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International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 3, June 2018, pp. 1611~1617
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i3.pp1611-1617  1611
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Effect of the Thickness of High Tc Superconducting
Rectangular Microstrip Patch Over Ground Plane
with Rectangular Aperture
Nabil Boukhennoufa1
, Lotfi Djouane2
, Houcine Oudira3
, Mounir Amir4
, Tarek Fortaki5
1,2,3
Department of Electronics, University of Mohamed Boudiaf, M‟sila, Algeria
1,2,3
Laboratory of Electrical Engineering, University of Mohamed Boudiaf, M‟sila, Algeria
4
Scientific and Technical Research Center in Welding and Control, Algiers, Algeria
5
Department of Electronics, University of Mostefa Ben Boulaid, Batna, Algeria
Article Info ABSTRACT
Article history:
Received Jan 29, 2018
Revised Apr 12, 2018
Accepted Apr 18, 2018
In recent years, a great interest has been observed in the development and use
of new materials in microwave technology. Particularly, a special interest has
been observed in the use of superconducting materials in microwave
integrated circuits, this is due to their main characteristics. In this paper, the
complex resonant frequency problem of a superconductor patch over Ground
Plane with Rectangular Aperture is formulated in terms of an integral
equation, the kernel of which is the dyadic Green‟s function. Galerkin‟s
procedure is used in the resolution of the electric field integral equation. The
surface impedance of the superconductor film is modeled using the two
fluids model of Gorter and Casimir. Numerical results concerning the effect
of the thickness of the superconductor patch on the characteristics of the
antenna are presented.
Keyword:
Full-wave analysis
High Tc superconducting
Microstrip patch
Rectangular aperture
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Nabil Boukhennoufa,
Department of Electronics,
Laboratory of Electrical Engineering,
University of Mohamed Boudiaf, M‟sila,
BP 166 M'sila 28000, Algeria.
Email: boukhennoufa.nabil@gmail.com
1. INTRODUCTION
Microwave passive devices such as resonators, filters and antennas are one of the main applications
of the high TC superconducting (HTS) materials. They show superior performance and characteristics to the
normal metal devices, such as: the power losses are low, reduction of attenuation and noise level, besides the
propagation time of signals in the circuit can be greatly reduced [1]-[6]. This allows to be used in several
applications such as mobile communications, radars and filters [7]-[10]. The study of the resonant
characteristics of High Tc superconducting microstrip antennas has been first studied by [4] using the cavity
model. Since the cavity model does not consider rigorously the effects of surface waves and fringing fields at
the edge of the patch. Recently; Silva has studied the resonant characteristics of High Tc superconducting
microstrip antennas using the full-wave analysis [11], [12]. It is noted that in the above works, the effect of
thin superconducting patch was not studied.
In this paper, the effect of thin superconducting patch loading on the resonant frequency and
bandwidth of rectangular microstrip structures illustrated in Figure 1 is investigated. The complex resonant
frequency problem considered here is formulated in terms of an integral equation using vector Fourier
transforms [13]. The surface impedance of the superconductor film is modeled using the two fluids model of
Gorter and Casimir [5], [11], [14]. The paper is organized as follows. First, the integral equation for the
unknown patch currents is formulated. The derivation is performed in the Fourier transform domain and
 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617
1612
utilized the dyadic Green‟s function of the considered structure, without taking into account the effect of the
superconductivity. To include the effect of the superconductivity of the patch, surface complex impedance,
Zs is considered. The Galerkin moment method is used to solve the integral equation. The characteristic
equation for the complex resonant frequencies is given. Various numerical results are given in Section 3.
Finally, conclusions are summarized in Section 4.
Figure 1. Geometrical structure of a superconducting rectangular microstrip patch
2. ANALYSIS METHOD
In this paper an efficient technique to derive the dyadic Green‟s functions for Superconducting
microstrip patch over ground plane with aperture is proposed. The transverse field inside isotropic region
(0<z<d) can be obtained via the inverse vector Fourier transforms as:
s s s s x y2
1
( ,z ) ( , ). ( ,z )dk dk
4
   
 
  E r F k r e k (1)
s s s s x y2
1
( ,z ) ( , ). ( ,z )dk dk
4
   
 
  H r F k r h k (2)
Where: s s
x y i .
s s
y xs
k k1
( , ) e
k kk
 
   
k r
F k r , s
ˆ ˆx y r x y , s x y
ˆ ˆk k k x y , s sk  k .
z zi z i z
s s s( ,z ) e ( ) e ( )

   
k k
e k A k B k (3)
z zi z i z
s s s s( ,z ) ( ) e ( ) e ( )

     
 
k k
h k g k A k B k (4)
In (3) and (4), A and B are to component unknown vectors and
e h
z z zdiag k ,k   k ,
h
0 x z
s e
0z
k
( ) diag ,
k
 
 
 
  
  
g k (5)
e
zk and h
zk are propagation constants for TM and TE waves respectively in substrate [15]-[18].
Writing (3) and (4) in the plane z=0 and z=d, and by eliminating the unknowns A and B, we obtain the matrix
form:
s s
s s
( ,d ) ( ,0 )
( ,d ) ( ,0 )
 
 
   
    
   
e k e k
T
h k h k
(6)
x
y
b
a
d
0z
e
Superconducting
Patch
Dielectric substrate
000 ,,  zx
a o
Rectangular Aperture ao x bo
Int J Elec & Comp Eng ISSN: 2088-8708 
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch … (Nabil Boukhennoufa)
1613
With
11 12 1
z21 22
cos i sin
, d
i sin cos

    
     
    
T T θ g θ
T θ k
T T g θ θ
(7)
Equation (7) combines e and h on both sides of substrate as input and output quantities. The
continuity equations for the tangential field components at the interface z=d are:
s s s( ,d ) ( ,d ) ( ,d ) ( ) 
   se k e k e k e k (8)
s s s( ,d ) ( ,d ) ( ) 
 h k h k j k (9)
s( )j k in (9) is related to the vector Fourier transform of s( )J r , the current on the patch, as [19]
s s s s x y( ) ( , ) . ( )dk dk
   
 
  j k F k r J r ,
x s
s
y s
J ( )
( )
J ( )
 
  
 
r
J r
r
(10)
The continuity equations for the tangential field components at z=0 are:
s s s 0( ,0 ) ( ,0 ) ( ,0 ) ( ) 
   se k e k e k e k (11)
s s 0 s( ,0 ) ( ,0 ) ( ) 
 h k h k j k (12)
In (12), 0 s( )j k is the vector Fourier transform of the current 0 s( )J r on the ground plane with a
rectangular aperture. In the unbounded air region above the patch the electromagnetic field given by (3) and
(4) should at z   ( z )  according to Summerfield‟s condition of radiation, and this yields:
s 0 s s( ,d ) ( ) ( ,d ) 
 h k g k e k (13)
s 0 s s( ,0 ) ( ) ( ,0 ) 
  h k g k e k (14)
Where 0 s( )g k can be easily obtained from the expression of s( )g k given in (5) by allowing
x z r 1     . Combining (6), (8), (9) and (1)-(14), we obtain a relation among s( )j k , s( )j k , ( )se k
and 0 ( )se k given by:
xx xy xx xy x 0x x
yx yy yx yy y 0y y
Q Q WW WW EE J
Q Q WW WW EE J
       
           
             
(15)
xx xy xx xyx 0 x 0x
yx yy yx yyy 0 y 0y
WW WW Y YJ EJ
WW WW y yJ EJ
       
           
           
(16)
To include the effect of the superconducting of the microstrip film, the dyadic Green‟s function is
modified by considering a surface complex impedance Zs, is determinate by using the model of Gorter and
Casimir [5], [11], [14].
0
sZ
2


 (17)
If the thickness of the superconducting film R is less than three penetration depths, a better boundary
 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617
1614
condition is given by [5]:
s
1
Z
R.
 (18)
Where the complex conductivity is given by [5], [7]
 
4 4
2
n 0 0
CC
T T
1 i
TT
   
     
              
(19)
With λ0 is the skin depth at zero temperature, σn is the conductivity of normal electrons and Tc
critical temperature of the superconductor.
The electric field and the surface current densities total in the interface z=d (E ,J )T T are the electric
fields and the surface current densities in the film (E ,J )i i
T T and out the film (E ,J )O O
T T respectively.
i o
T T T
i o
T T T
  

 
E E E
J J J
(20)
By substituting Equation (20) in Equation (15), we obtain
o
xx s xy xx xy x 0x x
o
yx yy s yx yy y 0y y
Q Z Q WW WW EE J
Q Q Z WW WW EE J
        
                        
(21)
xx xy xx xyx 0 x 0x
yx yy yx yyy 0 y 0y
WW WW Y YJ EJ
WW WW y yJ EJ
       
           
           
(22)
Boundary conditions require that the transverse electric field of (21) vanishes on the
superconducting patch and the current of (22) varnishes off ground plane, to give the following coupled
integral equations for the patch current and aperture field:
xx s x xy y xx x 0 xy y 0 x y x y[ (Q Z ) J Q J WW E WW E ] exp( i k x i k y ) dk dk 0
 
 
       (23)
yx x yy s y yx x 0 yy y 0 x y x y[ Q J (Q Z ) J WW E WW E ] exp( i k x i k y ) dk dk 0
 
 
       (24)
xx x xy y xx x 0 xy y 0 x y x y[WW J WW J Y E Y E ] exp( i k x i k y ) dk dk 0
 
 
      (25)
yx x yy y yx x 0 yy y 0 x y x y[WW J WW J Y E Y E ] exp( i k x i k y ) dk dk 0
 
 
      (26)
3. NUMERICAL RESULTS AND DISCUSSION
Table 1 summarizes the calculated resonance frequencies and those obtained through the cavity
model [6] for three different widths of the patch and differences between these results dues less than 2% are
obtained. Excellent agreement between our results and those calculated by Full-wave analysis [11] and those
obtained by Cavity Model [6] is observed and represented in Table 2.
Int J Elec & Comp Eng ISSN: 2088-8708 
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch … (Nabil Boukhennoufa)
1615
Table 1. Comparison of Calculated Resonant Frequencies with those Presented by Richard et al [6]
a=1630m, n=106
S/M, Tc =89K, 0 =140nm, e=350nm; T=77K, r =23.81, d=254m and a0 =0
b (µm)
Resonance Frequencies (GHz)
Error (%)
Cavity Model [6] Our results
935 28.95 28.76 0.66
1050 26.12 26.29 0.65
1100 25.05 25.33 1.12
Table 2. Comparison of Calculated Resonant Frequencies with those Presented by Richard et al [6] and Silva
et al [11] a=1630m, b=935m,n=106
S/M, Tc =89K, 0 =140nm, e=350nm; T=50K, d=254m and a0=0
Relative Permittivity
(r)
Resonance Frequencies (GHz)
Full-wave analysis [11] Cavity Model [6] Our results
11 41.041 41.638 41.585
16 34.856 35.300 34.816
23.81 28.671 28.937 28.764
The influence of the thickness of the superconducting film on the operating frequency and
bandwidth of the antenna without and with rectangular aperture is studied in Figure 2 and Figure 3. The
thickness of the rectangular patch is normalized with respect to the penetration depth to zero temperature. In
the case of the antenna having a rectangular aperture, the size thereof is 163µm x 93.5µm. The characteristics
of the superconducting film are: 0=100nm, n=9.83 105
S/M and Tc=89K. For the microstrip antenna, the
following parameters are used: a=1630m, b=935m, b=254m and r =23.81. The operating temperature
is T = 50K.
Figure 2. Resonant frequency of a superconducting
microstrip antenna with and without aperture in the
ground plane according to the standardized thickness
of the superconducting film
Figure 3. Bandwidth of a superconducting microstrip
antenna with and without aperture in the ground
plane according to the standardized thickness of the
superconducting film
It is noted that when the thickness of the superconductor film increases, the resonant frequency and
bandwidth of the antenna without increasing opening as well as to the antenna aperture. Note that the effect
of the thickness of the superconducting film is larger for small values of e (e0.10). When e exceeds 0.10,
the increase in the thickness of the superconducting film slowly increases the resonant frequency and
bandwidth. Extreme care should be taken when designing a microstrip antenna with a thin superconducting
film, since a small uncertainty when the patch is made may result in a significant gap in the frequency and
bandwidth of the antenna.
Figure 4 plots the radiation patterns in the E-plane (=0) and H-plane (=/2) of a rectangular
microstrip patch over the ground planes with and without rectangular apertures in both the air half-space
above the patch and the concerning radiation above the patch. It is clear that it decreases with the increase of
the size of the aperture.
0,0 0,2 0,4 0,6 0,8 1,0
28,0
28,1
28,2
28,3
28,4
28,5
28,6
28,7
28,8
ResonantFrequency-Fr-(GHZ)
The thickness of superconducting film
with Rectangular Aperture
without Rectangular Aperture
0,0 0,2 0,4 0,6 0,8 1,0
1,29
1,30
1,31
1,32
1,33
1,34
1,35
1,36
1,37
1,38
1,39
bandwidth(%)
The thickness of superconducting film
with Rectangular Aperture
without Rectangular Aperture
 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617
1616
Figure 4. Radiation patterns of rectangular patches over the ground planes with and without rectangular
apertures (a) H-plane, (b) E-plane ; with Lp=15mm, Wp=10mm, ɛ r= 7, d=1mm 0=100nm, n=9.83 105
S/M
and Tc=89K
4. CONCLUSION
We have presented a rigorous full-wave analysis of rectangular microstrip patch over Ground Plane
with Rectangular Aperture using superconducting materials. The problem has been formulated in terms of
integral equations using vector Fourier transforms. An efficient technique has been used for determining the
dyadic Green‟s functions. Galerkin‟s method has been used to solve the surface current density on the
rectangular patch. The calculated results have been compared with calculated and measured ones available in
the literature and excellent agreement has been found.
Extreme care should be taken when designing a microstrip antenna with thin superconducting patch;
since small uncertainty in thickness of the superconducting patch can result in an important detuning of the
frequency.
REFERENCES
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[8] A. Singh, Kamakshi, M. Aneesh and J.A. Ansari. “Slots and Notches Loaded Microstrip Patch Antenna for
Wireless Communication”, TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 13,
no 3, pp. 584-594, 2015.
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Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch Over Ground Plane with Rectangular Aperture

  • 1. International Journal of Electrical and Computer Engineering (IJECE) Vol. 8, No. 3, June 2018, pp. 1611~1617 ISSN: 2088-8708, DOI: 10.11591/ijece.v8i3.pp1611-1617  1611 Journal homepage: http://iaescore.com/journals/index.php/IJECE Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch Over Ground Plane with Rectangular Aperture Nabil Boukhennoufa1 , Lotfi Djouane2 , Houcine Oudira3 , Mounir Amir4 , Tarek Fortaki5 1,2,3 Department of Electronics, University of Mohamed Boudiaf, M‟sila, Algeria 1,2,3 Laboratory of Electrical Engineering, University of Mohamed Boudiaf, M‟sila, Algeria 4 Scientific and Technical Research Center in Welding and Control, Algiers, Algeria 5 Department of Electronics, University of Mostefa Ben Boulaid, Batna, Algeria Article Info ABSTRACT Article history: Received Jan 29, 2018 Revised Apr 12, 2018 Accepted Apr 18, 2018 In recent years, a great interest has been observed in the development and use of new materials in microwave technology. Particularly, a special interest has been observed in the use of superconducting materials in microwave integrated circuits, this is due to their main characteristics. In this paper, the complex resonant frequency problem of a superconductor patch over Ground Plane with Rectangular Aperture is formulated in terms of an integral equation, the kernel of which is the dyadic Green‟s function. Galerkin‟s procedure is used in the resolution of the electric field integral equation. The surface impedance of the superconductor film is modeled using the two fluids model of Gorter and Casimir. Numerical results concerning the effect of the thickness of the superconductor patch on the characteristics of the antenna are presented. Keyword: Full-wave analysis High Tc superconducting Microstrip patch Rectangular aperture Copyright © 2018 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Nabil Boukhennoufa, Department of Electronics, Laboratory of Electrical Engineering, University of Mohamed Boudiaf, M‟sila, BP 166 M'sila 28000, Algeria. Email: boukhennoufa.nabil@gmail.com 1. INTRODUCTION Microwave passive devices such as resonators, filters and antennas are one of the main applications of the high TC superconducting (HTS) materials. They show superior performance and characteristics to the normal metal devices, such as: the power losses are low, reduction of attenuation and noise level, besides the propagation time of signals in the circuit can be greatly reduced [1]-[6]. This allows to be used in several applications such as mobile communications, radars and filters [7]-[10]. The study of the resonant characteristics of High Tc superconducting microstrip antennas has been first studied by [4] using the cavity model. Since the cavity model does not consider rigorously the effects of surface waves and fringing fields at the edge of the patch. Recently; Silva has studied the resonant characteristics of High Tc superconducting microstrip antennas using the full-wave analysis [11], [12]. It is noted that in the above works, the effect of thin superconducting patch was not studied. In this paper, the effect of thin superconducting patch loading on the resonant frequency and bandwidth of rectangular microstrip structures illustrated in Figure 1 is investigated. The complex resonant frequency problem considered here is formulated in terms of an integral equation using vector Fourier transforms [13]. The surface impedance of the superconductor film is modeled using the two fluids model of Gorter and Casimir [5], [11], [14]. The paper is organized as follows. First, the integral equation for the unknown patch currents is formulated. The derivation is performed in the Fourier transform domain and
  • 2.  ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617 1612 utilized the dyadic Green‟s function of the considered structure, without taking into account the effect of the superconductivity. To include the effect of the superconductivity of the patch, surface complex impedance, Zs is considered. The Galerkin moment method is used to solve the integral equation. The characteristic equation for the complex resonant frequencies is given. Various numerical results are given in Section 3. Finally, conclusions are summarized in Section 4. Figure 1. Geometrical structure of a superconducting rectangular microstrip patch 2. ANALYSIS METHOD In this paper an efficient technique to derive the dyadic Green‟s functions for Superconducting microstrip patch over ground plane with aperture is proposed. The transverse field inside isotropic region (0<z<d) can be obtained via the inverse vector Fourier transforms as: s s s s x y2 1 ( ,z ) ( , ). ( ,z )dk dk 4         E r F k r e k (1) s s s s x y2 1 ( ,z ) ( , ). ( ,z )dk dk 4         H r F k r h k (2) Where: s s x y i . s s y xs k k1 ( , ) e k kk       k r F k r , s ˆ ˆx y r x y , s x y ˆ ˆk k k x y , s sk  k . z zi z i z s s s( ,z ) e ( ) e ( )      k k e k A k B k (3) z zi z i z s s s s( ,z ) ( ) e ( ) e ( )          k k h k g k A k B k (4) In (3) and (4), A and B are to component unknown vectors and e h z z zdiag k ,k   k , h 0 x z s e 0z k ( ) diag , k             g k (5) e zk and h zk are propagation constants for TM and TE waves respectively in substrate [15]-[18]. Writing (3) and (4) in the plane z=0 and z=d, and by eliminating the unknowns A and B, we obtain the matrix form: s s s s ( ,d ) ( ,0 ) ( ,d ) ( ,0 )                  e k e k T h k h k (6) x y b a d 0z e Superconducting Patch Dielectric substrate 000 ,,  zx a o Rectangular Aperture ao x bo
  • 3. Int J Elec & Comp Eng ISSN: 2088-8708  Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch … (Nabil Boukhennoufa) 1613 With 11 12 1 z21 22 cos i sin , d i sin cos                  T T θ g θ T θ k T T g θ θ (7) Equation (7) combines e and h on both sides of substrate as input and output quantities. The continuity equations for the tangential field components at the interface z=d are: s s s( ,d ) ( ,d ) ( ,d ) ( )     se k e k e k e k (8) s s s( ,d ) ( ,d ) ( )   h k h k j k (9) s( )j k in (9) is related to the vector Fourier transform of s( )J r , the current on the patch, as [19] s s s s x y( ) ( , ) . ( )dk dk         j k F k r J r , x s s y s J ( ) ( ) J ( )        r J r r (10) The continuity equations for the tangential field components at z=0 are: s s s 0( ,0 ) ( ,0 ) ( ,0 ) ( )     se k e k e k e k (11) s s 0 s( ,0 ) ( ,0 ) ( )   h k h k j k (12) In (12), 0 s( )j k is the vector Fourier transform of the current 0 s( )J r on the ground plane with a rectangular aperture. In the unbounded air region above the patch the electromagnetic field given by (3) and (4) should at z   ( z )  according to Summerfield‟s condition of radiation, and this yields: s 0 s s( ,d ) ( ) ( ,d )   h k g k e k (13) s 0 s s( ,0 ) ( ) ( ,0 )    h k g k e k (14) Where 0 s( )g k can be easily obtained from the expression of s( )g k given in (5) by allowing x z r 1     . Combining (6), (8), (9) and (1)-(14), we obtain a relation among s( )j k , s( )j k , ( )se k and 0 ( )se k given by: xx xy xx xy x 0x x yx yy yx yy y 0y y Q Q WW WW EE J Q Q WW WW EE J                                   (15) xx xy xx xyx 0 x 0x yx yy yx yyy 0 y 0y WW WW Y YJ EJ WW WW y yJ EJ                                 (16) To include the effect of the superconducting of the microstrip film, the dyadic Green‟s function is modified by considering a surface complex impedance Zs, is determinate by using the model of Gorter and Casimir [5], [11], [14]. 0 sZ 2    (17) If the thickness of the superconducting film R is less than three penetration depths, a better boundary
  • 4.  ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617 1614 condition is given by [5]: s 1 Z R.  (18) Where the complex conductivity is given by [5], [7]   4 4 2 n 0 0 CC T T 1 i TT                          (19) With λ0 is the skin depth at zero temperature, σn is the conductivity of normal electrons and Tc critical temperature of the superconductor. The electric field and the surface current densities total in the interface z=d (E ,J )T T are the electric fields and the surface current densities in the film (E ,J )i i T T and out the film (E ,J )O O T T respectively. i o T T T i o T T T       E E E J J J (20) By substituting Equation (20) in Equation (15), we obtain o xx s xy xx xy x 0x x o yx yy s yx yy y 0y y Q Z Q WW WW EE J Q Q Z WW WW EE J                                   (21) xx xy xx xyx 0 x 0x yx yy yx yyy 0 y 0y WW WW Y YJ EJ WW WW y yJ EJ                                 (22) Boundary conditions require that the transverse electric field of (21) vanishes on the superconducting patch and the current of (22) varnishes off ground plane, to give the following coupled integral equations for the patch current and aperture field: xx s x xy y xx x 0 xy y 0 x y x y[ (Q Z ) J Q J WW E WW E ] exp( i k x i k y ) dk dk 0            (23) yx x yy s y yx x 0 yy y 0 x y x y[ Q J (Q Z ) J WW E WW E ] exp( i k x i k y ) dk dk 0            (24) xx x xy y xx x 0 xy y 0 x y x y[WW J WW J Y E Y E ] exp( i k x i k y ) dk dk 0           (25) yx x yy y yx x 0 yy y 0 x y x y[WW J WW J Y E Y E ] exp( i k x i k y ) dk dk 0           (26) 3. NUMERICAL RESULTS AND DISCUSSION Table 1 summarizes the calculated resonance frequencies and those obtained through the cavity model [6] for three different widths of the patch and differences between these results dues less than 2% are obtained. Excellent agreement between our results and those calculated by Full-wave analysis [11] and those obtained by Cavity Model [6] is observed and represented in Table 2.
  • 5. Int J Elec & Comp Eng ISSN: 2088-8708  Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch … (Nabil Boukhennoufa) 1615 Table 1. Comparison of Calculated Resonant Frequencies with those Presented by Richard et al [6] a=1630m, n=106 S/M, Tc =89K, 0 =140nm, e=350nm; T=77K, r =23.81, d=254m and a0 =0 b (µm) Resonance Frequencies (GHz) Error (%) Cavity Model [6] Our results 935 28.95 28.76 0.66 1050 26.12 26.29 0.65 1100 25.05 25.33 1.12 Table 2. Comparison of Calculated Resonant Frequencies with those Presented by Richard et al [6] and Silva et al [11] a=1630m, b=935m,n=106 S/M, Tc =89K, 0 =140nm, e=350nm; T=50K, d=254m and a0=0 Relative Permittivity (r) Resonance Frequencies (GHz) Full-wave analysis [11] Cavity Model [6] Our results 11 41.041 41.638 41.585 16 34.856 35.300 34.816 23.81 28.671 28.937 28.764 The influence of the thickness of the superconducting film on the operating frequency and bandwidth of the antenna without and with rectangular aperture is studied in Figure 2 and Figure 3. The thickness of the rectangular patch is normalized with respect to the penetration depth to zero temperature. In the case of the antenna having a rectangular aperture, the size thereof is 163µm x 93.5µm. The characteristics of the superconducting film are: 0=100nm, n=9.83 105 S/M and Tc=89K. For the microstrip antenna, the following parameters are used: a=1630m, b=935m, b=254m and r =23.81. The operating temperature is T = 50K. Figure 2. Resonant frequency of a superconducting microstrip antenna with and without aperture in the ground plane according to the standardized thickness of the superconducting film Figure 3. Bandwidth of a superconducting microstrip antenna with and without aperture in the ground plane according to the standardized thickness of the superconducting film It is noted that when the thickness of the superconductor film increases, the resonant frequency and bandwidth of the antenna without increasing opening as well as to the antenna aperture. Note that the effect of the thickness of the superconducting film is larger for small values of e (e0.10). When e exceeds 0.10, the increase in the thickness of the superconducting film slowly increases the resonant frequency and bandwidth. Extreme care should be taken when designing a microstrip antenna with a thin superconducting film, since a small uncertainty when the patch is made may result in a significant gap in the frequency and bandwidth of the antenna. Figure 4 plots the radiation patterns in the E-plane (=0) and H-plane (=/2) of a rectangular microstrip patch over the ground planes with and without rectangular apertures in both the air half-space above the patch and the concerning radiation above the patch. It is clear that it decreases with the increase of the size of the aperture. 0,0 0,2 0,4 0,6 0,8 1,0 28,0 28,1 28,2 28,3 28,4 28,5 28,6 28,7 28,8 ResonantFrequency-Fr-(GHZ) The thickness of superconducting film with Rectangular Aperture without Rectangular Aperture 0,0 0,2 0,4 0,6 0,8 1,0 1,29 1,30 1,31 1,32 1,33 1,34 1,35 1,36 1,37 1,38 1,39 bandwidth(%) The thickness of superconducting film with Rectangular Aperture without Rectangular Aperture
  • 6.  ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 8, No. 3, June 2018 : 1611 – 1617 1616 Figure 4. Radiation patterns of rectangular patches over the ground planes with and without rectangular apertures (a) H-plane, (b) E-plane ; with Lp=15mm, Wp=10mm, ɛ r= 7, d=1mm 0=100nm, n=9.83 105 S/M and Tc=89K 4. CONCLUSION We have presented a rigorous full-wave analysis of rectangular microstrip patch over Ground Plane with Rectangular Aperture using superconducting materials. The problem has been formulated in terms of integral equations using vector Fourier transforms. An efficient technique has been used for determining the dyadic Green‟s functions. Galerkin‟s method has been used to solve the surface current density on the rectangular patch. The calculated results have been compared with calculated and measured ones available in the literature and excellent agreement has been found. Extreme care should be taken when designing a microstrip antenna with thin superconducting patch; since small uncertainty in thickness of the superconducting patch can result in an important detuning of the frequency. REFERENCES [1] S. Bedra, T. Fortaki, A. Messai and R. Bedra, “Spectral Domain Analysis of Resonant Characteristics of High Tc Superconducting Rectangular Microstrip Patch Printed on Isotropic or Uniaxial Anisotropic Substrates”, Wireless Personal Communications, vol. 86, no 2, pp. 495-511, 2016. [2] F. Benmeddour, C. Dumond, F. Benabdelaziz and F. Bouttout, “Improving the performances of a high Tc superconducting circular microstrip antenna with multilayered configuration and anisotropic dielectrics”, Progress In Electromagnetics Research C, vol. 18, pp. 169-183, 2011. [3] N. Sekiya, A. Kubota, A. Kondo, S. Hirano, A. Saito and S. Ohshima, “Broadband superconducting microstrip patch antenna using additional gap-coupled resonators”, Physica C, pp. 445-448, 2006. [4] A. Cassinese, M. Barra, I. Fragala, M. Kusunoki, G. Malandrino, T. Nakagawa, L.M.S. Perdicaro, K. Sato, S. Ohshima and R. Vaglio, “Superconducting antennas for telecommunication applications based on dual mode cross slotted patches”, Physica C, pp. 372-376, 2002. [5] B.B.G. Klopman and H. Rogalla, “The propagation characteristics of wave-guiding structures with very thin superconductors; Application to coplanar waveguide YBa2 CU3O7-x resonators”, IEEE Trans. Microwave Theory Tech., vol. 41, no. 5, pp. 781-791, 1993. [6] M.A. Richard, K.B. Bhasin and P.C. Clapsy, “Superconducting microstrip antennas: An experimental comparison of two feeding methods”, IEEE Trans. Antennas Propagat., Vol. 41, No 7, pp. 967-974, 1993. [7] T. Firmansyah, Herudin, Suhendar, R. Wiryadinata, M. Iman Santoso, Y. R. Denny and T. Supriyanto, “Bandwidth and Gain Enhancement of MIMO Antenna by Using Ring and Circular Parasitic with Air-Gap Microstrip Structure”, TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 15, no .3, pp. 1155-1163, 2017. [8] A. Singh, Kamakshi, M. Aneesh and J.A. Ansari. “Slots and Notches Loaded Microstrip Patch Antenna for Wireless Communication”, TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 13, no 3, pp. 584-594, 2015. [9] D. Fitsum, D. Mali and M. Ismail, “Dual-Band Proximity Coupled Feed Microstrip Patch Antenna with „T‟ Slot on the Radiating Patch and „Dumbbell‟ Shaped Defected Ground Structure”, Indonesian Journal of Electrical Engineering and Computer Science, vol. 3, no. 2, pp. 435-440, 2016.
  • 7. Int J Elec & Comp Eng ISSN: 2088-8708  Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Patch … (Nabil Boukhennoufa) 1617 [10] D. Fistum, D. Mali and M. Ismail, “Bandwidth Enhancement of Rectangular Microstrip Patch Antenna using Defected Ground Structure”, Indonesian Journal of Electrical Engineering and Computer Science, vol. 3, no. 2, pp. 428-434, 2016. [11] S.G. da Silva, A.G. d‟Assuçäo and J.R.S. Oliveira, “Analysis of high Tc superconducting microstrip antennas and arrays”, SBMO/IEEE MTT-S IMOC., 1999. [12] T. Fortaki, D. Khedrouche, F. Bouttout and A. Benghalia, “Vector Hankel transform analysis of a tunable circular microstrip patch”, Commun. Numer. Meth. Engng, pp. 219-231, 2005. [13] T. Itoh, “A full-wave analysis method for open microstrip structures”, IEEE Trans. Antennas Propagat., vol. 29, no. 1, pp. 63-67, 1981. [14] Z. Cai and J. Bornemann, “Generalized spectral-domain analysis for multilayered complex media and high-Tc superconductor applications”, IEEE Trans. Microwave Theory Tech., vol. 40, no. 12, pp. 2251-2257, 1992. [15] T. Fortaki and A. Benghalia, “Rigorous full-wave analysis of rectangular microstrip patches over ground planes with rectangular apertures in multilayered substrates that contain isotropic and uniaxial anisotropic materials”, Microwave Opt. Technol. Lett., vol. 41, no. 6, pp. 496-500, 2004. [16] T. Fortaki, D. Khedrouche, F. Bouttout, and A. Benghalia, “Numerical analysis of rectangular microstrip patch over ground plane with rectangular aperture”, Commun. Numer. Meth. Engng. (John Wiley & Sons), vol. 20, no. 6, pp. 489-500, 2004. [17] T. Fortaki. and A. Benghalia, “Study of rectangular microstrip patch over ground plane with rectangular aperture in the presence of a high-permittivity dielectric layer below the aperture”, Proceeding of the 16th International Conference on Microelectronics, Tunis, Tunisia, December 2004. [18] C. Zebiri M. Lashab and F. Benabdelaziz, “Effect of anisotropic magneto-chirality on the characteristics of a microstrip resonator”, IET Microw. Antennas Propag., vol. 4, no. 4, pp. 446-452, 2010. [19] L. Djouane, S. Bedra, R. Bedra and T. Fortaki, “Neurospectral modeling of rectangular patch with rectangular aperture in the ground plane”, International Journal of Microwave and Wireless Technologies, vol. 7, no. 6, pp. 759-768, 2015.