Eq25879884

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 the
study the modeling and the simulation of physical integro-differentials operators which is based on the
systems 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 ADS
this paper a new method to improve the analysis simulator to make a simple comparison between the
of the wideband antenna witch is the bond graph two methods.
approach. This type of antenna is gotten by using
several shapes as the parasitic antenna that has a II. STRUCTURE OF WIDEBAND PATCH
narrow bandwidth. This study describes the ANTENNA
modeling of a parasitic antenna by bond graph To have an antenna with a wideband, we
approach and the simulation of the scattering proposed parasitic antenna shown by figures 1(a) and
parameters of this antenna. Our aim, also, is to (b) which represents respectively the 3D schematic
control 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 the
parasitic patch. parasitic patch to follow the same equations for the
rectangular shape, the same width and length of the
Keywords - Parasitic antenna, Bond Graph patch was made to ease the determinations of the
Modeling, Microstrip Patch Antenna (MPA), parameters of our antenna.
Square Patch, Scattering Formalism. Parasitic patch
Main patch

z εr1 H2
I. INTRODUCTION x y ε r2 H1
A microstrip patch antenna is a critical
component for any wireless communication systems Feed line
because it has many favorable characteristics as
planar configuration, low profile, light weight, easy Fig. 1 (a) 3D schematic structure of parasitic antenna
analysis and easy integration with other microwave (b) side view of parasitic antenna
circuits but, in general, rectangular patch antennas
have the disadvantage of a narrow bandwidth. This The proposed antenna is formed by two
last parameter is an important one for certain systems elementary patches, the main patch and the parasitic
as 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 patch
antenna is gotten by the network of patch antennas or without forgetting the importance of coupling
by the parasitic antennas [1]. In the setting of this between the two radiating elements [1] [4] as figure 2
article, we have constructed the precise and simple shows, the main patch is considered as virtual ground
electric models from the geometric measurements of plan for the parasitic patch. Cc denotes the capacitive
the patch antenna to be able to control the coupling coupling caused by the two resonators. These are the
between the two elementary (main patch and main patch (R1 L1 C1) and the parasitic patch (R2 L2
parasitic patch). On the other hand, we can follow the C2).
resonance frequency and width band of a simple
way. This electric model has been constructed while
even applying the technical for the simple patch [2].
First we have determined the model bond graph of
the parasitic antenna. Then we have transformed this

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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
W
patch 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
2H
III. 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  
2
using 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  0
following 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 2
The inductance L is given by: εeff  r  1  12  (17)
2 2  W
1
L 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 
1
QD  : 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 dyn
QR  : Radiation quality factor (8)
4 fr H
0.786 f r Z a 0 (W ) H
QC  : Losses in the
Pa
conductor (9)

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• 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
c
Port Port
1 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

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Fig. 5 Decomposition of reduced bond graph model

V yCc
i  , i  I R0 (26)
R0
These are reduced voltage and current. ε2
ε'1 ε'1
 1  1 1 1  a1 
     P1
2 1  1 b1 
  (27) 0 1 P' P' 0 P2
 1    φ1 φ'1 φ'1
 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-model
We use the preceding equations; we can find for each 1 1
case 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 R0
following 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 model
We 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  1
determine 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 ε'2 ε'2 ε2   y mp
 H 22 
z Cc y mp  1
P1
0 1 1 0 P2 
φ1 φ'2 φ'2  H 1
φ1
 
 z Cc y mp  1
ymp ypp

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The equation 23 we permit to extract in the following The simulation given by figure 8 shows the variation
matrix. 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 can
be given by the product of the first and the second
wave 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 graph
antenna bandwidth according to the capacity of approach), we find the same characteristics of the
coupling 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 all
Fig.7 Variation of parasitic antenna bandwidth carried out works, without forgetting the members of
according 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 for
the coupling capacity Cc modifies the bandwidth as this study in particularly L.A.C.S members
shown on the figure 7. (Laboratory of analysis and command systems).
Indeed, Cc essentially depends on surfaces
occupied by the two patches, the permittivity of
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883 | P a g e

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