computational simulation of antennas array of 17 elements

8/18/2019 Computational Simulation of Antennas Array Of 17 Elements

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Computational Simulation of Antennas

Array with 17 elements.C. Calderón-Ramón1, J. Martínez-Castillo2, J. E. Lopez- Calderón3,V. Velázquez-Martínez1, O. Cárcamo-Sarmiento1, D. Torres-Hoyos1

1 FIME, FIEC, FA, Universidad Veracruzana, Poza Rica Veracruz, México.

2Centro de Micro y Nano Tecnología, Universidad Veracruzana, Veracruz, Ver, México.

3 FIME, UANL, San Nicolás de los Garza, Nuevo León, México.

[email protected]

Abstract — In this study described the use of the previouslyFinite Difference Time Domain method, for analyze the behavior

electromagnetic with a diffractor or Perfect Electric Conductor

inside of an antennas circular array of 17 elements, this array

consists of one transmission antenna and 16 receiving antennas RX. The system uses a Gaussian pulse as excitation with a

frequency of 7.5 GHz. The method solves Maxwell's derivative

equations using the finite difference equations. A diffractor is

discretized in geometric square form, using the Perfect Electric

Conductor conditions for its implementation in the computational

algorithm and the analysis of the electromagnetic fields in the

same. We used the absorption boundary condition due it is

necessary that the electromagnetic waves are absorbed or

attenuated, thus truncating its spread outward of the region of

calculation. We matched the electric and magnetic fields of system.

Keywords — Finite difference time domain method; perfectelectric conductor; diffractor; absorption boundary condition.

I. I NTRODUCTION

The differential equations play a pivotal role in themodeling of number of physical phenomenon. Theapplications of such equations include, fluid mechanics, biology, physics, engineering, behavior electromagnetic and biomedicine. The finite difference time domain method(FDTD) is becoming increasingly popular for numericalcalculations of electromagnetic scattering and absorption [1] by several materials, media dispersive. The antenna array [2]is used by example in biomedical applications basedmicrowave system, in this research the system consists in anantennas array, placed in circular form, with 17 elements, we

have made a two dimensional Finite Difference Time Domain(FDTD) computational electromagnetics analysis of thissystem as has been proposed by [3], where computationalalgorithm was made in Matlab. Some research present theexistence and uniqueness solutions of differential equation ofan arbitrary order with integral boundary condition; we haveused the absorption boundary conditions for cut the propagation of the signal on the limits of the calculus region,in this paper was used the Perfectly Matched Layer (PML) [4].Evaluation results show that proposed system of antenna array

is suitable for the development of for a breast cancer earlydetection system at non-ionizing frequencies [5], we wouldonly change the diffractor with a phantom representing themalignant tissue, but this is a future work.

II. ELECTROMAGNETIC COMPUTATIONAL TOOLS

A.

Finite Difference Time Domain method.

It is used in order to transform the Maxwell´s differentialequations and transform them to finite difference equations onthe time domain, electromagnetic equations algebraicallysolving the system of calculation by dividing the region intosmall uniform cells, called Yee cells [1]. Subsequently limitrequires infinite propagation of electromagnetic wavetransmitting antenna fed by (TX) using the BoundaryConditions of Absorption, the method used is PerfectlyMatched Layers (PML)[4], which are described in thefollowing section. Finally use Perfect Electrical Conductor

conditions (PEC) to determinate the Electric and MagneticField equations, modeling a diffractor inside the antenna array.

In this paper, the application of the FDTD and PML[6]methods are for a two dimensional and magnetic transversalmode (TM) system, which is our case of study.

The set of six equations used [7] in the analysis ofelectromagnetic propagation are:

(1)

(2)

(3)

(4)


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(5)

(6)

The system to two dimensions: considering that in the Z-axis are no changes in the geometry or electrical properties of

the propagation medium is made. This means that thederivatives of the field in the Z direction are equal to zero

. Applying this consideration to the previousderivative equations (1) - (6), we have:

(7)

(8)

(9)

(10)

(11)

(12)

For the propagation mode TM, we know that Hx=0, Hy=0, Ez=0 and there are no magnetic currents. Then the system of(7)-(12) are reduced [8]:

(13)

(14)

(15)

We used of the FDTD method to the equations (13) - (15)for convert to finite difference time domain equations,equations, which they are defined in (16)-(18).

(16)

(17)

(18)

B.

Perfectly matched layer (PML) method

This PML is used when it is necessary to model devicesthat interact with electromagnetic fields, where it is necessarythat the electromagnetic waves are "absorbed" or attenuated[9], thus truncating its spread outward of the region ofcalculation. One of the problems presented for a successfulimplementation is the reflection at the periphery of the regioncalculus, which would affect the results. It is characterized bythe breakdown of the transverse field to the direction of

propagation into rectangular projections, and the use of bothelectrical conductivity and magnetic in numerical layer for theabsorption of electromagnetic fields. It is the most usedabsorbing boundary condition for its versatility and itsefficiency.

There is a new version of the model of PML improvement proposed by [7], with an optimized technique forimplementation of the model, using a reduced set of equations.This new formulation is based on the physical representation


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of the medium, which is achieved by the electrical andmagnetic characteristics, using a system of equations torepresent three different media as we shown in Table 1 and theFig. 1.

TABLE 1 ELECTRIC PARAMETERS OF THE PML REGION.

Medium Absorption Boundary Condition PML

Free

spaceAbsorbent

regionPEC

Where, represent the electric conductivity, and * isthe magnetic conductivity.

Fig. 1. Three zones of the calculus region

The equations to implement the PML technique in thesystem, require the decomposition of Hz in its orthogonalcomponents Hzx and Hzy, which they are defined in equations(19) and (20).

(19)

(20)

III. PROPOSED ANTENNA ARRAY

The array was a group of 17 antennas, placed in circularform, with ! = 21.5°, with an antenna of transmission (TX1),

and 16 antennas of reception (RX1 to RX16), they detect thesignal of propagation for sense the electromagnetic parametersas: electric field, magnetic field, reflected power, incident power, total power, a diffractor is placed inside of the system.

The calculus region is divided in 1300 by 1300 Yee cell,each antenna and the square diffractor are placed in a positionwith (i, j) coordinates, as we shown in the Table 2 an the Fig.

2. The propagation signal was a frequency of 7.5 GHz. Forcomputational algorithm we utilized Matlab program.

TABLA 2 ANTENNAS POSITION IN CELLS

Antennas position (i, j coordinates)

TX1(650,450)

RX1(578,464)

RX2(515,502)

RX3(471,561)

RX4(451,632)

RX5(458,705)

RX6(490,771)

RX7(545,820)

RX8(613,847)

RX9(687,847)

RX10(755,820)

RX11(810,871)

RX12(842,705)

RX13(849,632)

RX14(829,561)

RX15(785,502)

RX16(722,464)

Fig. 2. Antenna array of 17 elements with a diffractor inside.

IV. NUMERIC RESULTS

We can test electric parameters in each antenna RX, theantenna TX1 fed a Gaussian pulse with central frequencyequal to 7.5 GHz. The signal is diffracted by the PEC.

We shown some the electromagnetic numeric results in theFig. 3, where a) the component Ex propagation in the xdirection, b) Eyt electric field component propagation in the

direction "y" and c) the vector sum of the components Ex andEy; besides the diffractor and energy scattered by himself, at1250 iterations of time it is also observed.

The calculus region in the Fig. 3 is 1300i and 1300 j Yeecells, the fee start in 400i and 650 j. PEC is located in 650i, 650 j as shown in the Fig. 3 the Exy vector sum of the total electricfield. The electric field unit is V/m.


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"#$ !" %&'(&)*)+

",$ !$ %&'(&)*)+

Fig. 3 Vector sum electric field Exy, to 1250 iterations,7.5 GHz, with a circular diffractor inside.

In Fig. 5 the propagation of magnetic field Hz, obtainedvarious iterations of time shown.

#$

,$

%$

Fig. 4. Exy Electric Field, with a diffractor inside, toa) 950,b) 1150, c) 1450 iterations.

a)

b)


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c)

d)

Fig. 5. Hz Magnetic Field, to a) 850, b) 1000,c)1150 and d)1250 iterations.

CONCLUSION

In this study, we have utilized the numerical methodFDTD to solve the derivative Maxwell´s equations using theFDTD method and PML method to truncate the propagationof the electromagnetic wave to the outside of the calculusregion. The results obtained with the methods were good due

to that we found the symmetry in the electromagnetic signal inthe antennas with position equivalent, and minimal reflection,as we wait. We can say that the methods of the computationalelectromagnetic in its general form are a very good option,easy to use and they can solve the Maxwell´s differentialequations in simple manner. All results obtained by usingMatlab.

R EFERENCES

[1].

Taflove, S. Hagness, “Computational Electrodynamics, the FiniteDifference Time Domain Method”, Norwood M.A, USA: ArtechHouse, 2005.

[2].

Elsherbeni, V. Demir, “The Finite-Difference Time-Domain

Method for Electromagnetics with MATLAB Simulations”,

SciTech Publishing Inc, Raleigh N.C, USA, pp. 187-215, 2009.[3].

J. Berenger, “A perfectly matched layer for the absorption ofelectromagnetic waves”, Journal of Computational Physics,vol 114, pp.185-200, 1994.

[4].

A. Benavides, M. Alvarez, M. Enciso, J. Sosa, “Analysis of polynomial and geometric conductivity profiles in PML layers:a comparison”, Progress in Electromagnetics ResearchSymposium, PIERs, 2010.

[5].

S. C. Hagness, A. Taflove, J. Bridges, “Two DimensionalFDTD Analysis of a Pulsed Microwave Confocal System for

Breast Cancer Detection: Fixed- Focus and Antenna ArraySensors”. IEEE Transactions on Biomedical Engineering,vol.45, No. 12, pp. 1470-1479, 1998.

[6].

A. Benavides, M. Nieto, M. Enciso, J. Sosa, “Parametricanalysis of perfect matched layer model of finite differencetime domain method, Applied Mechanics and Materials”, vol15, pp. 139-144, 2009.

[7].

A. M Benavides, M. Alvarez, C. Calderón, J. Sosa, M. Galaz,M. RodrÍguez, M. Enciso, C. Márquez, “A novel set ofreduced equations to model perfect matched layer (PML) inFDTD”, RMF E, Vol 57(1), pp. 25-31, 2011.

[8].

C. Calderón Ramón, Doctoral Thesis, ESIME Culhuacán, IPN,2015.

[9]. C. M. Calderón, H. M. Pérez, A. M. Benavides, L. J. Morales,“Desarrollo de un Arreglo Circular de Antenas utilizandoherramientas de Electromagnetismo Computacional. Centro deInformación Tecnológica”, vol. 25 (1), pp. 41-54, 2014.

computational simulation of antennas array of 17 elements

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