ANALYSIS OF YAGI-UDA, U-SLOT AND SHORTED FINITE
MICROSTRIP ANTENNAS USING SURFACE EQUIVALENCE
PRINCIPLE AND MULTIPLE NETWORK THEORY (SEMN)
1
1
Farzad Tavakkol-Hamedani, Ahad Tavakoli and Lotfollah Shafai
1
Amirkabir University of Technology (Tehran Polytechnic)
424 Hafez Ave., Tehran, Iran
2
University of Manitoba, Winnipeg, Manitoba, Canada, R3T 5V6
2
I. INTRODUCTION
SEMN method has been introduced for the analysis of finite structures [1]. Also,
electric and magnetic field integral equation (EFIE and MFIE) formulations of SEMN
method have been utilized for the analysis of finite rectangular microstrip patch antennas
[2]. Here, we have utilized MFIE formulation of SEMN method for analyzing Yagi-Uda,
U-slot and shorted finite microstrip antennas and compared the computed numerical
results with the available results in the literature.
In each case, the top view of the antenna (involving the tip point of the probe, the
origin and x and y unit vectors of the rectangular coordinate system and the rectangular
surface segments used in the SEMN method) is depicted. Also, the dimensions of the
antenna a, b and c and the number of segments m, n and q in respectively x, y and z
directions and the substrate relative dielectric constant r are presented. The probe
diameter is assumed to be zero. As the excitation electromagnetic fields at tip points of
the probe are zero, the contact point of the probe and patch (or ground plane) is modeled
by the first four surface segments around it and electromagnetic excitation fields are
assumed to be zero on their surfaces. Utilizing greater number of segments (and therefore
smaller segments) for the total surface of the antenna and contact points of the probe,
more accurate numerical results are drived. For computing the input impedance of a
finite microstrip antenna that is installed on a large ground plane, we utilize the image
theory and analyze a new (second) finite microstrip antenna that is composed of the first
finite microstrip antenna and its symmetry with respect to the ground plane. Thus, the
required input impedance will be half of the input impedance of the second finite
microstrip antenna.
II. YAGI-UDA FINITE MICROSTRIP ANTENNA
A Yagi-Uda microstrip antenna consists of a driven patch, a reflector patch and
two or three director patches. The main lobe of this antenna, due to the effect of mutual
coupling and Yagi-Uda principle can be tilted away from the broadside and toward the
direction of the director patches. The reflector patch may be removed to reduce the
antenna size without significant degradation of performance [3]. Fig. 1 depicts a finite
Yagi-Uda microstrip antenna (without the reflector patch) and the comparison of its numerical
results with the results in [3]. There are small differences between the dimensions of the antenna
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852
considered here and the one used in [3]. Also, a larger ground plane has been utilized in
[3].
III. U-SLOT RECTANGULAR PATCH ANTENNA
A properly designed U-slot in a rectangular patch antenna with thick substrate can
tune out the probe inductance and provide wide bandwidth. Fig. 2 depicts a finite
rectangular microstrip patch antenna installed on a large ground plane and the
comparison of the calculated (using SEMN method) and measured [4] input impedances.
It is seen that because of the thickness of the substrate, the input impedance has a large
inductive component. Fig. 3 shows the microstrip antenna of Fig. 2(a) with a U-slot and
probe positioned at the center of the patch and its calculated input impedance using
SEMN method. As it is seen from Fig. 3(b), we have two resonances. The lower
resonance frequency is due to the slot and the higher one is due to the microstrip patch
antenna. Also, it is seen that the inductive reactance of the microstrip patch antenna has
been considerably reduced. Using FDTD method for the same antenna of Fig. 3(a) but
with a narrower slot, similar numerical results have been derived in [4]. However, as a
result of using narrower slot higher microstrip patch antenna resonance frequency and
lower input resistance were derived.
IV. SHORTED AND TRUNCATED MICROSTRIP ANTENNA
The shorted and truncated rectangular microstrip antenna is constructed by shortcircuiting the zero potential plane of an ordinary microstrip antenna and reducing the size
of the ground plane to the size of the patch. It can realize the same resonant frequency at
about half the size of the standard microstrip antenna. Fig. 4 depicts a shorted and
truncated microstrip antenna and its computed numerical results using SEMN method.
Using FDTD method the same resonance frequencies were derived In [5]. From Figs.
4(c) and (d), it is derived that the antenna has good isotropic radiation pattern
characteristics and is sensitive to both vertically and horizontally polarized waves.
REFERENCES
[1] F. Tavakkol-Hamedani and A. Tavakoli, “A new approach to analysis of arbitrary
shaped, single or multilayered printed antennas based on surface equivalence
principle and multiple network theory,” in Dig. IEEE AP-S Int. Symp., Montreal, July
1997, pp. 2358-2361.
[2] F. Tavakkol-Hamedani, A. Tavakoli and L. Shafai, “Analysis of finite microstrip
antennas using surface equivalence principle and multiple network theory (SEMN),”
to appear in Proc. AP2000 int. Symp. on Antenna and Propagation.
[3] D. P. Gray, J. W. Lu and L. Shafai, “Experimental study of parasitically steered, fixed
beam microstrip patch arrays” in Dig. IEEE AP-S Int. Symp., Montreal, July 1997, pp.
1276-1279.
[4] K. M. Luk, K. F. Tong, S. M. Shum, K. F. Lee and R. Q. Lee, “FDTD analysis of Uslot rectangular patch antenna” in Dig. IEEE AP-S Int. Symp., Montreal, July 1997,
pp. 2111-2114.
[5] B. S. Yildirim and El-B. El-Sharawy, “FDTD analysis of a shorted and truncated
microstrip antenna for mobile communications systems” in Dig. IEEE AP-S Int.
Symp., Montreal, July 1997, pp. 1856-1859.
853
y
Dielectric:
Conductor:
a=167.51
mm,
b=55.84 mm
x
c=5.9 mm, r=2.88,
m=30, n=8, q=1.
b
a
(a)
E-Plane Gain Patterns
S11(dB)
SEMN (MFIE)
Experiment
0
30
0
SEMN (MFIE)
ENSEMBEL
-5
0 10
-30
-60
60
-10
-10
-90
90
-15
-20
-120
120
-25
-150
150
-180,180
-30
1.52
1.54
1.56
1.58
1.6
1.62
1.64
1.66
Freq. (GHz)
(b)
(c)
Fig. 1. (a) A finite Yagi-Uda microstrip antenna and the comparison of (b) input return
loss ( S11 ) calculated by SEMN method and ENSEMBEL software [3] and (c) E-plane
gain patterns calculated by SEMN method and measured in [3] (at fo=1.55 GHz).
a=26 mm, b=36 mm, c=5 mm, r=1,
m=12, n=18, q=1.
y
180
Experiment
SEMN (MFIE)
160
140
120
b
x
X
100
80
R
60
40
20
0
3.5
4
4.5
5
5.5
6
a
Freq. (GHz)
(a)
(b)
Fig. 2. (a) A finite rectangular microstrip patch antenna (installed on a large ground
plane) and (b) the comparison of the computed (using SEMN method) and measured [4] input
resistance (R) and reactance (X).
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854
Dielectric:
Conductor:
a=26 mm, b=36 mm, c=5 mm, r=1,
m=12, n=18, q=1. y
1000
R
800
600
400
b
X
x
200
0
-200
-400
3
3.5
4
4.5
Freq. (GHz)
a
(a)
(b)
Fig. 3. (a) The microstrip antenna of Fig. 2(a) with a U-slot and probe positioned at the
center of the patch and (b) computed input resistance (R) and reactance (X) using SEMN
method.
a=30 mm, b=30 mm, c=5 mm,
200
r=10, m=12, n=12, q=1.
R
R
y
150
100
Shorted
X
50
b
x
0
-50
-100
0.8
a
(a)
1
1.2
1.4
1.6
2.4
2.6
0-0.5
30
-10
-30
Co-Polar
-20
-60
60
-1.5
X-Polar
-90
90
-120
30
-1
60
-30
-90
120
-150
2.2
E-Plane Gain Pattern
0 0
-60
2
(b)
H-Plane Gain Patterns
-30
1.8
Freq. (GHz)
90
-120
150
120
-150
-180,180
150
-180,180
(c)
(d)
Fig. 4. (a) A shorted and truncated microstrip antenna and computed (using SEMN
method) (b) input resistance (R) and reactance (X), (c) E-plane and (d) H-plane gain
patterns at fo=851.5 MHz.
855