two different frequences.

Figure 17 illustrates the profile of the local SAR across the homogenous spherical caput theoretical account. The distance was measured from the point of the beginning closest to the caput theoretical account. The SAR

values were normalized to the upper limit to demo the consequence of the frequence. We can detect that the SAR decreased faster in the

higher frequence scope as expected due to the weak deepness incursion.

8.Conclusion

As a decision, we can state that the of import parametric quantities impacting the energy absorbed in the human caput exposed to radiation from wireless is the distance between the caput and the aerial. Although the power ingestion in the instance of the 1800 MHz frequence is lower than 900 MHz, the maximal values of SAR are more important for the higher frequences. The distribution of SAR in the spherical theoretical account illustrated in Figures

11, 12 and 13, indicates that big values of SAR are located in a volume near to the surface of the caput. In other words, the soaking up is greater in the tegument of the caput and the surface

of the encephalon. Contrarily, the skull absorbs radiations ill due to its low conduction and the difference in the dielectric belongingss of the related tissues. In add-on, the maximal SAR values are well higher for the heterogenous theoretical account of caput. It can be inferred from the consequences that there is a good understanding

between the local SAR values of our survey and the literature. In farther plants, we will analyze how to cut down the SAR in the human caput emitted from cell phone radiation utilizing the metamaterials