MODELING AND EVALUATION OF THE EFFECTS OF ELECTROMAGNETIC COMPATIBILITY IN TELECOMMUNICATIONS

 

Samuel Garcia TUKA Biaba Genie Electrique/Electrotechnique ISTA Kinshasa et ISTA Kindu Kinshasa, RD Congo tukasamuel23@gmail.com

 

 

 

Abstract - In the field of communications, mobile telephony has constituted a new axis of study, because it has for the first time caused the exposure of populations to ultra-high frequency electromagnetic fields emitted by nearby sources (telephone antenna, relay antenna or BTS, ...). The possible effects of the electromagnetic waves used are of concern to researchers and faced with the abundance of these strange radiations coming from our means of communication, a question arises concerning their effects on human health and in particular on biological tissuesas well as the potential risks for people exposed to interactions between electromagnetic fields and the human body which are real and therefore require protective measures.

 

Mathematical and numerical analysis using Maxwell's equations and computer tools such as Matlab and Excel, will allow us to model and simulate the total electric field radiated by the mobile phone, in order to characterize the distribution of electromagnetic power in the system organic. This approach will allow us to draw a conclusion on the modeling of electromagnetic compatibility in communication and impact on health.

 

Keywords: EMC, communications, mobile telephone, wave electromagnetic, induced current, biological system.

 

I.   INTRODUCTION

 

The interaction of electromagnetic fields with biological tissues has been the subject of many years of research motivated by the public health problems posed by the sharp increase in recent decades of sources of exposure to electromagnetic fields. Recently individual communication by GSM phones (Global System for Mobiles) has become widely used in the public [19]. This development has resulted in an increase in the number of people exposed to the intense electromagnetic field, the average exposure time, and the amount of radiation absorbed [1].

 

The existence of a low health risk at the individual level could then result in significant consequences for the population.

 

Indeed, the galvanic coupling corresponds to the case of a physical contact between the electromagnetic field source (cell phones) with the biological medium (human head) causes the flow of a ohmic current in the brain. The consequences may result depending on the intensity and frequency of contact current tissue heating see a burn.

Many fears are now expressed about the harmful health of the radiofrequency fields emitted by mobile phones. Since the head and the skin are the most exposed organs, the cerebral blood circulation, the skin microcirculation in the face and the electrical activity of the brain are specifically concerned [14] [20].

 

To carry out this study and quantify the consequences on biological tissues exposed to electromagnetic fields,

 

we proceeded by solving Maxwell's equations and by using computer tools such as Matlab and Excel in order to model and evaluate the field total electric power, this allows us to quantify: the electromagnetic power received by the brain during communication, the wavelength in the muscles, the depth of penetration of the electromagnetic field in the brain, the skin effect, the variation of the brain temperature and propose mitigating measures to prevent the biological or health effects of these radiofrequency waves.

 

II.  DEVELOPMENT

 

A.  Coupling Mechanisms Between the Electromagneic

Field and the Biological Tissue [16]

 

In the case of biological media, the phenomena of energy absorption in tissues can be relatively complex and depend on many factors. They are related primarily to the coupling between the emission source and the biological environment.

 

Galvanic coupling corresponds to the case of physical contact between the source and the medium. This contact causes the flow of an ohmic current in the body of the person and the consequences may result depending on the intensity and frequency of contact current tissue heating, see a burn. Radiated coupling includes three fundamental mechanisms by which electric and / or magnetic fields, of variable frequency over time, interact with biological media including :

 

- Coupling with low frequency electric fields:

 

- Coupling with low frequency magnetic fields:

 

- Energy absorption from electromagnetic fields :

 

The human exposure to electric or magnetic fields generally low frequency causes a significant energy absorption and no measurable temperature rise.

Against by, exposure to electromagnetic fields at frequencies above 100 kHz can cause absorption of energy and a significant rise in temperature.

 

In general, exposure to electromagnetic fields results in a highly inhomogeneous deposition and distribution of energy within the body which must be assessed by dosimetry. Finally, it remains to highlight the indirect effects caused by exposure to electromagnetic fields for people carrying active medical implants (pacemaker, defibrillator, insulin pump ...) that result in malfunctioning of the implanted material.

 

B.  Theoretical Approach to Wave-tissue Interactions

 

Mathematical modeling of the interaction of electromagnetic fields requires knowledge of the properties of the radiation source, the geometry of the exposed body as well as its electrical properties (conductivity, permittivity and permeability).

 

The importance of these interactions depend on:

 

-      Intensity

-      Frequency

-      The orientation of the electromagnetic field to which the tissue is exposed

-      The  geometry of  the  fabric  and  its  electromagnetic characteristics:

* magnetic permeability (μ)

* dielectric permittivity (ε)

* conductivity (σ)

-       The coupling between the field and the body, that is to say: tissues, organs ...

 

The latter is equal to that of the vacuum for biological tissues because these are considered to be non-magnetic. Electrical conductivity and magnetic permeability are specific to each tissue and depend on many factors such as frequency and temperature.

 

The behavior of the electromagnetic field produced by an external source and propagating towards a biological medium is described by Maxwell's equations using simple geometric configurations [23]. In this article, we consider an interaction of a plane wave with a homogeneous and isotropic linear medium.

 

-      A  medium  is  linear  if  the  response  to  a  linear combination of excitations is itself a linear combination of the responses obtained for each of the excitations.

-      A medium is isotropic if its structure is equivalent in all directions.

-      A medium is homogeneous if its properties do not vary from one point to another.

 

Several interactions can take place with frequent exposure to an electromagnetic field. This leads to short-term effects, direct (biological responses) or indirect.

According to the WHO, the current state of scientific knowledge does not demonstrate the long-term danger of exposure to low-intensity electromagnetic fields.

 

To further this research, we will highlight the following physical laws in order to explain the actions and effects of electromagnetic waves on the human body [10]:

 

Maxwell-Faraday: Ñ * E = -¶B/¶t  (1) Maxwell-Ampère: Ñ * H = j+¶D/¶t   (2) Maxwell-Gauss : Ñ * D = r            (3)

La loi d’Ohm : j= sE         (4)

 

B=m0H   (5)

 

D=e0E   (6)

 

The coupling that appears in equations (1 and 2) helps to explain the phenomena of propagation and radiation.

 

C.  Propagation of an electromagnetic wave in biological tissues

 

Biological media lie between dielectrics (insulators) and perfect conductors. Suppose that the charges are uniformly distributed in the environment, then we can write:

 

Ñ(r/e) = (1/e) *Ñ(r/e) (7)

 

Because ρ is independent of the observation point M.

 

We know that ÑE =   r/e              (8) In this case, from equation (3), we write:

Ñ(r/e) = Ñ(ÑE )  (9) From equation (1 and 2), we can write:

Ñ´(Ñ´E ) = -ms(¶E/¶t) -ms(¶2E/¶t2)               (10)

 

For an electromagnetic field which is sinusoidally dependent on time, and considering the equations presented above (see equations: (1), (2), (3), (4), (5) and (6)), for the vector field like the electric field E, each of the components in a homogeneous and isotropic linear medium (LHI) assumed to be infinite, can be written in the following compact form [9]:

 

E =Re [(e) Exp (-j (vt))]                (11)

 

By analyzing this writing, the real field is written:

E = E0*Cos (vt-j0)     (12)

 

Considering the attenuation and phase shift per unit length respectivel [8]:

 

a = wÖ[(m0/2)*a/w]         (13) For : 0 £ a £ 1

b = wÖ[(m0/2)Ö[2+ (a/ew) 2]]                 (14)

 

The expression of the field E which propagates along the z axis is written:

 

E = E0*[ Exp (-a*z)]Cos (vt-bz-j0)       (15)

Pz = (b/2m0w) E2 *[ Exp (-2a*z)]Cos (vt-bz-j0) (22) If j0 is zero, the mean power transported becomes :

0

0

Pz = (b/2m0w) E2 *[ Exp (-2a*z)]Cos (vt-bz)                   (23)

 

For frequencies of the order of 1 GHz, ωt> βz, the average power transported becomes :

0

Pz = (b/2m0w) E2 x*[ Exp (-2a*z)]Cos (vt)                (24) The absorbed power density D in Watt per cubic meter

[(W/m3] in the medium and transformed into heat is given by:

 

0x

The penetration of electromagnetic fields in the tissue

D=-dPz/dz = (r/2)* E2

*[ Exp (-2a*z)] (25)

will be very quickly limited because of a part of the skin effect and partly because of the dissipation of energy in the middle. To understand these phenomena, we considered analytically the equation (13) which explains the spread of the electric field in the vacuum and the equation (15) models propagation of the electric field in the biological environment. The skin effect results in a decrease of the field E (z) at a distance *z* from the interface according to the relationship:

Equation (25)  shows  that  the  energy absorbed  is  a

function of the conductivity of the medium and decreases in the direction of propagation. By introducing the density, we can also obtain from equation (25), the specific absorption rate  (SAR)  which is  expressed in  Watt  per

kilogram [W / kg] as follows :

 

0x

SAR = D/r = (s/2r)* çE2   ç           (26)

 

E.  The electromagnetic wavelength in the muscle

E = E0*[ Exp (-a*z)]  (16)

 

Where E0 is the field strength at the interface.

 

D. Electromagnetic power received by the brain[15]

 

For a wave which propagates in the brain along the z axis and whose electric field E is polarized in the x direction and the magnetic field vector H is polarized in the y direction, the expression of the fields E and H is written as follows:

The wavelength (λ) corresponds to the length of a complete cycle of a wave. This length corresponds to the distance between two identical points of the wave at a given moment, that is to say two points located at the same amplitude. In the case of a transverse wave, the length of a complete cycle corresponds to the distance between two peaks of the wave or two troughs.

 

l=c/f                (27)

 

c = wave speed in meter per second [m/s] (=3.108 m/s)

Ex = E0x*[ Exp (-a*z)]* Exp (-j (vt-bz) (17)

Hy = H0y*[ Exp (-a*z)]* Exp[ j (vt-bz+j)] (19) Where E0 and H0 represent the amplitude of the field at

the origin z = 0 and φ represents the phase difference

between the E and H fields given by:

 

tan(j)=a/b       (20)

 

The   average  power  carried  per   unit  area   for   a monochromatic plane wave moving in the direction of propagation is given by the following relation:

 

<P>=1/2*(E´H)             (21)

 

 

In the case of the Ex / Hy wave, the vector P has only one component along the z axis, namely:

λ= wavelength in meters [m]

 

f = frequency in Hertz

 

F.  Energy received by the brain from electromagnetic waves

 

This energy can be defined from the thermodynamic equation of energy conservation:

 

0x

Ez= (s/2)* çE2   ç*t        (28)

 

Ez=r*Cp*Dq                   (29)

 

r: The mass and volume of a human brain in 870 kilogram per cubic meter [kg/m3]

t: irradiation time in hours [h]

 

Dq: the temperature variation in the brain in degree celsius

[°C]

 

 

Cp: Average specific heat capacity of the brain in Joule per kilogram celsius [J/kg °C]

 

From equations (28 and 29) we can deduce the variation in brain temperature as follows:

The fact that biological systems are very complex and made up of several types of tissues with different electromagnetic characteristics (permittivity and conductivity), made these models very complex to produce. The model must be representative of a user's head and allow an analysis of the power absorbed in the different tissues. Digital models are usually built from magnetic resonance images (IRM) (Simunic et al., 1996).

 

Numerical simulations are generally carried out by the

FDTD  (Finite  Difference Time  Domain)  method  (Yee,

1966) which consists in solving Maxwell's equations in the

0x

Dq = (s/2r)* çE2

ç*t/rCp

(30)

temporal and spatial domain. A mobile phone operating at

900 Mega Hertz [MHz] and with a powerful peak of 2 Watts

0x

With : (s/2r)* çE2

ç= P

moy

average power received by the

[W],  the  simulations  indicate  a  SAR  of  1,1  Watt  per

brain in millewatt per cubic meter [mW/ Cm3]

 

We will below, proceed to the numerical simulation of various electromagnetic quantities modeled above.

 

III. SIMULATION AND INTERPRETATION OF RESULTS

 

A.  Assumptions and necessary data

1) Hypothesis [2]

 

We will use the previous theoretical analysis to evaluate the  power  distribution  induced  by  a  1.8  Giga  Hertz

[GHz]electromagnetic wave  (GPS)  in  a  spherical  brain model with a radius of 10 Centimeter [Cm].

 

2) Data needed

 

Pi =1 mW/ Cm3:Incident wave power [13];

Z0 =120p Ohm [W]  : Intrinsic vacuum impedance [3];

er=35 and s= 0,7 in mileseconds per meter [ms/m][13];

e0=10-9/36p Faraday per meter [F/m]   and e0=4p10-7  in

Tesla per Ampere meter [T/Am];

a = 0,1 and b = 4 in radian per meter [rad/m] [4];

 

The mass and volume of a human brain are estimated on average to be 1,3 kilogram [kg] and 1,5 liters respectively. Which corresponds to an average density [4]:

 

r=870 kilogram per cubic meter [kg/m3]

 

It can be said that the biological system and the brain are generally made up of 70% water, and it is these molecules that are mainly subjected to internal friction responsible for heat. It is therefore logical to take the average specific heat capacity of the brain a value close to that of water, namely:

 

Cp=4000 Joule per kilogram celsius [J/kg °C] [5].

 

 

 

 

3) Modeling of biological tissues [14]

kilogram[W / kg]. Dosimetric analysis also shows that the

head absorbs about 50% of the power emitted by the radio

telephone, the skin absorbing 15%, the muscle 10%, the cerebrospinal fluid 5% and the brain 13%.

 

B.  Presentation and analysis of simulation results

1) Electric fields in the tissues as a function of the depth to be crossed

 

100

50

0

0                10               20               30

Crossing depth z in centimeter[Cm]

 

 

 

Fig.1. Curve of electromagnetic fields in tissues as a function of the depth crossed

 

We find that the penetration of electromagnetic fields into the tissues will be very quickly limited because of the skin effect on the one hand and the energy dissipation in the medium on the other hand. The skin effect results in a decrease in the electric field at a distance z from the interface.

 

2) Wavelength variations in the muscle as a function of the Frequency

 

 

4

2

0

0               5             10             15

frequency in Giga Hertz [GHz]

 

 

 

Fig. 2.Variation of wavelength in muscle as a function of frequency.

 

The curve in Figure 2 above shows the variations in muscle wavelength as a function of frequency. It shows that at a frequency of 2 Giga Hertz [GHz], the length of the wave propagating in the muscle is 1,5 centimeter [Cm]. The electrical parameters used to construct this figure (as well as the following ones) are taken from [6].