A review of various fractal geometries

1. A REVIEW OF VARIOUS FRACTAL
GEOMETRIES FOR WIRELESS
APPLICATIONS
Rupleen Kaur
Dept. of Electronics and
Communication Engg.
Guru Nanak Dev University,
Regional Campus Gurdaspur.
Punjab, India
rupleeenkaur@gmail.com
Satbir Singh
Dept of Electronics and
Communication Engg.
Guru Nanak Dev University,
Regional Campus Gurdaspur.
Punjab, India
satbir1_78@yahoo.co.in
Naveen Kumar
Executive Director, Athal Services
Private Limited.
Chandigarh, India
chd.naveen@gmail.com
Abstract: With the advancement in antenna technology,
there is a great need of a low profile, multiband and
wideband antennas for wireless communication. Fractal
antennas are different from others because of their self
similarity and self repetitive properties. Fractal
microstrip patch antennas have small size, light weight
and support multiple frequencies. In this paper, we have
discussed various fractal geometries so as to understand
the multiband behavior of microstrip patch antenna. We
have also explained fractal antennas for various wireless
communication applications such as in WiMAX
technology.
Keywords: Fractal microstrip patch antenna, Fractal
geometries, wireless communication.
I. INTRODUCTION
Microstrip patch antenna was developed by Bob
Munson in 1972. It consists ofradiating patches that are
placed on the top of the dielectric substrate and a
conductive layer is present on the bottomsurface of the
substrate, forming a ground for the antenna. The shape
and dimensions of the patch are the important features
of the antenna. Microstrip patch antennas are light in
weight because of absence of machined parts and are
simpler, compact and easy to manufacture with printed
circuit technology [1].
In 1988, first Fractal antenna was built by Dr.
Nathan Cohen. Fractal antennas have self similar and
self repetitive characteristics. The idea behind fractal
antennas came from patterns existing in nature. They
have space filling properties that are well utilized in
designing antennas for wideband behavior. Fractal
antennas are the combination of antennas that are
operating at different frequencies with a small size.
In wireless communication, military communication
and navigation communication, we require an antenna
that provides multiband support, compact size, higher
gain and optimal performance. To meet these
requirements fractal antennas are needed. Fractal
antennas do not have any deterministic size [2]. These
antennas are smaller in size and support multiband
frequencies. Therefore such antennas require less space
which is highly desirable for wireless communication
and advanced military communication where space is a
major issue. Self similar property in fractal antennas
shows wideband behavior. This property is used to
expand the length of the material by keeping the total
area same. Space filling property reduces the size of the
antenna and hence helps in making a low profile
antenna required in most of the communication systems
[3]. Therefore using fractal geometries a compact and
wideband antenna can be designed. A single fractal
antenna can be used to operate on many resonant
frequencies. These antennas provide same radiation
patterns and gain as conventional antennas but occupy
less space. Multiple iterations exist in single basic
shape. These iterations can continue infinitely but
occupying finite space. Therefore Fractal antennas are
compact in size and supports multiband frequencies [4].
II. FRACTAL GEOMETRIES FOR
PATCH ANTENNA
Fractal designs offer better parameters and
controlled designs. Fractal antennas not only provide
multiband characteristics but also have self similarity of
the geometry. A Fractal antenna provides excellent
performance at many different frequencies
simultaneously. These antennas are nature inspired
antennas. There are four commonly used geometries.
(1) Sierpinski Gasket
Sierpinski gasket is named after the mathematician
Sierpinski. In this the central triangle is subtracted from
the main triangle shape. After subtraction three equal
triangles appear on the structure, each being half the

2. size of original triangle. Iterations can occur infinite
number of times and hence sierpinski gasket is obtained
[5, 6].
Fig.1 Sierpinski Gasket [5]
(2) Sierpinski Carpet
This geometry is similar to sierpinski gasket, but it
uses squares in place of triangles. It starts with a square
at first, and divides itself in nine smaller squares while
dropping the central square. The same process is again
repeated with smaller squares. The Sierpinski Gasket
shape is widely used because by using this shape a
single antenna can be operated on multiple frequencies
[5, 7].
Fig. 2 Sierpinski Carpet [5]
(3) Koch Curve
This geometry starts with a straight line. This line is
then again divided into three equal parts. The middle
segment is substituted with two other segments of
approximately same length. This is known as first
iteration [5, 8].
Fig.3 Koch Curve [5]
(4) Hilbert Curve
This geometry is simplest from all since it covers
the area it occupies. In this the line segments do not
intersect with each other and hence reduces complexity
[5, 9].
Fig.4 Hilbert Curve [5]
III. APPLICATIONS OF FRACTAL ANTENNA
A large number of fractal antenna designs have been
proposed. The purpose of this paper is to show various
applications and remarkable growth of fractal antenna
in the fields of wireless communication.
A. Fractal Antenna for UWB Devices
The presented antenna is an ultra wideband
inscribed triangular circular antenna. This antenna has
been designed for UWB devices. The antenna shows
ultra bandwidth from 2.25 GHz to 15 GHz. These
characteristics have been achieved by using CPW fed
and fractal geometries. It is seen that the fourth iteration
shows wideband characteristics which is suitable for
designing UWB devices. The antenna is rested on FR4
substrate with dielectric constant 4.3. The thickness of
substrate is 1.53mm with initial dimensions of 30mm
diameter. In order to achieve UWB characteristics the
gap between patch and ground is set to h= 0.4mm. The
length of the ground plane is 28mm and the width is
25mm. The radiation patterns of the antenna are omni-
directional in H plane and bidirectional in E plane.
Fractal antenna is designed by using High Frequency
Structure Simulator (HFSS) software. It is observed that
wideband characteristics improve as the number of
iterations increases. The coplanar ground plane makes
the design more suitable for applications that need less
space. The antenna can be used for various military and
commercial applications. The design of the antenna is
shown in figure 5 [10, 11].
Fig.5. Proposed fractal antenna with coplanar feed [10]
B. Fractal Antenna for Aerospace Navigation
The presented antenna is a square patch antenna
based on Koch geometry. The antenna is designed for
Aeronautical radio navigation. The antenna shows
multiband behavior at 2.7-2.9GHz for aeronautical
radio navigation and 9.0-9.3GHz for Maritime radio
navigation. In this a square patch is taken whose design
changes according to the variations in the fractal
geometries. The material of the substrate is Roger
RT/Duroid 5880 ™ having permittivity 2.2 and
thickness 0.32cm. The dimensions of the substrate are

3. A+2 cm Side Square. A coaxial cable is used as feed in
the center of the patch. It is seen that the third iteration
shows multiband nature used for aeronautical radio
navigation. The antenna is designed using High
Frequency Structure Simulator (HFSS) software. It is
observed that as the number of iterations increases,
perimeter of patch also increases and hence the
effective area of antenna decreases. This antenna gives
effective directivity than multiband antenna. This
antenna can be used for various commercial
applications. The design of the antenna is shown in
figure 6 [12, 13].
Fig.6. Fractal antenna front-Top views [12]
C. Fractal Antenna for Wireless Power
Transmission Systems
The presented antenna is a rectangular patch
antenna that is iterated upto 3rd level. The antenna is
designed for multiband applications and Wireless
Power Transmission (WPT) System. The main
application of WPT system is in Solar Power Satellites
(SPS). The antenna resonates at four frequencies i.e.,
1.86, 2.29, 3.02 and 4.05 GHz. The material of the
substrate is FR4 with permittivity 4.4 and thickness h =
1.52mm. The length of the ground and the substrate is
54.36mm and width is 46.72mm. The length and width
of the patch is 37mm and 28mm respectively. The final
results of the antenna can be obtained from third
iteration of microstrip patch antenna. The antenna is
designed using High Frequency Structure Simulator
(HFSS) software. The wideband characteristics increase
as the number of iterations increases. The antenna can
also be used for short range satellite applications. The
design of the antenna is shown in figure 7 [14, 15].
Fig.7. Fractal antenna top view [14]
IV. CONCLUSION
The present review paper exhibits the performance
of microstrip patch antenna using various fractal
geometries. In this paper, we have discussed various
designs and applications of fractal patch antenna. From
this paper we have concluded that Sierpinski Gasket
shape is widely used because in this shape a single
antenna can be operated on multiple frequencies. Here a
square patch fractal antenna covers a large frequency
band. The paper also provides a Literature Review table
for different applications.
REFERENCES
[1] MS.A.J. Upadhjay,Prof. P.J. Brahmbhatt, “Design a Dual Band
Microstrip Antenna for Wireless (GPS) Application”, Journal of
Information, Knowledge and Research in Electronics and
Communications Engineering Vol. 2, pp 497-499, Oct 2013.
[2] Amapreet Kaur, NaveenKumar, Dr. Basudeo Prasad, “ A Study
of various Fractal Antenna Design Techniques for Wireless

4. Applications”, International Journal of Electronics and
Communication Technology Vol.4, pp 47-50 , June 2013.
[3] R. Jothi Chitra,V.Nagarajan, “Double L-Slot Microstrip Patch
Antenna Array for WiMAXand WLAN Applications”, Computers
and Eectrical Engineering, pp 1026-1041, Jan 2013.
[4] M. Samsuzzaman, M.T. Islam, N. Misran,M.A. MohdAli, “ Dual
bandX shape Microstrip PatchAntenna for Satellite Applications”,
IEEE International Conference on Electrical Engineering and
Informatics, pp 1223-1228, 2013.
[5] Carles Puente-Baliarda, Jordi Romeu, Rafael Pous, Angel
Cardama, “On the Behavior of the Sierpinski Multiband Fractal
Antenna”, IEEEtransactions onantennas and propagation,Vol. 46,
No. 4, pp 517-524, April 1998.
[6] Asit K. Panda,Manoj K. Panda,SudhanshuS. Patra,“A Compact
Multiband Gasket Enabled Rectangular Fractal Antenna”, IEEE
International Conference on Computational Intelligence and
Communication Networks, pp 11-14, 2011.
[7] Munesh Chandra, Pradeep Kr. Kushwaha, Shailendra Saxena,
“Modified Fractal Carpets”, IEEE International Conference on
Computational IntelligenceandCommunication Networks, pp 537-
540, 2011.
[8] S. Yadav, R. Choudhary, U. Soni, B. Peshwani, M.M Sharma,
“Koch curve fractal antenna for Wi-MAX and C-Band wireless
applications”, IEEE International conference– ConfluenceThe Next
Generation Information Technology Submit, pp 490-494, 2014.
[9] Li-li Sun, Xu-dong Sun, Wei Wang, “Factors effect on Hilbert
fractal antenna performance”, IEEE International Conference on
Information Science and Engineering, pp6623-6626, 2010.
[10] Raj Kumar, Dhananjay Magar, K. Kailas Sawant, “On the
design of inscribed triangle circular fractal antenna for UWB
applications”, International Journal of Electronics and
Communication, pp 68-75, 2012.
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of Multiband Fractal Microstrip Patch Antenna for Wireless
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Intelligence and Communication Networks, pp 32-36, 2013.
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TABLE 1: LITERATURE REVIEW TABLE
S.
no.
ANTENNA DESIGN FREQUENCY BAND RETURN LOSS GAIN APPLICATION
1. Circular Patch Fractal
Antenna
3.0 GHz, 4.275 GHz, 6.3
GHz, 10.2 GHz, 11.2 GHz
-15.5db, -20.2db,-20.4db,-
20.8db,-25.5db,-25db
>5dbi UWB Devices
2. Square Patch Fractal
Antenna
3.0 GHz,07.49GHz,
09.68GHz, 11.21GHz
-22.20db, -18.70db, -
30.96db, -15.82 db
12.02 dbi Aeronautical radio
navigation,
Aeronautical/Maritime
radio navigation
3. Koch Fractal Microstrip
Antenna
1-5 GHz 13-16 db 2.98-3.01 dbi Solar Power Satellites,
WiMax, Short range
satellite applicationantenna