Eq25879884

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Eq25879884

  1. 1. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884 Modelling and Determination of the Scattering Parameters Of Wideband Patch Antenna By Using A Bond Graph Approach Riadh MEHOUACHI*, Hichem TAGHOUTI*, Sameh KHMAILIA*, Abdelkader MAMI** * (Department of Electrical Engineering, Laboratory of Analysis and Command Systems, National Engineering School of Tunis, P.O. Box 37, 1002 Tunisia) ** (Laboratory of High Frequency Circuits, Department of Physics, Sciences Faculty of Tunis, 2092 El Manar Tunis Tunisia)ABSTRACT In the setting of research works which last model to the reduced bond graph model by thestudy the modeling and the simulation of physical integro-differentials operators which is based on thesystems functioning at high frequency causal ways [3] to determine the scattering(transmission lines, filter based on localized parameters (reflexion and transmission coefficient).elements, patch antenna, etc...) , we propose in Finally we repeat the simulation using ADSthis paper a new method to improve the analysis simulator to make a simple comparison between theof the wideband antenna witch is the bond graph two methods.approach. This type of antenna is gotten by usingseveral shapes as the parasitic antenna that has a II. STRUCTURE OF WIDEBAND PATCHnarrow bandwidth. This study describes the ANTENNAmodeling of a parasitic antenna by bond graph To have an antenna with a wideband, weapproach and the simulation of the scattering proposed parasitic antenna shown by figures 1(a) andparameters of this antenna. Our aim, also, is to (b) which represents respectively the 3D schematiccontrol the bandwidth through the capacity of structure and the side view of the proposed MPA.coupling between the main patch and the We chose the square shape, the main and theparasitic patch. parasitic patch to follow the same equations for the rectangular shape, the same width and length of theKeywords - Parasitic antenna, Bond Graph patch was made to ease the determinations of theModeling, Microstrip Patch Antenna (MPA), parameters of our antenna.Square Patch, Scattering Formalism. Parasitic patch Main patch z εr1 H2I. INTRODUCTION x y ε r2 H1 A microstrip patch antenna is a criticalcomponent for any wireless communication systems Feed linebecause it has many favorable characteristics asplanar configuration, low profile, light weight, easy Fig. 1 (a) 3D schematic structure of parasitic antennaanalysis and easy integration with other microwave (b) side view of parasitic antennacircuits but, in general, rectangular patch antennashave the disadvantage of a narrow bandwidth. This The proposed antenna is formed by twolast parameter is an important one for certain systems elementary patches, the main patch and the parasiticas that to the reading level of systems known as patch which has the same geometric measurements.Radio Frequency Identification (RFID). This type of We can apply the electric model to the parasitic patchantenna is gotten by the network of patch antennas or without forgetting the importance of couplingby the parasitic antennas [1]. In the setting of this between the two radiating elements [1] [4] as figure 2article, we have constructed the precise and simple shows, the main patch is considered as virtual groundelectric models from the geometric measurements of plan for the parasitic patch. Cc denotes the capacitivethe patch antenna to be able to control the coupling coupling caused by the two resonators. These are thebetween the two elementary (main patch and main patch (R1 L1 C1) and the parasitic patch (R2 L2parasitic patch). On the other hand, we can follow the C2).resonance frequency and width band of a simpleway. This electric model has been constructed whileeven applying the technical for the simple patch [2].First we have determined the model bond graph ofthe parasitic antenna. Then we have transformed this 879 | P a g e
  2. 2. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884 1 W   1    0.441  0.082  r 2   (10) 60  2H  r   Z a (W )     r    r  1 W    2 (1.451  ln[  0.94])   r 2H  Is the impedance of an air filled microstrip line Z a 0 (W )  Z a (W , ε r  1)Fig. 2 Equivalent circuit of the proposed parasitic Wpatch antenna 2 W Pa (W )  2 (  H  )(1  W ) W  2 ln[2 exp( W  0.94)  (11)   H W H H  2H   0.94 2HIII. THEORETICAL CONSIDERATION Tgδ: is the tangent of loss in the dielectric and is given by:3.1 Analysis of parasitic antenna: The width of (MPA) can be determined by H  W   (12) δ   0.882  0.164 (ε r  1) / ε r  (( ε r  1)(0.756  ln(  1.88)) / πε r   2using the following equation [2][5]: W  H  1 2 C dyn (ε ) W (1) ε dyn  (13) 2 f r μ0 ε 0 εr  1 C dyn (ε 0 ) Where ƒr resonant frequency ε0 ε r A 1  ε reff (ε r , H ,W ) ε ε A (14) ε0 and µ0 are the permittivity and the permeability in C dyn (ε )     0 r  Hγn γm 2γn  c0 Z (ε r  1, H ,W ) H free space respectively. The determinations of the parameters of the 1, j  0 γj  main and the parasitic are determined by the 2, j  0following equations 1 377 W W  (15) ε eff ε 0W 2 Z (W , H , εr )   1.393  0.667 ln   1.44  2  πx  H H  H C cos  0  (2) 2H W  W f( )  6  (2π  6) exp( 36.66 H )0.7528 (16)C : capacitance H W : the distance of the feed point from the edge of The effective dielectric constant of microstrip line and is given by:the patch. 1 H : thickness of dielectric ε  1 εr  1  H 2The inductance L is given by: εeff  r  1  12  (17) 2 2  W 1L 2 (3) The capacity of Gap in presence of dielectric which wresC wres  2πf r (4) describes the coupling between the two patches is given by:The resistance R is calculate using equation (5) ε0 ε r  πs   0.02 H 1  QT C gd  ln coth   0.65C f  εr  (1  2 ) (18)R QT : Quality factor (5) π  4H   S εr  wr C Cf  C f1  C f 2 C f : Fringe capacity 1  1 1 1 QT      (6) 1  Z (W , H , εr  1) ε0 εrW  Cf1    L (19)  QR QC QD  2γn  cZ 2 ( L, H , εr ) H  1QD  : Losses in the dielectric (7) 1  Z (W , H , εr  1) ε0 εrW  Tgδ Cf 2    W (20) 2γm  cZ 2 ( L, H , εr ) H  c0 ε dynQR  : Radiation quality factor (8) 4 fr H 0.786 f r Z a 0 (W ) HQC  : Losses in the Paconductor (9) 880 | P a g e
  3. 3. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884 • zCc: the reduced impedance of the element put in series 3.2 Characteristics of parasitic antenna The figure 3 indicates that our system is composed of The summary of antenna characteristics are shown three main parts that are port 1 (power source), port 2 (load) and quadruple (process). The causality on table1, the main patch and the parasitic patch have assignment in input-output of this process [10] is the same measurements and characteristics. shown by figure 4 ε2 Port2 ε1 Port1 Process φ1 φ2 Main patch characteristics value (mm) Main patch width (W) 37.9mm Fig .4 Reduced bond graph model with flow-effort causality Relative permittivity (εr1) 2.6 ▪ ε1 and ε2 are respectively the reduced variable Tang (δ) 0.002 (effort) at the entry and the exit of the system. Thickness of dielectric (H1) 3.2mm ▪ φ1and φ2 are respectively the reduced variable (flow) at the entry and the exit of the system. Table 1. Summary of patch characteristics This type of reduced and causal bond graph has the following matrix:   1   H 11 H 12  1 I. SCATTERING PARAMETERS OF THE     H H 22   2  (21) PARASITIC ANTENNA  2   21   First we propose to determine the scattering We can note parameters [6] of the parasitic antenna [2] from its H H12  H   11 H 22  reduced bond graph model [7] without forgetting (22) causality assignment. Finally we compare the results  H 21  found by the method of bond graph with the results Hij represent the integro-differentials operators determined by using the classic method (HP-ADS associated to the causal ways connecting the port Pj software). to the port Pi and obtained by the general form given below. n Tk  k z H ij   (23) k 1  C   1   Li   Li L j   Li L j Lk  ...   1  ... (24) m cPort Port1 0 1 0 2 ▪Hij= complete gain between Pj and Pi. ▪ Δ= the determinant of the causal bond graph ▪Pi= input port. y ypp ▪Pj= output port. Quadrupl e ▪Tk= gain of the k th forward path between Pi and Pj m ▪n= total number of forward path between Pi and Pj p ▪Li= loop gain of each causal algebraic loop in the Fig.3 Reduced bond graph model of the parasitic bond graph model. antenna ▪LiLj= product of loop gains of any tow non-touching 4.1 Determination of the bond graph model of the loops (no common causal bond). ▪LiLjLk= product of the loop gains of any three pair parasitic antenna wise no touching loops. The equivalent circuit of parasitic antenna ▪Δk= the factor value of Δ for the k th forward path, that is already shown permits us to determine the this value calculates himself as Δ when one only reduced bond graph model [11] given by the following figure. keeps the causal loops without touching the k th • ymp and ypp: are respectively the reduced chain of action. equivalent admittance of the main patch and parasitic We noted: patch.  i  i  i  i ai  , ai  (25) 2 2 881 | P a g e
  4. 4. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884 Fig. 5 Decomposition of reduced bond graph model V yCci  , i  I R0 (26) R0These are reduced voltage and current. ε2 ε1 ε1 1  1 1 1  a1      P1 2 1  1 b1   (27) 0 1 P P 0 P2 1    φ1 φ1 φ1 2  1 1 1  a2      2 1  1 b      (28) 2   2  zmp zpp b1   w11 w12  a2  a  a  w    W  2   b  b  (29) 1   21 w22  2   2 Fig. 6 The first and the second sub-modelWe use the preceding equations; we can find for each 1 1case of causality one wave matrix. ymp  τ cmps   (34) τ Lmp s τ Rmp 1 1  H 11  H 22  H 1  H 11  H 22  H W   (30) 2 H 21 1  H 11  H 22  H 1  H 11  H 22  H  1 1 y pp  τ cpp s   (35)With τ Lpp s τ RppH  H11 H 22  H12 H 21 (31)The following scattering matrix gives us the zCc   Cc s (36)scattering parameters: Where: b1   s11 s12  a2  a   Ci  R0  Ci b   s    S  1   a  A  (32) 2   21 s22  2   2 Li  Li The relation between equations permits us to get the R0following equations: R0: the scaling resistance and s: The Laplace w11   s 22 s 1 21 operator.  1 We have the integro-differentials operators given by w12  s 21 the previously equations.  1 1 w21  ( s12 s 21  s11s 22 ) s 21 L1  : Loop gains of algebraic given by sub-  1 z mp yCc w22  s11 s 21 model.The corresponding scattering matrix is given by: 1 1  1  : Determinant of causal bond graph z mp yCc  w w 1 ( w w  w w )  1S   12 22 T 11 22 21 12 w22  (33) of the first sub model.  1  w w 1  The following equations represent the integro-  w22  21 22   differentials operators of the modelWe can make a decomposition of the reduced bond  z Cc  H 11 graph model [3] [9] [10] given by figure 3 to z Cc y mp  1determine the W matrix easily, this decomposition is given by figure 5 and 6 H  1  12 z Cc y mp  1 zCc Decomposition  H  1  21 z Cc y mp  1 (37)  ε1 ε2 ε2 ε2   y mp  H 22  z Cc y mp  1 P1 0 1 1 0 P2  φ1 φ2 φ2  H 1 φ1    z Cc y mp  1 ymp ypp 882 | P a g e
  5. 5. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884The equation 23 we permit to extract in the following The simulation given by figure 8 shows the variationmatrix. of parasitic antenna bandwidth according Cc if we use the HP-ADS software. 1  zCc y pp  zCc  y pp  2 zCc y pp  zCc  y pp  (38)W1    2  zCc y pp  zCc  y pp zCc y pp  zCc  y pp  2With the same method we can determine W2 1 2  ymp ymp W2   2  y pp  (39) 2  ymp  The wave matrix of the complete model canbe given by the product of the first and the secondwave matrix [8]. W W12 WT  W1 * W p   11 W   (40)  21 W22  Fig.8 Variation of parasitic antenna bandwidth according Cc (under HP-ADS software)4.2 Simulations results We used a simple programming and We can see that the two results are similar,simulation under Maple software to determine if we use the traditional method (HP-ADS software)scattering parameters. The variation of parasitic or we used this new method (the bond graphantenna bandwidth according to the capacity of approach), we find the same characteristics of thecoupling between the two patches is represented by reflection coefficient.figure 6. IV. CONCLUSION This study designed the parasitic antenna that has a narrow bandwidth. We notice that the bandwidth is variable by varying the coupling capacity which is proportional to the dimensions of the parasitic patch and the distance between the two patches. In this paper we chose the tool of modelling using band graph approach to analyze the parasitic antenna, this tool offers us several advantages as the possibility to simulate structures of a simple, fast, efficient and more economic manner. For these reasons, it is possible to apply this new analysis method in many wireless systems and microwaves domain. ACKNOWLEDGEMENTS We would like to thank especially Prof. MAMI Abdelkader and Dr. TAGHOUTI Hichem for the time and guidance given throughout the allFig.7 Variation of parasitic antenna bandwidth carried out works, without forgetting the members ofaccording Cc (using bond graph approach) the unit of electronics and high frequency circuits Mr. MEHOUACHI Riadh and Miss. KHMAILIA Our survey showed us that the variation of Sameh and all those who contributed and aided forthe coupling capacity Cc modifies the bandwidth as this study in particularly L.A.C.S membersshown on the figure 7. (Laboratory of analysis and command systems). Indeed, Cc essentially depends on surfacesoccupied by the two patches, the permittivity of REFERENCESsubstrate that separates them as well as the distance [1] K. chin, H. Chang, and J. Liu, "Design ofbetween the two resonant poles. Figure 6 show that LTCC Wideband Patch Antenna for LMDSthe wideband increases progressively if the capacity Band Applications’’ Antenna and wirelessof Cc coupling increases; the variation of Cc between propagation letters, Vol.9, 20101.7pF and 4pF increases the wideband with 50 MHz. [2] R. Mehouachi, H. Taghouti, S. Khmailia and M. Abdelkader "Modeling and Simulation of the Patch Antenna by using 883 | P a g e
  6. 6. Riadh MEHOUACHI, Hichem TAGHOUTI, Sameh KHMAILIA, Abdelkader MAMI /International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.879-884 Band Graph approach", International Mathematics, Berlin, Germany, Vol. 1, Journal of Advances in Engineering and pp.651-656 Technology, Vol. 2, Issue 1, pp. 474-484 [8] H. Taghouti, A. Mami, "Discussion around the Scattering matrix Realization of a[3] H. Hichem and M. Abdelkader, " Microwave filter using the Bond Graph Extraction, Modelling and Simulation of Approach and Scattering Formalism" , Scattering Matrix of a Chebychev Low-Pass American Journal of Applied Sciences 9 (4): Filter with cut-off frequency 100 MHz from 459-467, 2012 ISSN 1546-9239. its Causal and Decomposed Bond Graph [9] T. Hichem, M. Abdelkader "Application of Model", ICGST-ACSE Journal, Vol 10, the reduced bond graph approaches to Issue 1,November 2010, pp. 29-37 determinate the scattering parameters of a high frequency filter", Proceedings of 10 th[4] K. chin, H. Chang, and J. Liu, B. Chen, J. International conference on Sciences and Cheng and J. Fu "Staked patch antenna techniques of Automatic control & computer array on LTCC substrate operated at 28 engineering, STA’2009-SSI-548, pp 379- Ghz," J. of Electromagn. Waves and Appl., 391, Hammamet, Tunisia, December 20- Vol. 25,527-538, 2011 22,2009.[5] M. Mohd Shah, M. Abdul Aziz and M. [10] Hichem Taghouti and Abdelkader Mami, Suaidi ‘’Dual Linearly Polarized Microstrip ‘’New extraction method of the scattering Array Antenna" Trends in parameters of a physical system starting Telecommunications Technologies from its causal bond graph model:[6] F. Andrea, P. Marco, " Generalised Mixed- Application to a microwave filter’’, Mode S-Parameters" , IEEE Transactions International Journal of the Physical on Microwave Theory and Techniques, Vol. Sciences Vol. 6(13), pp. 3016–3030, 4 July, 51,no.1,p.p 458-463, 2006 2011. DOI: 10.5897/IJPS10.216.[7] M. L. Kouba, Maher Amara, "Contribution [11] A. Maher, S. Scavarda, "A procedure to à l’Etude des Aspects match bond graph and scattering formalisms Energétique en Robtique mobile", 15th ". Journal of the Franklin Institute Vol. 328, IMACS World Congress on Scientific ISSUES 5-6? pp. 887-89? 1991. Computation, Modelling and Applied 884 | P a g e

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