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# Multi-band hybrid fractal shape antenna for X and K band applications

Authors:
• Al Muthanna University : College of Basic Education

## Abstract and Figures

Fractal shapes has unusual properties. These unique features will affect antenna parameters when designed in fractal shapes. Two fractal shapes combined together to generate new fractal shape dipole antenna. Seirpinski and modified Koch fractal shapes allow this antenna to operate at too far apart frequencies lies in X and K band. Fractal dimension of modified Koch is found to be 1.08 which led the antenna to be electrically small. This is explaining the resonant points at higher frequencies. Uniting X and K band in single antenna will make the possibility of combining the applications of these two bands in one device. Good results have been obtained from calculating antenna parameters.
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International Journal of Engineering & Technology, 7 (4.36) (2018) 193-196
International Journal of Engineering & Technology
Website: www.sciencepubco.com/index.php/IJET
Research paper
Multi-band hybrid fractal shape antenna for X and K band
applications
Ammar Nadal Shareef 1*, Abbas Abdulhussein Mohammed 2, Amer Basim Shaalan 3
Department of Sciences, AlMuthanna University, Samawa, Iraq.
Department of Sciences, AlMuthanna University, Samawa, Iraq.
Physics Department, Al-Muthanna University, Samawa, Iraq.
Abstract
Fractal shapes has unusual properties. These unique features will affect antenna parameters when designed in fractal shapes. Two fractal
shapes combined together to generate new fractal shape dipole antenna. Seirpinski and modified Koch fractal shapes allow this antenna to
operate at too far apart frequencies lies in X and K band. Fractal dimension of modified Koch is found to be 1.08 which led the antenna to
be electrically small. This is explaining the resonant points at higher frequencies. Uniting X and K band in single antenna will make the
possibility of combining the applications of these two bands in one device. Good results have been obtained from calculating antenna
parameters.
Keywords:
1. Introduction
In the past, antennas had simple shape based on Euclidean geometry
and operate on single specific frequency [1]. Its parameters will
change when operating on different frequencies. By the time the
swift growth of the wireless mobile technology, show need to small
wide band and multi band antennas [2]. A multiband antenna is
designed to operate on several bands to avoid using two antennas.
These antennas many times use designs where part of it is active for
one band, and another part is active for other band [3]. Microstrip
patch antenna is a promising choice for the future technology
because of its advantages like light weight and low profile [4-6].
Fractal geometry deals with self-similar shapes that remain
unchanged under different scales [7]. Combine fractal geometry
with electromagnetic theory have led to access of new shapes in
antenna designs [8]. The term fractal antenna is used to describe
those antenna that are based on such mathematical concepts that
enable one to obtain a new generation of antennas with new features
[9].
In this paper, a new fractal shape dipole antenna design is proposed.
The design is created by combining Sierpinski and modified Koch
fractal shapes. New features obtained from this antenna shape. It
exhibits a multiband behavior that is a property of Sierpinski
triangle shape. The principal frequency located at X -band while the
other resonant points located at k-band, which means that the
antenna is electrically small so it operates at higher frequencies.
This property is obtained from modified Koch fractal shape. Good
computation results we get using
commercially available finite element code HFSS [10].
2. Iterated Function System (IFS) and
Antenna Structure
Iterated function systems (IFS) represent a method for constructing
a wide variety of fractal structures [11]. It is based on the use of a
series of affine transformations (w). Mathematically written as:
w (x, y) = (ax+ by+ e, cx+ dy+ f ) (1)
Where, the coefficients (a, b, c, d, e, f) are real numbers responsible
for movement of fractal element. The coefficients (a, d) are
responsible for scaling and (b, c) are responsible for rotation and (e,
f) responsible for linear transmission. The iterated function system
(IFS) of Sierpinski triangle and Koch curve has been published in
literatures vastly [8]. IFS of modified Koch fractal shape that is used
in our model is represented by:
 


 
  
  

  
 
 
 
 
 

.................... (2)
 
  
  
  
  
  

 
 


The generated shape of modified Koch is shown in Fig.1.
194
Fig.1. Modified Koch fractal shape
3. Fractal Dimension
Fractal dimension is an infinite dimensions lies between Euclidean
0, 1, 2, and 3 dimensions. It is a measure of how complicated a self-
similar figure is [12]. The in between dimensions are inherent
character of fractal shapes. Fractal antenna parameters are found to
be related to fractal dimension value. Sierpinski triangle fractal
dimension is equal to 1.58 and Koch fractal dimension is 1.26 [13].
Fractal dimension is calculated with the following equation [14]:
 
 (3)
Where N is the number of copies and 1/E is similarity ratio
Modified Koch fractal dimension is calculated using equation (3) to
be 1.08.It is obvious that whenever fractal dimension decrease, the
electrical size of the antenna decrease too which led the antenna to
operate at higher frequency.
4. Results and Discussion
New fractal shape obtained by combining second iteration of
Seirpinski triangle and modified Koch curve. Calculations are done
with HFSS code. Antenna shape is illustrated in Fig.2 and its
feeding configuration by using coupling aperture is illustrated in
Fig.3.
Fig.2. Antenna fractal shape: Second iteration of Seirpinski combined with
modified Koch.
Fig.3. Feed configuration of the antenna.
The calculated return loss which represents the matching points of
the antenna are shown in Fig.4.
Fig.4. Return loss of the antenna.
It is obvious from this figure, the principal frequency located at
9GHz and the other matching points located at frequencies of k-
band. This property of uniting too far apart bands in one single
antenna makes it very useful in future wireless devices.
The resistance of the feed line of the antenna is set to 50 ohm.
Resistance versus frequency is shown in Fig.5.
Fig.5. Resistance versus Frequency.
8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00
Frequency [GHz]
-40.00
-35.00
-30.00
-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
Return Loss (dB)
8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00
Freq [GHz]
-300.00
-200.00
-100.00
0.00
100.00
200.00
300.00
400.00
500.00
600.00
Input Imedance
Blue Color (ReZ)
Red Color (ImZ)
International Journal of Engineering & Technology
195
This model of antenna has acceptable values of gain; this is
shown in Figures 6 and 7.
Fig.6. Gain of antenna for the frequencies (9 GHz-21 GHz)
Fig.7. Gain of antenna for the frequencies (22 GHz-30 GHz).
Summary of calculated results obtained include input
impedance, gain, directivity, and efficiency are listed in table 1.
Table.1. antenna parameters.
Efficiency
Directivity (dB)
Gain (dB)
Input
Impedance(Ω)
VSWR
Return Loss (dB)
Frequency (GHz)
99%
9.29
9.22
45
1.29
-17.7
9
95%
9.40
9.08
49.39
1.54
-13.4
17
99%
8.44
8.40
50.15
1.02
-38.3
18
96%
8.55
8.23
49.15
1.43
-15.7
19
97%
9.55
9.29
50.81
1.35
-16.5
21
88%
9.57
8.43
51.78
1.04
-33.5
22.8
89%
8.90
8.04
47.32
1.05
-31.1
25.2
93%
8.14
7.68
33.48
1.56
-13.1
26
73%
11.52
8.57
34.75
1.53
-13.4
27
66%
13.73
9.15
34.73
1.48
-14.1
30
Three directional patterns of antenna are shown in figure 9.
Fig.9. Three dimensional pattern of the antenna.
5.Conclusion
New fractal shape of antenna design has been presented in this
paper. Combine two fractal shapes, Seirpiniski and modified
Koch, has led to generate new features in this antenna model.
IFS of modified Koch is calculated to generate the fractal shape.
Also, fractal dimension of modified Koch is calculated, it is
equal 1.08. Low value of fractal dimension makes the antenna
electrically small and resonate at higher frequencies. The
antenna is operate at too far apart frequencies lies in X and K
band. This could make the potential of combining the
applications of the two bands in one device. Good results
obtained from calculating antenna parameters like gain and
efficiency.
-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00
Theta [deg]
-24.00
-22.00
-20.00
-18.00
-16.00
-14.00
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
-0.00
2.00
4.00
6.00
8.00
10.00
Gain (dB)
Blak Color (phi=90deg,Freq.=9 GHz)
Blue Color (phi=135deg,Freq.=17GHz)
Red Color (phi=30deg,Freq.=18GHz)
Yellow Color (phi=85deg,Freq.=19GHz)
Green Color (phi=60deg,Freq.=21GHz)
-200.00 -100.00 0.00 100.00 200.00
Theta [deg]
-20.00
-15.00
-10.00
-5.00
0.00
5.00
10.00
Gain (dB)
Black Color (phi=45deg, Freq.=22.8GHz)
Blue Color (phi=60deg, Freq.=25GHz)
Red Color (phi=30deg, Freq.=26GHz)
Yellow Color (phi=25deg, Freq.=27GHz)
Green Color (phi=30deg, Freq.=30GHz)
196
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