performances of microstrip fractal antenna with water...
TRANSCRIPT
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CHAPTER 7
PERFORMANCES OF MICROSTRIP FRACTAL ANTENNA WITH WATER
LAYERS
7.1 INTRODUCTION
Modern telecommunication system requires antennas that have multiband and wider
bandwidth characteristics as well as smaller dimensions than conventionally possible. This
demand has initiated antenna research in various directions, one of which is fractal
geometry shaped antennas. As well known there is an important relation between antenna
dimensions and wavelength, which states if antenna size is less than λ/4 (λ is wave length)
the antenna will not be an efficient radiator because radiation resistance, gain and
bandwidth is very much reduced. Fractal geometry is a very good solution for this problem.
Fractals are geometric shapes, which are self similar; repeating themselves at different
scales. Hence these structures are recognized by their self similarity properties and
fractional dimension as whole.
In the recent years, the geometrical properties of self-similar and space filling nature has
motivated antenna design engineers to adopt this geometry as viable alternative to meet the
target of multiband operation. Fractional dimensions, self-similar and scaling properties,
characterize these structures. The structures that are studied as antenna are not the ones that
we obtained after infinite iteration but those after finite iterations as desired by the
designer. The space filling property lead to curves that is electrically very long but fit into a
compact physical space. This property can lead to the miniaturization of antennas. With the
development of fractal theory, the nature of fractal geometries in antenna design has led to
the evolution of a new class of antennas, called fractal shaped antennas. Fractal geometries
in the antenna application are becoming major concern for many researchers these days.
Due to the fractal configuration large electrical length is fitted into the small physical
volume. Thus the high convoluted shape of a fractal allows reducing the overall volume
occupied by the resonating element. As we know, mobile communications has become an
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important part of the human life. Mobile means practical for user and easily transportable.
Thus the mobile terminals for wireless application should be light, small and should have
low energy consumption to satisfy these requirements. Due to greater integration of
electronics, the size of transceiver needed for the mobile applications have decreased
drastically. Hence the size of the antenna should be compatible with the dimensions of the
receiver or the repeater system, especially at the lower microwave spectrum.
Fractals mean broken or irregular fragments. Fractals describe a complex set of geometries
ranging from self similar/ self-affine to other irregular structure. Fractals are generally
composed of multiple copies of themselves at different scales and hence do not have a
predefined size which makes their use in antenna design very promising. Fractal antenna
engineering is an emerging field that employs fractal concepts for developing new types of
antennas with notable characteristics. Fractal shaped antennas show some interesting
features which results from their geometrical properties. The unique features of fractals
such as self-similarity and space filling properties enable the realization of antennas with
interesting characteristics such as multi-band operation and miniaturization. A self-similar
set is one that consists of scaled down copies of itself. This property of self-similarity of
the fractal geometry aids in the design of fractal antennas with multiband characteristics.
The self-similar current distribution on these antennas is expected to cause its multiband
characteristics.
The space-filling property of fractals tends to fill the area occupied by the antenna as the
order of iteration is increased.Higher order fractal antennas exploit the space-filling
property and enable miniaturization of antennas. Fractal antennas and arrays also exhibit
lower side-lobe levels.
Koch fractal geometry was originally introduced by a Helge von Koch in 1904. One starts
with a straight line, called the initiator. This is partitioned into three equal parts, and the
segment at the middle is replaced with two others of the same length. This is the first
iterated version of the geometry and is called the generator. The process is reused in the
generation of higher iterations. The number of iterations defines the order of the fractals.
7.2. RECENT DEVELOPMENTS IN FRACTAL PATCH ANTENNA
138
In 1998, Z. Baharav presented his work on fractal arrays based in iterated functions system.
Self similar feature in the radiation patterns will allow a multi-band frequency usage of the
fractal array [1]. Most of the previous works done in this area deals with fractal arrays in
which the distance between the elements is some fractal function (like the Cantor set),
whereas their amplitude is constant. This work, on the other hand, deals with uniformly
spaced elements, whereas the elements amplitude distribution is a fractal function. In this
work we will use the Iterated Function System (IFS) method to produce fractals. It can lead
to an automated method for fractal encoding of signals. The use of the IFS will enable one
to create fractal arrays with many degrees of freedom.
In 1999, M. Navarro et al. worked on the topic ―Self-Similar surface current distribution
on fractal Sierpinski Antenna verified with Infra-red Thermograms‖ [2]. In this research he
presented the experimental verification of the fractal Sierpinski Antenna Surface current
distribution. Measures data from an infrared camera agree with a numerical data showing a
self -similar behavior in the current density distribution over the fractal antenna surface.
The obtained results gave a better insight on the multiband behavior of the fractal-shape
antenna.
In 2001, P. Felber et al. had done some research on fractal antennas [3]. In this research he
limited his study only to fractal antenna elements and fractal arrays. Traditional wideband
antennas (spiral and log-periodic) and arrays can be analyzed with fractal geometry to shed
new light on their operating principles. More to the point, a number of new configurations
can be used as antenna elements with good multiband characteristics. Due to the space
filling properties of fractals, antennas designed from certain fractal shapes can have far
better electrical to physical size ratios than antennas designed from an understanding of
shapes in Euclidean space. In 2004, K. Sathya et al. performed research on size reduction
of low frequency microstrip patch antenna with Koch shaped fractal slot. In this, a
microstrip patch antenna with Koch shaped fractal slot implemented with a foam substrate
= 1.02 was shown to bring a size reduction of about 84% compared to an ordinary
microstrip patch antenna for the same resonant frequency [4]. A compromised design of a
two element array pattern of the single structure gives considerable gain as well as 66%
size reduction. In 2005, P. Hazadra et al. performed the research on model analysis of
fractal microstrip patch antennas [5]. The full wave simulation of complex structure is very
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difficult and time consuming that is why cavity model has been found which is very useful
in obtaining basic parameters of structures like resonant frequencies, field distribution and
radiation pattern. The results obtained are in good agreement with the full wave simulation
performed by IE3D simulator.
Later in 2006, N. Gupta performed the research on ―Two compact microstrip patch antenna
for 2.4 GHz band‖. In this two low profile patch antenna for wireless LAN 802.11b
communication standard was proposed and investigated [6]. The proposed patch antenna
shows a significant size reduction compared to the simple square patch antenna, the gain
and bandwidth of the proposed antennas found to be increased significantly using stacked
configuration. In 2007, V. R. Gupta et al. performed analysis on fractal microstrip patch
antenna [7]. In this research they studied the effect of increase in electrical length at each
iterative step in the generation of the fractal. Although there are number of methods to
reduce the size of the antenna operating at the lower frequencies and fractal is one among
them. In this research it was found that Fractal patch antenna are good candidates for size
reduction as large electrical length can be fitted into the small physical volume. However to
make the antenna resonate at a particular frequency the useful range of size reduction lies
only up to third iteration. In 2008, F.H. Kashani at el. performed the research on a novel
broadband fractal sierpinski shaped, microstrip antenna. In this research new microstrip
Sierpinski modified and fractalized antenna using multilayer structure for achieving wide
band behavior in X- band which in 7-10.6 GHz portion overlaps UWB working range [8].
Working range for this antenna is from 7.7 GHz to 16.7 GHz (bandwidth = 9 GHz). In this,
a new small microstrip antenna for ultra wideband application was designed and modified.
However in 2009, A. Azari et al. performed the research on ultra wide band fractal
microstrip antenna design. In this research he presented new fractal geometry for microstrip
antennas. In this research a new hexagonal fractal was presented [9]. This fractal antenna
has a very high bandwidth; multiband in nature and good properties as well as significant
gain improvement was achieved. In 2010, Fawwaz J. Jibrael at el. performed the research
on ―A new multiband patch microstrip plusses fractal antenna‖.
The proposed antenna has shown to possess an excellent size reduction possibility with
good radiation performance for wireless applications [10].
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Therefore, it is being observed that no research works have done on dielectric loaded
fractal patch antennas, though loading severely affects the performances of the patch
antennas, hence attention have paid to describe the effects of dielectric loading on its
operating performances. Figure 7.1 shows the proposed fractal geometry of patch antenna
designed for the pentagonal fractal patch antenna up to third iteration. The proposed
antenna has shown four resonant bands at frequency of 2.471 GHz , 7.032 GHz, 8.651
GHz, and 11.86 GHz, and at these frequencies the antenna has S11 < - 10 dB (VSWR < 2).
Hence it can be used as a multiband antenna in wireless applications successfully.
Figure 7.1 Proposed fractal geometries of pentagonal patch antenna
7.3. DESIGN SPECIFICATIONS
Design parameters for pentagonal patch antenna are given below.
Third Iteration
First Iteration
Second Iteration
Zero Iteration
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Geometry Pentagonal
Side arm length 28.52 mm
Substrate (FR-4) εr = 4.4, h = 0.8mm, tanδ = 0.02
Centre frequency 2.45 GHz
Feed location(From Center) 8.21 mm
Coaxial cable dimension Inner radius: 0.5 mm
Outer radius:0.9 mm
Dielectric cover (Distilled water) εr=81, h=0.1mm to 0.3 mm
Side arm length of the pentagonal 28.52 mm
7.4. ANTENNA GEOMETRY AND CONFIGURATION
The antenna geometry is chosen as pentagonal patch antenna and fr = 2.435 GHz as
operating frequency. The antenna are designed on FR-4 substrate (ε r= 4.4) with substrate
thickness t = 0.8 mm and tanδ = 0.02, and fed with a 50 Ω coaxial cable. The simulation
result shows that it acts as a single band, narrow bandwidth patch antenna. This antenna
can be converted into fractal patch antenna with a pentagonal slot as fractal geometry for
multi band operation. This can be achieved by some level of iteration.
7.5. SIMULATED RESULTS
7.5.1. 0th
Iteration in Pentagonal Patch Antenna
In order to present the design procedure of achieving impedance matching for this case,
feed location is set at -8.125 mm and radius of the patch is 19.107 mm. The obtained
simulated results are shown in Figures 7.3 -7.6. After optimization we met the design
challenges such as return losses should be less than -10 dB, VSWR < 2 and low
spurious feed radiation. For simple pentagonal patch antenna we achieve resonant
frequency at 2.4375 GHz with return loss of -28.99 dB as shown in Figure 7.3. As
shown in Figure 7.4 input impedance of the antenna is 48.33 ohm at 2.4375 GHz. As
shown in Figure 7.5 VSWR at 2.5375 GHz is 1.0736 which is very close to 1, so this
design is providing satisfactory performance. The radiation pattern shows that the
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antenna is omni directional and is linearly polarized with small levels of cross
polarization.
Figure 7.2 Geometry of 0th iteration in pentagonal patch antenna
Figure 7.3 Return loss vs frequency for 0th iteration
-30
-25
-20
-15
-10
-5
0
1 1.5 2 2.5 3 3.5 4
S1
1(d
B)
Frequency (GHz)
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Figure 7.4 Input impedance vs frequency for 0th iteration
Figure 7.5 VSWR vs frequency for 0th iteration
Figure 7.6 Radiation pattern for simple pentagonal antenna
0
10
20
30
40
50
1 1.5 2 2.5 3 3.5
Z11, Ω
Frequency (GHz)
1
2
3
4
5
6
2.2 2.3 2.4 2.5 2.6
VS
WR
Frequency (GHz)
0.16
0.32
0.48
0.64
90
60
30
0
-30
-60
-90
-120
-150
-180
150
120
Ansoft Corporation HFSSDesign1Radiation Pattern 1
Curve Info
rETotal
Setup1 : LastAdaptive
Phi='0deg'
rETotal
Setup1 : LastAdaptive
Phi='90deg'
144
7.5.2. 1st Iteration in Pentagonal Patch Antenna
The first iteration stands for the making of a slot in the patch, as shown in the Figure 7.7.
The slot has been cut off from the patch and then the outputs were measured, this cutting of
the slots make our antenna as a fractal antenna. The response was also observed after the
simulation on the HFSS software, but the result obtained was not satisfactory. Hence we
moved on to the second iteration for achieving further improvements in results. The figure
below shows the pentagonal patch antenna after the first iteration. In the first iteration a
pentagonal slot cut on center of the patch antenna, as shown in the Figure 7.7. The
simulated results show dual band behavior of this antenna as shown in Figure 7.7-7.8.
After that we moved to the second iteration, here we cut two side by side pentagonal slots
which exhibits multi band operation and obtained results are good in agreements, as shown
in the Figure 7.12-7.14. We then moves to the third iteration, here we cut three pentagonal
slots on the patch antenna and obtained results are not much satisfactory. So we stop here.
After comparing results of first, second and third iteration we conclude that results of
second iteration are found to be good hence here we analyzed environmental effects with
water loading(cover) of thickness 0.1 mm to 0.3 mm and obtained results are shown in the
Figure 7.17-7.19, 7.22-7.24.
Figure 7.7 Geometry of 1st iteration in pentagonal patch antenna
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In order to present the design procedure of achieving impedance matching for the first
iterated pentagonal patch antenna case, feed location is set at 11.1 mm and radius of the
patch is 19.107 mm. The radius for the iterated patch is 2.697 mm. After optimization we
met the design challenges such as return loss should be less than -10 dB, VSWR< 2 and
low spurious feed radiation.
Figure 7.8 Return loss vs frequency for 1st iteration
Figure 7.9 Input impedance vs frequency for 1st iteration
-24
-19
-14
-9
-4
1 2 3 4 5
S11, d
B
Frequency (GHz)
0
20
40
60
80
1 2 3 4 5 6 7
Z11,Ω
Frequency (GHz)
146
Figure 7.10 VSWR Vs frequency for 1st iteration
Figure 7.11 Radiation pattern for 1st iterated pentagonal antenna
For 1st iterated pentagonal patch antenna we achieved two resonant frequencies one at 2.40
GHz and second at 3.95 GHz with return loss of -12.51 dB and -29.15 dB respectively as
shown in Figure 7.8. As shown in Figure 7.9 input impedance of the antenna is 80.74 ohm
at 2.4 GHz and 51.15 ohm at 3.95 GHz, as shown in Figure 7.10 VSWR at 2.4 GHz and
3.95 GHz is 1.62 and 1.07 respectively.
0
1
2
3
4
5
6
2 2.6 3.2 3.8 4.4 5
SW
R
Frequency (GHz)
0.12
0.24
0.36
0.48
90
60
30
0
-30
-60
-90
-120
-150
-180
150
120
Ansoft Corporation HFSSDesign1Radiation Pattern 1
Curve Info
rETotal
Setup1 : LastAdaptive
Phi='0deg'
rETotal
Setup1 : LastAdaptive
Phi='90deg'
147
7.5.3. 2nd
Iteration in Pentagonal Patch Antenna
The second iteration stands for the making of two slots in the original patch, as shown in
the Figure 7.12 the slots has been cut off from the patch and then the outputs were
measured, this cutting of the slots make our antenna as a 2nd
iterated fractal patch antenna.
Figure 7.12 Geometry of 2nd
iteration in pentagonal patch antenna
The response was observed after the simulation on the HFSS software, but the result
obtained was satisfactory, even though we moved on to the third iteration for achieving
further improvements in results. The figure below shows the Pentagonal patch antenna after
the iteration. In order to present the design procedure for achieving impedance matching for
the second iterated pentagonal patch antenna case, feed location is set at 11.8 mm and
radius of the patch is 19.107 mm. The radius for both the iterated patch is 2.897 mm. After
optimization we met the design challenges such as return loss should be less than -10 dB,
VSWR < 2 and low spurious feed radiation.
Figure 7.13 Return loss vs frequency for 2nd
iteration
-30
-25
-20
-15
-10
-5
0
1 3 5 7 9
S11
(dB
)
Frequency (GHz)
148
Figure 7.14 VSWR vs frequency 2nd
iteration
Figure 7.15 impedance vs frequency for 2nd
iteration
Figure 7.16: Radiation pattern for 2nd
iterated pentagonal antenna
1
2
3
4
5
6
1.5 3.5 5.5 7.5 9.5
VS
WR
Frequency (GHz)
0
15
30
45
60
75
1 3 5 7 9
Z11,Ω
Frequency (GHz)
0.80
1.60
2.40
3.20
90
60
30
0
-30
-60
-90
-120
-150
-180
150
120
Ansoft Corporation HFSSDesign1Radiation Pattern 1
Curve Info
rETotal
Setup1 : LastAdaptive
Phi='0deg'
rETotal
Setup1 : LastAdaptive
Phi='90deg'
149
For 2nd
iterated pentagonal patch antenna we achieved three resonant frequencies, first at
2.16 GHz, second at 3.56 GHz and third at 7.92 GHz with return loss of -17.68 dB and -
21.51 dB and -41.11 dB respectively as shown in Figure 7.13. Above third resonant
frequency the variation in the stop band noise is quite large. As shown in Figure 7.15 input
impedance of the antenna is 62.94 ohm at 2.16 GHz, 46.63 ohm at 3.56 GHz and 49.12
ohm at 7.92 GHz.
7.5.4. 3rd
Iteration in Pentagonal Patch Antenna
The third iteration stands for the making of three slots in the original patch, as shown in the
figure 7.17 the slots has been cut off from the patch and then the outputs were measured.
This cutting of the slots make our antenna as a 3rd
iterated fractal patch antenna. The
response was observed after the simulation on the HFSS software, but the result obtained
was not satisfactory. Too much variation in results was there. So, we can conclude one
thing here that as the number of iterations goes beyond a limit, the performance of the
antenna decreases.
Figure 7.17 Geometry of 3rd
iteration in pentagonal patch antenna
150
In order to present the design procedure of achieving impedance matching for the third
iterated pentagonal patch antenna case, feed location is set at 12 mm and radius of the patch
is 19.107 mm. The radius for the entire three iterated patch is 4.397 mm. After optimization
we met the design challenges such as return losses should be less than 10 dB, VSWR< 2
and low spurious feed radiation.
Figure 7.18 Return loss vs frequency for 3rd
iteration
Figure 7.19 VSWR vs frequency for 3rd
iteration
-30
-25
-20
-15
-10
-5
0
1 3 5 7 9 11
S11,d
B
Frequency, GHz
1
2
3
4
5
6
0 2 4 6 8 10 12
SW
R
Frequency, GHz
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Figure 7.20 Impedance vs frequency for 3rd
iteration
Figure 7.21 Radiation pattern for 3rd
iterated pentagonal antenna
0
15
30
45
60
75
90
105
0 2 4 6 8 10 12
Z1
1,Ω
Frequency, GHz
0.20
0.40
0.60
0.80
90
60
30
0
-30
-60
-90
-120
-150
-180
150
120
Ansoft Corporation HFSSDesign1Radiation Pattern 1
Curve Info
rETotal
Setup1 : LastAdaptive
Phi='0deg'
rETotal
Setup1 : LastAdaptive
Phi='90deg'
152
Table 7.1 S11, Impedance and VSWR of the proposed fractal patch antenna
Types
Simulated
Frequency
(GHz)
S11(dB) Impedance
(Ω) SWR
0 Iteration 2.4375 -28.99 51.75 1.0736
1st Iteration
2.405 -12.16 82.06 1.6515
3.9775 -21.55 53.28 1.1824
2nd
Iteration
2.16 -16.39 67.31 1.3502
3.56 -18.14 39.03 1.2832
7.96 -27.62 48.2 1.0868
3rd
Iteration
1.96 -11.91 72.13 1.6795
3.36 -12.2 37.81 1.6506
7.96 -18.39 92.85 1.2734
10.08 -28.71 79.9 1.0761
Table 7.2 Simulated directivity, gain, radiated power and radiation efficiency of the
proposed fractal patch antenna
Iterations Directivity
(dB) Gain (dB)
Radiated power
(W)
Radiation
efficiency
0 Iteration 1.6 0.7491 0.005299 46.71%
1 Iteration 0.189 0.7366 0.0071 89.84%
2 Iteration 0.8385 0.55768 0.2908 85.66%
3 Iteration 0.7091 0.7183 0.0155 78.64%
For 3rd
iterated pentagonal patch antenna we achieved four resonant frequencies, first at
1.96 GHz, second at 3.36 GHz, third at 7.96 GHz and fourth at 10.08 GHz with return loss
of -11.91 dB, -12.20 dB, -18.39 dB and -28.71 dB respectively as shown in Figure 7.18.
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The graph is not as sharp as in the case of first and second iteration. Ripples are very large
in the stop bands. As shown in Figure 7.20 input impedance of the antenna is 72.13 ohm at
1.96 GHz, 30.69 ohm at 3.36 GHz, 49.89 ohm at 7.96 GHz and 46.59 ohm at 10.08 GHz.
One can see too much variation in the input impedance from the graph. As shown in Figure
7.19 VSWR at resonant frequencies are 1.67, 1.65, 1.27 and 1.07 GHz respectively.
7.5.5. Fractal Patch Antenna with Dielectric Loading
Figure 7.22 Return loss variation vs frequency with accumulation of water
Figure 7.23 VSWR vs frequency variations with accumulation of water
-33
-28
-23
-18
-13
-8
-3
1 3 5 7 9
S11(d
B)
Frequency (GHz)
dB(S11) at t='0mm'
dB(S11) at t='0.1mm'
dB(S11) at t='0.2mm'
dB(S11) at t='0.3mm'
0
1
2
3
4
5
6
1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
VS
WR
Frequency (GHz)
VSWR at t='0mm'
VSWR at t='0.1 mm'
VSWR at t='0.2 mm'
VSWR at t='0.3mm'
154
Figure 7.24 Input impedance vs frequency variations with accumulation of water
Table 7.3 Impedance and VSWR of the proposed fractal patch antenna for second iteration with
dielectric cover of thickness 0.1 mm to 0.3 mm
Cover
thickness
(water)
Simulated frequency
(GHz)
S11
(dB)
Impedance
(Ω) SWR
0
2.16 -16.39 67.31 1.37
3.56 -18.14 39.03 1.28
7.96 -27.62 56.66 1.08
0.1
2 -16 55.71 1.37
3.18 -13.27 34.5 1.55
7.2 -25.47 76.62 1.11
0.2
1.94 -19.59 55.71 1.89
3.04 -12.05 32.27 1.66
6.84 -29.85 55.57 1.23
0.3
1.92 -18.83 44.17 1.25
3.04 -12.05 32.98 1.66
6.86 -31.4 47.08 1.4
0
15
30
45
60
75
1 3 5 7 9
Z11,Ω
Frequency (GHz)
mag(Z11)at t='0mm'
mag(Z11)at t='0.1mm'
mag(Z11)at t='0.2mm'
mag(Z11)at t='0.3mm'
155
Table 7.4 Simulated directivity, gain radiated power and radiation efficiency of the proposed
fractal patch antenna for second iteration
With superstrate
Directivity 0.69
Gain 0.62
Radiated Power 0.112 W
Radiation Effect 89.83%
7.6. CONCLUSIONS
For the above simulated result for first, second, third iteration are tabulated in the Table 7.1
and 7.2, it is found that all the parameters of the antennas are satisfactory. After dielectric
loading results are tabulated in the Table 7.3 and 7.4 which reveal that the dielectric
loading can change all the parameter such as resonant frequency, return loss, impedance,
VSWR etc. of the patch antenna. It has been also observed that as the dielectric thickness
increases, the resonant frequency shift at lower side hence deteriorates the multi band
characteristics of the pentagonal patch antenna. As found, the main performances of the
patch antennas may be adversely affected if permittivity and thickness of the dielectric are
not chosen properly, hence next chapter is dedicated to look into opportunity to
compensate the effects of environmental conditions;. dielectric loading on the antenna
behaviors.
156
REFERENCES
1. Z. Baharav, ―Fractal arrays based on Iterated Functions System (IFS),‖ Antennas and
Propagation Society International Symposium, 1999, IEEE, Vol.4, pp- 2686 – 2689,
1999.
2. M.Navarro, J.M.Gonzlez. C.Puente, J.Romeu and A.Aguasca, ―Self-similar surface
current distribution on fractal Sierpinski antenna verified with infra-red thermograms,‖
Electronics Letters, Vol. 35, No. 17, pp.1393-1394, 19th Aug. 1999.
3. P. Felber, ―Fractal antennas -A literature study,‖ A project report for ECE 576 Illinois
Institute of Technology, January 16, 2001.
4. Sathya, ―Size reduction of low frequency microstrip patch antennas with Koch fractal
slots‖Mtech Thesis,IISC Banglore.
5. P.Hazdra, and M.Maz´anek , ―The miniature inverted Koch square microstrip patch
antenna,‖ Proceedings of ISAP2005, Seoul, Korea pp.121-124,2005.
6. V.Gupta and N. Gupta , ―Two compact microstrip patch antennas for 2.4 GHz band – a
comparison,‖ Microwave Review, pp. 29-31, November, 2006.
7. V. R. Gupta and N. Gupta, ―Analysis of a fractal microstrip patch antenna,‖ International
Journal of Microwave And Optical Technology, Vol. 2, No. 2, pp. 124-129, April 2007.
8. F.H. Kashani et al, ―A novel broadband fractal Sierpinski shaped, microstrip antenna,‖
Progress in Electromagnetics Research, Vol. 4, 179–190, pp. 179-190, 2008.
9. A. Azari, ―Ultra wideband fractal microstrip antenna design,‖ Progress Electromagnetics
Research , Vol. 2, 7-12, 2008.
10. J. F. Jibrael
and M. H. Hammed, ―A new multiband patch microstrip plusses fractal antenna
for wireless applications,‖ ARPN Journal of Engineering and Applied Sciences, Vol. 5,
No. 8, pp.17-21, August 2010.