FULL-WAVE ANALYSIS OF SCATTERING FROM A STUB-LOADED
MICROSTRIP PATCH ANTENNA
Sachendra N. Sinha
Department of Electronics & Computer Engg.
Indian Institute of Technology, Roorkee-247667
INDIA
&
Pujara Dhaval Kumar
Department of Electronics & Communication Engg.
Nirma Institute of Technology, Ahmedabad-382481
INDIA
Abstract: - The design of a microstrip reflectarray requires precise prediction of the phase and amplitude of the field
scattered by either an unloaded patch or a stub-loaded patch. In this paper, we present a full-wave formulation, using
sub-domain expansion functions and spectral-domain Green’s functions, for a rectangular patch loaded with a Tshaped stub. The formulation is general in the sense that it can be used to analyze an unloaded patch and a patch
loaded with either a linear or L-shaped or T-shaped stub. Numerical results on the radar cross-section (RCS) are
presented for various geometries as a function of frequency and angles of incidence. The effect of various parameters,
such as, dielectric constant, substrate thickness, on the scattering properties of the patch is also discussed.
Key-Words: - Microstrip reflectarray, Microstrip antennas, Stub-loaded patch antennas
In this paper, we present a full-wave analysis of a
rectangular patch antenna loaded with a T-shaped stub.
The formulation is general in the sense that it can be
used to analyze an unloaded patch, patch with a linear
stub, patch with an L-shaped stub and the patch with a
T-shaped stub.
1. Introduction
The increasing demands of satellite and space
communication systems and the approaching maturity
in the field of microstrip antenna design, has given rise
to a novel antenna concept known as microstrip
reflectarray [1]-[3]. This antenna combines some of the
best features of the reflector antennas and the phased
arrays and is specially attractive for space applications,
in view of its light weight and easy deployment
mechanism. It consists of a flat array of microstrip
patches, illuminated by a primary feed, giving rise to a
flat reflector surface in which the feed system losses of
a conventional array are eliminated. A planar phase
front in front of the aperture is obtained by adjusting
the phase of the field scattered by the individual
patches of the array. Two methods are generally used
to control the phase of the scattered field. One method
is to utilize linear or L-shaped stubs of variable lengths
and the second is to utilize patches of variable size.
Thus, an inherent requirement for microstrip
reflectarray synthesis is the accurate knowledge of the
scattering properties of a patch with and without stubs.
However, very little or no data is available in the open
literature on the scattering properties of a stub-loaded
patch.
2. Problem Formulation
The top view of the geometry of the problem
considered is shown in Fig.1. Here we have chosen the
microstrip antenna, loaded with a ‘T’ shaped stub
Thus, the same antenna structure can be used to find
scattering from a linear-stub loaded microstrip patch,
‘L’ shaped stub loaded microstrip patch, and the patch
with a T-shaped stub, just by changing the size of
different arms of the ‘T’ shaped stub. The entire
structure can be divided in to three parts, namely, the
surface S1 of the patch, the surface S2 of the linear stub
attached to a radiating edge, and a surface S3
representing the T-arm of the stub. The surface S2
includes the attachment regions, shown by dotted lines,
where the linear stub is connected with the patch and
the T-arm. These attachment regions have been shown
to extend into the surfaces S1 and S3 and have been
included to enforce current continuity at the two
junctions. The reason for adding attachment regions is
1
to maintain the current continuity at the junction
points.
Computation of various elements of the submatrices in
(4) has been carried out using rooftop functions and the
spectral domain dyadic Green’s function for an electric
current element located on a grounded dielectric slab
[2].
Attachment
regions
3.Computation of Radar Cross-section
The scattering behaviour of a stub-loaded microstrip
patch is described in
terms ofstub
its Radar Cross Section
T-shaped
(RCS). It is defined as [4]
   4r 2 | Escat | 2Surface S3
(5)
patch
(Surface S1)
   4r 2 | Escat |2
Surface
S2
y
x
(6)
Where Escat and Escat are the -polarized and -
T-shaped
Stub
(Surface S3)
polarized scattered fields. In (5) and (6), the scattered
field can be calculated by a summation of the radiated
field from each mode on the antenna structure.
Mathematically this can be written as,
Fig. 1 Problem Geometry
N
E scat   I n E n
(7)
n 1
Where En is the field from the nth expansion mode
In is the nth current co-efficient.
The entire stub loaded microstrip patch is assumed to
be excited by an incident plane wave of unit amplitude.
All fields and currents are time harmonic with the ejwt
time dependence suppressed. The total fields on the
whole antenna structure ( E , H ) are the vector sum of
4. Results and Discussion
Using the formulation presented in the previous
sections, a detailed numerical study has been carried
out on unloaded and stub-loaded patch antennas. Radar
cross-section(RCS) has been computed as a function of
angle of incidence, relative dielectric constant, and
substrate thickness. In this section, we present some
typical results, which establish the accuracy of the
present method. All results have been obtained by
selecting suitable number of expansion function
required to achieve convergence.
the incident fields ( E inc , H inc ) and the scattered fields
due to current J 1 on S1, J 2 on S2, and J 3 on S3. The
following equations may thus be written:
E  E inc  E scat ( J 1  J 2  J 3 )
(1)
H  H inc  H scat ( J 1  J 2  J 3 )
(2)
Enforcing the boundary condition that the tangential
component of the total electric field be zero on the
conductor, we obtain the operator equation
scat
J1   Etanscat ( J 2 )  Etanscat ( J 3 )  Etan
Etan
inc
Fig. 2 shows the variation of RCS of an unloaded
rectangular patch as a function of frequency. The
parameters of patch were: L = W = 1.5 cm, substrate
thickness d = 0.787 mm, r = 2.33, tan  = 0.001, angle
of incidence (, ) = (60, 180). The peak value of
RCS is seen to occur at 6.4 GHz and 12.6 GHz, which
correspond to the first and second resonance of the
patch.
(3)
over S, where S  S1, S2, S3
Following the moment procedure, (3) can be reduced
to matrix form
[ Z11 ] [ Z12 ] [ Z13 ]
[ Z ] [ Z ] [ Z ]
22
23 
 21
[ Z 31 ] [ Z 32 ] [ Z 33 ]

 I n1 
 
 In2  
 I n3 
 

V1 
 
V2 
V3 
 
(4)
where the matrix [Zpq] represents the coupling between
regions Sp to Sq, p,q = 1,2,3.
2
0
0
RCS    (dBsm)
-50
-10
Calculated results
Calculated results , Shively and Baily [5]
For
For
For
For
For
For
-100
-150
Theta = 0 degree
Theta = 30 degree
Theta = 45 degree
Theta = 60 degree
Theta = 75 degree
Theta = 90 degree
-200
Measured results , Shively and Baily [5]
-250
RCS  (dBsm)
-20
-300
-10
10
30
50
70
90
Fi (degree)
-30
Fig 3 RCS versus Fi for various values of Theta
-40
0
-50
RCS   (dBsm)
-50
-60
6
7
8
9
10
11
12
13
14
For Theta = 0 degree
-100
For Theta = 30 degree
For Theta = 45 degree
-150
For Theta = 60 degree
For Theta = 75 degree
-200
For Theta = 90 degree
-250
Frequency (GHz)
Fig. 2 RCS versus frequency of an unloaded
microstrip patch antenna.
-300
0
20
40
60
80
Fi (degree)
Also shown in the figure are the computed and
measured results by Shivley and Bailey [5]. A good
agreement can be observed.
Next, we have studied the variation of RCS with the
angles of incidence  and . Fig. 3 and 4, respectively,
show  and  as a function of  for various values
of . For this study, the antenna parameters used are:
L= 2.6 cm, W = 3.66 cm, d = 0.158 cm, r = 2.17  =
60, and  = 45. These figures show that the RCS is a
very strong function of angles of incidence. Therefore,
in the design of a reflectarray using patches of variable
size, the effect of feed location will greatly influence
the patch design.
Fig 4 RCS versus Fi for various values of Theta.
The effect of substrate thickness and r has also been
studied for various patch sizes and angles of incidence.
The detailed results can be found elsewhere [6].
A comprehensive study has been carried out on a stubloaded antenna and the results are available in [6].
Here we present only some typical results for a patch
antenna loaded with a linear stub on one of its nonradiating edges. Figs. 5-6 present the RCS of a
rectangular patch antenna for different stub lengths.
3
The patch used is same as that used in the study
presented in Figs.3-4.
In Fig. 6, we have included the data of Metzler and
Schaubert [7] for comparison. These authors have used
entire-domain basis functions to analyze the problem.
It is found that their results show a false peak around a
frequency of 2.8 GHz, which should not have been
there. It clearly shows a limitation of their method.
Since the sub-sectional domain basis functions used by
us can represent the patch current more accurately, this
type of false peak does not appear in our results.
0
-5
RCS   (dBsm)
-10
-15
-20
-25
-30
5. Conclusion
-35
A comprehensive investigation on an unloaded and a
stub-loaded patch antenna has been carried out using a
full-wave technique. Rooftop functions have been
used, which can represent the patch current with a high
degree of accuracy. This analysis can be used to
generate the scattering data required in the design of
microstrip reflectarrays.
-40
-45
2.5
5.5
4.5
3.5
Frequency (GHz)
Fig. 5 Scattering from a microstrip antenna loaded
with a linear stub.
(For 110 degree stub length)
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
References:
[1] S.D. Targonski and D.M. Pozar, Analysis and
design of a microstrip reflectarray using patches of
variable size, Digest of IEEE Symposium on
Antennas and Propagat., vol. 3, 1994, pp. 18201823.
[2] R.D. Javor, X.D. Wu, and K. Chang, Design and
performance of a microstrip reflectarray antenna,
IEEE Transac. on Antennas and Propagat., vol.
AP-43, 1995, pp. 932-938.
[3] J. Huang and R.J. Pogarzelski, A Ka band
microstrip reflectarray with elements having
variable rotation angles, IEEE Transac. on
Antennas and Propagat., vol. AP-46, 1998, pp.
650-656
[4] D. G. Shivley and M.D. Deshpande, Scattering
from arbitrarily shaped microstrip patch antennas,
Electromagnetics, vol. 14, 1984, pp. 1-18.
[5] D.G. Shiveley and M.C. Bailey, Analysis of
microstrip patch antennas with nonzero surface
resistance, NASA Technical Paper, No. 220733,
1993.
[6] Pujara Dhaval Kumar, Scattering from a stubloaded microstrip patch antenna, M.Tech.
Dissertation, 2003.
[7] T. Metzler and D. Schaubert, Scattering from a
stub-loaded microstrip antenna, Digest of IEEE
Internat. Symp. on Antennas & Propagat., vol.1,
1989, pp. 446-449.
RCS   (dBsm)
Computed results, Metzler and
Schaubert [7].
Our Results.
2.5
3.5
4.5
5.5
Frequency (GHz)
Fig. 6 Scattering from a microstrip antenna
loaded with a linear stub.
(For 150 degree stub)
4