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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1738
Design and Analysis of Fractal Antenna
Dileep Kumar1, Dr. Priyanka Jaiswal2
1Master of Technology, Electronic and Communication Engineering, GITM, Lucknow, India
2Professor, Electronic and Communication Engineering, GITM, Lucknow, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - The design suggestionsforthreeantennas, eachof
which has a whole separate set of capabilities. The idea of
fractal geometry is used by all three in the process of
constructing small antennas that have superior performance
than that of Microstrip Patch antennas (MPAs). Fractals are
now one of the most fruitful areas of study in the world of
antenna design. Their most notable advantage is their
capacity to increase electrical length while basically
maintaining thesameamountofareaanddeliveringimproved
performance. The first idea is to create a hybrid fractal, which
combines elements from two different kinds of fractals—the
Sierpinski Carpet and the GiuseppePeanu—andsuperimposes
them on top of one other in order to provide the antenna the
capability of narrow-band operation. Due to its ability to
resonate in the S-band, it carries with it the potential to be
used for WiMAX applications. The second idea is to use an
iterative self-similar design to create a multi-band fractal,
which is the second part of the second proposal. The antenna
achieves its multi-band capabilities by cutting circles out of
squares while preserving electrical conductivity throughout.
The fact that it can resonate at five different frequencies
within the range of three gigahertztotwelvegigahertzgivesit
a wide variety of potential uses, all of whicharefeasible within
this frequency range. The third suggestionistouseanantenna
with a very wide band, the manufacture of which has already
been completed. The smallestofthethreepatches, thisonewas
designed by cutting hexagonal holes out of a circular patch,
and optimization was accomplished via the use of parametric
analysis.
Key Words: Design, Analysis, Fractal, narrow band, multi-
band, ultra wide band, antenna.
1. INTRODUCTION
One of the most fundamental justifications for thestatement
is the revolution that has occurred in the sphere of
communications. Wireless communication [1] refers to the
transmission of data between two or more locationsthat are
not connected by electrical conductors. This is one of the
fastest growing segments in the above areas. It provides
solutions to a variety of difficult and unpleasant conditions,
including: B. Cable laying in mountainous areas or long
distances. By using a mobile phone, you can save yourself
the trouble of carrying a wired device at home or at work,
and you can now communicate anytime, anywhere. WLAN
(Wireless Local Area Network) innovation permitsclients to
interface with the Internet without the requirement for
excess and costly rapid links, and is broadly perceived as an
adaptable and savvy option in contrast to conventional fast
information transmission. One ofthecritical mainimpetuses
behind this has been the consistent craving for pocketsized
and open specialized gadgets, also the effortlessness of plan
and assembling. Because of the developing interest for
consistent coordination of cell organizations, for example,
3G, GSM, WPAN and WLAN, it is broadly acceptedthatfuture
remote organizations will fundamentally incorporateshort-
range high velocity remoteadministrationsasa fundamental
component. The fast development of remote interchanges
has prompted the inundation of new gadgets and
frameworks intended to satisfythedevelopingneedforsight
and sound applications. Little universally useful radio wires
need to endure the heap that addresses the issues of cell
phones and remote organizations, so they need to have high
addition, widedata transfer capacity,inserted establishment,
etc.
1.1. Fractal Antenna
A fractal antenna is a device that employs a fractal, self-
comparative plan to upgrade the edge (on insidepartsor the
outside structure) of material that can get or communicate
electromagnetic radiation inside a given all out surface
region or volume. Staggered and space filling bends are
different names for fractal radiowires,howevertheessential
component is the repeat of a topic north of at least two scale
levels, or "cycles." thus, fractal receiving wires are
minuscule, multiband or wideband, and have applicationsin
cell and microwave correspondences. The reaction of a
fractal receiving wire shifts essentially from that ofordinary
receiving wire plans in that it might work with great to-
brilliant execution at a few frequencies simultaneously.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1739
Figure-1: Fractal Antenna
Figure-2.: Classes of fractals
2. NARROW BAND ANTENNA OF FRACTAL.
for example 12.5 mm, the proposed plan incorporates a
sticking the component square shape is introduced to
Giuseppe Peanu Fractal Slits, subsequently framing the
premise of the round Sierpinski opening course of action.
The substrate is made of low-cost fibreglass that is 1.6 mm
thick and coated with. A rectangular piece of 3mm X 25mm
serves as the ground.
Figure-3: front and backside view.
Table-1.: Design Parameter Dimension.
Serial
Number
Parameter Value
1 Length of substrate 30mm
2 Length of patch (front) 16 mm
3 Length of patch (back) 3 mm
4 Centre of circle (back) (0,-16)
5 Radius of bigger circle 2mm
6 Width of substrate 25mm
7 Length of notch on patch W/3 or L/3
8 Width of notch 1mm
9 Center of first circle
(front)
(0,6.5)
10 Radius of smaller circle 1mm
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1740
Figure-4: Gain of Realized.
Figure-5: Patterns of Radiation.
3. MULTI BAND FRACTAL ANTENNA
The antenna is made by continually and iteratively cutting
circles from squares with the dimensions given in the table
below. The patchs are fed using the Co-Planar Waveguide-
feeding approach, which is detailed in the table above. But
first, here's how the antenna is designed.
Figure-6: C.P.W-Fed Fractal.
Table-2: Dimension of the Circle and Square.
Iteration
no
Length of edge of
square.
Internal
radius.
1.0 50 mm 24.5 mm
2.0 36 mm 17.5 mm
3.0 25 mm 12 mm
4.0 17.6 mm 8.4 mm
Table-3: Details Size Parameter of the design
S.no Parameter Value
1 Width = length of substrate. 110.0 mm
2 Thickness of substrate. 1.530 mm
3 Spacing between FEED and
Adjacent Ground.
0.50 mm
4 Feed Length. 24.50 mm
5 Feed Width. 3.0 mm
6 Length of the C.P.W ground. 24.50 mm
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1741
Figure-7: Gain of Realized (3D), When Fc= 3.52GHz.
Figure-8: Patterns of Radiation.
4. ULTRA WIDE BAND FRACTAL ANTENNA
This operation is repeated five times,ensuringthatelectrical
communication is maintained at all times. A CPW feed with
the dimensions listed in table 5.2 is attached. The substrate
is FR4, which has a di-electricstableof4.4.Itsmeasurements
are in addition shown in the table above.
Figure-9: Proposed Design For Antenna.
Table-4: Design Parameter.
Serial
Number
Radius of
Outer Circle
(in mm).
Length of sides of
regular
hexagon the regular
1.0 10.0
millimeter.
09.950 millimeter.
2.0 8.7060
millimeter.
08.6560 millimeter.
3.0 7.5740
millimeter.
07.5240 millimeter.
4.0 6.5830
millimeter.
06.5330 millimeter.
5.0 5.7170
millimeter.
05.6670 millimeter.
Table-5: Dimension Parameter for Antenna
Parameter Length Width
Feed-line. 11.50 millimeter. 03.0 millimeter.
Substrate. 45.0 millimeter. 44.0 millimeter.
Ground
Patch.
9.0 millimeter. 19.50 millimeter.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1742
Figure-10: Patterns of Radiation, At fc= 3.7653
Gigahertz.
Figure-11: Realized-Gain (3-D).
5. CONCLUSION
The goal in writing this thesis was to better comprehend
and contribute to the process of combining antenna theory
with fractal geometry. It explains how to create Microstrip
and Fractal antennas, as well as the theory behind them.
Three designs have been proposed: a narrow-band, a multi-
band, and an ultra-wide band, the last of which has been
manufactured. The radiation and gain patterns of each have
been extensively examined. In addition, the effectiveness of
introducing fractal into antenna theoryhasbeenhighlighted.
The study of a Fractal hybrid thatdemonstratednarrowband
behaviour. The design began with a Giuseppe Peanu fractal,
which served as the foundation foranotherfractal geometry,
Sierpinski geometry. This antenna's Bandwidth Percentage
was determined to be 40.421 percent, indicating that it is a
narrowband antenna with a resonance frequency of 3.386
GHz.
It may be manufactured to use the attributes of the
individual bands since resonant frequencies exist at
numerous points over the SHF. It was a CPW-fed fractal
created by iteratively carving out circles inside squares
while maintaining electrical connection, on a dielectric
substrate FR4 with a dielectric constantof4.4andnoground
plane. The resulting antenna radiated at several frequencies
in the SHF range (3.52 GHz, 5.7 GHz, 8 GHz, 9.95 GHz, and 12
GHz), making it multi-band capable.
An unique Ultra Wide-Band Application design that used
hexagonal holes cut within a circularpatchrepeatedlyovera
FR4 substrate. It was CPW-fed, and the slot gap was
optimised using parametric analysis. The antenna was also
made from scratch. However, due to a lack of advanced
equipment, measurements could not be carried out.
REFERENCES
1. http://en.wikipedia.org/wiki/Antenna_(radio)
2. K. Fujimoto and J. James, Mobile Antenna Systems
Handbook. Artech House, 1994
3. W. Beynon, “Marconi, Radio waves and the Ionosphere,”
Radio Science, vol. vol.10, no.7,pp. 657–664, July, 1975.
4. Choukiker, Yogesh Kumar (2013) “Investigations on some
compact wideband fractal antennas” PhD thesis
5. Agrawal, Sonu (2013) Design and Analysis of Hexagonal
Shaped Fractal Antennas. MTech thesis
6. Zhi Ning Chen and Michael Y. W. Chia, “Broadband Planar
Antennas, Design and Applications,” John Wiley & Sons, Ltd.
7. K. L. Wong, PlanarAntennasforWirelessCommunications.
Wiley-Interscience, 2000
8. A. F. Peterson, S. L. Ray, and R. Mittra, Computational
Methods for Electromagnetics. IEEE Press Series on
Electromagnetic Wave Theory, 1997.
9. E. K. Miller, L. Medgyesi Mitschang, and E. H. Newman,
Computational Electromagnetics: Frequency-Domain
Method of Moments. IEEE Press, 1992
10. W. C. Chew, J. Jin, E. Michielssen, and J. Song, Fast and
Efficient Algorithms in Computational Electromagnetics.
Artech House, 2001
11. IE3D User Manual. Zeland Sofware Inc, 2003.
12. FEKO User‟s Manual, Suite 5.1. EM Software & Systems,
South Africa
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1743
13. User Manual for the CST. IMST GmbH, Germany, 2004.
14. User Manual for HFSS. Ansoft Corporation Pittsburg, PA,
USA., 2000
15. J. Robinson and Y. Rahmat-Samii, “Particle Swarm
Optimization In Electromagnetics,” IEEE Transactions on
Antennas and Propagation, vol. 52, no. 2, pp. 397–407,2004.
16. C. G. Christodoulou, M. Georgioipoulos, and A. H. E.
Zooghby, Applications of Neural Networks in Smart
Antennas for Mobile Communications. Applied
Computational Intelligence, CRC Press, LLC, 2000.
17. C. Christodoulou, M.Georgiopoulos,andC.Christopoulos,
Applications of Neural
Networks in Electromagnetics. Artech House, 2001.
18. Y. Rahmat-Samii and E. Michielssen, Electromagnetic
Optimization by Genetic Algorithms.NewYork:John Wiley&
Sons, 1999.
19. D. S. Linden, Automated Design and Optimizationof Wire
Antennas Using Genetic Algorithms. PhD thesis,
Massachusetts Institute of Technology, Department of
Electrical Engineering and Computer Science, 1997.
20. D. T. Pham, A. Ghanbarzadeh, E. Ko¸ c, S. Otri, S. Rahim,
and M. Zaidi, “The Bees Algorithm: A Novel Tool forComplex
Optimisation Problems,” in Proc. 2nd Int. Virtual Conf. on
Intelligent Production Machines and Systems (IPROMS
2006), 2006
21. E. K. P. Chong and S. H. Zak, An Introduction to
Optimization. Wiley-Interscience Series in Discrete
Mathematics and Optimization, 2001.
22. C. Puente, J. Romeu, R. Bartoleme, and R. Pous, “Fractal
multiband antenna based on Sierpinski gasket,” Electron.
Lett., vol. 32, pp. 1-2, 1996.
23. C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama,
“On the behavior of the Sierpinski multiband fractal
antenna,” IEEE Trans. Ant. Propagat., vol. 46, pp.
517524,1998.
24. N. Cohen, “Fractal antenna applications in wireless
telecommunications,” in Professional Program Proc. of
Electronics Industries Forum of New England, 1997, IEEE,
pp. 43-49, 1997.
25. C. Puente-Baliarda, J. Romeu, R. Pous, J. Ramis, and A.
Hijazo, “Small but long Koch fractal monopole,” Electron.
Lett., vol. 34, pp. 9-10, 1998.
26. E. E. C. de Oliveira, P. H. da F. Silva, A. L. P. S. Campos, S.
Gonc, A.D.Silva, “Overall Size Antenna Reduction using
Fractal Geometry”, Microwave and Optical Technology
Letters, vol. 51, no. 3, March 2009, pp. 671 -674.
27. B. B. Mandlebrot, The Fractal Geometry of Nature.
W.H.Freeman and Company, 1983.

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Design and Analysis of Fractal Antenna

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1738 Design and Analysis of Fractal Antenna Dileep Kumar1, Dr. Priyanka Jaiswal2 1Master of Technology, Electronic and Communication Engineering, GITM, Lucknow, India 2Professor, Electronic and Communication Engineering, GITM, Lucknow, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - The design suggestionsforthreeantennas, eachof which has a whole separate set of capabilities. The idea of fractal geometry is used by all three in the process of constructing small antennas that have superior performance than that of Microstrip Patch antennas (MPAs). Fractals are now one of the most fruitful areas of study in the world of antenna design. Their most notable advantage is their capacity to increase electrical length while basically maintaining thesameamountofareaanddeliveringimproved performance. The first idea is to create a hybrid fractal, which combines elements from two different kinds of fractals—the Sierpinski Carpet and the GiuseppePeanu—andsuperimposes them on top of one other in order to provide the antenna the capability of narrow-band operation. Due to its ability to resonate in the S-band, it carries with it the potential to be used for WiMAX applications. The second idea is to use an iterative self-similar design to create a multi-band fractal, which is the second part of the second proposal. The antenna achieves its multi-band capabilities by cutting circles out of squares while preserving electrical conductivity throughout. The fact that it can resonate at five different frequencies within the range of three gigahertztotwelvegigahertzgivesit a wide variety of potential uses, all of whicharefeasible within this frequency range. The third suggestionistouseanantenna with a very wide band, the manufacture of which has already been completed. The smallestofthethreepatches, thisonewas designed by cutting hexagonal holes out of a circular patch, and optimization was accomplished via the use of parametric analysis. Key Words: Design, Analysis, Fractal, narrow band, multi- band, ultra wide band, antenna. 1. INTRODUCTION One of the most fundamental justifications for thestatement is the revolution that has occurred in the sphere of communications. Wireless communication [1] refers to the transmission of data between two or more locationsthat are not connected by electrical conductors. This is one of the fastest growing segments in the above areas. It provides solutions to a variety of difficult and unpleasant conditions, including: B. Cable laying in mountainous areas or long distances. By using a mobile phone, you can save yourself the trouble of carrying a wired device at home or at work, and you can now communicate anytime, anywhere. WLAN (Wireless Local Area Network) innovation permitsclients to interface with the Internet without the requirement for excess and costly rapid links, and is broadly perceived as an adaptable and savvy option in contrast to conventional fast information transmission. One ofthecritical mainimpetuses behind this has been the consistent craving for pocketsized and open specialized gadgets, also the effortlessness of plan and assembling. Because of the developing interest for consistent coordination of cell organizations, for example, 3G, GSM, WPAN and WLAN, it is broadly acceptedthatfuture remote organizations will fundamentally incorporateshort- range high velocity remoteadministrationsasa fundamental component. The fast development of remote interchanges has prompted the inundation of new gadgets and frameworks intended to satisfythedevelopingneedforsight and sound applications. Little universally useful radio wires need to endure the heap that addresses the issues of cell phones and remote organizations, so they need to have high addition, widedata transfer capacity,inserted establishment, etc. 1.1. Fractal Antenna A fractal antenna is a device that employs a fractal, self- comparative plan to upgrade the edge (on insidepartsor the outside structure) of material that can get or communicate electromagnetic radiation inside a given all out surface region or volume. Staggered and space filling bends are different names for fractal radiowires,howevertheessential component is the repeat of a topic north of at least two scale levels, or "cycles." thus, fractal receiving wires are minuscule, multiband or wideband, and have applicationsin cell and microwave correspondences. The reaction of a fractal receiving wire shifts essentially from that ofordinary receiving wire plans in that it might work with great to- brilliant execution at a few frequencies simultaneously.
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1739 Figure-1: Fractal Antenna Figure-2.: Classes of fractals 2. NARROW BAND ANTENNA OF FRACTAL. for example 12.5 mm, the proposed plan incorporates a sticking the component square shape is introduced to Giuseppe Peanu Fractal Slits, subsequently framing the premise of the round Sierpinski opening course of action. The substrate is made of low-cost fibreglass that is 1.6 mm thick and coated with. A rectangular piece of 3mm X 25mm serves as the ground. Figure-3: front and backside view. Table-1.: Design Parameter Dimension. Serial Number Parameter Value 1 Length of substrate 30mm 2 Length of patch (front) 16 mm 3 Length of patch (back) 3 mm 4 Centre of circle (back) (0,-16) 5 Radius of bigger circle 2mm 6 Width of substrate 25mm 7 Length of notch on patch W/3 or L/3 8 Width of notch 1mm 9 Center of first circle (front) (0,6.5) 10 Radius of smaller circle 1mm
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1740 Figure-4: Gain of Realized. Figure-5: Patterns of Radiation. 3. MULTI BAND FRACTAL ANTENNA The antenna is made by continually and iteratively cutting circles from squares with the dimensions given in the table below. The patchs are fed using the Co-Planar Waveguide- feeding approach, which is detailed in the table above. But first, here's how the antenna is designed. Figure-6: C.P.W-Fed Fractal. Table-2: Dimension of the Circle and Square. Iteration no Length of edge of square. Internal radius. 1.0 50 mm 24.5 mm 2.0 36 mm 17.5 mm 3.0 25 mm 12 mm 4.0 17.6 mm 8.4 mm Table-3: Details Size Parameter of the design S.no Parameter Value 1 Width = length of substrate. 110.0 mm 2 Thickness of substrate. 1.530 mm 3 Spacing between FEED and Adjacent Ground. 0.50 mm 4 Feed Length. 24.50 mm 5 Feed Width. 3.0 mm 6 Length of the C.P.W ground. 24.50 mm
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1741 Figure-7: Gain of Realized (3D), When Fc= 3.52GHz. Figure-8: Patterns of Radiation. 4. ULTRA WIDE BAND FRACTAL ANTENNA This operation is repeated five times,ensuringthatelectrical communication is maintained at all times. A CPW feed with the dimensions listed in table 5.2 is attached. The substrate is FR4, which has a di-electricstableof4.4.Itsmeasurements are in addition shown in the table above. Figure-9: Proposed Design For Antenna. Table-4: Design Parameter. Serial Number Radius of Outer Circle (in mm). Length of sides of regular hexagon the regular 1.0 10.0 millimeter. 09.950 millimeter. 2.0 8.7060 millimeter. 08.6560 millimeter. 3.0 7.5740 millimeter. 07.5240 millimeter. 4.0 6.5830 millimeter. 06.5330 millimeter. 5.0 5.7170 millimeter. 05.6670 millimeter. Table-5: Dimension Parameter for Antenna Parameter Length Width Feed-line. 11.50 millimeter. 03.0 millimeter. Substrate. 45.0 millimeter. 44.0 millimeter. Ground Patch. 9.0 millimeter. 19.50 millimeter.
  • 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1742 Figure-10: Patterns of Radiation, At fc= 3.7653 Gigahertz. Figure-11: Realized-Gain (3-D). 5. CONCLUSION The goal in writing this thesis was to better comprehend and contribute to the process of combining antenna theory with fractal geometry. It explains how to create Microstrip and Fractal antennas, as well as the theory behind them. Three designs have been proposed: a narrow-band, a multi- band, and an ultra-wide band, the last of which has been manufactured. The radiation and gain patterns of each have been extensively examined. In addition, the effectiveness of introducing fractal into antenna theoryhasbeenhighlighted. The study of a Fractal hybrid thatdemonstratednarrowband behaviour. The design began with a Giuseppe Peanu fractal, which served as the foundation foranotherfractal geometry, Sierpinski geometry. This antenna's Bandwidth Percentage was determined to be 40.421 percent, indicating that it is a narrowband antenna with a resonance frequency of 3.386 GHz. It may be manufactured to use the attributes of the individual bands since resonant frequencies exist at numerous points over the SHF. It was a CPW-fed fractal created by iteratively carving out circles inside squares while maintaining electrical connection, on a dielectric substrate FR4 with a dielectric constantof4.4andnoground plane. The resulting antenna radiated at several frequencies in the SHF range (3.52 GHz, 5.7 GHz, 8 GHz, 9.95 GHz, and 12 GHz), making it multi-band capable. An unique Ultra Wide-Band Application design that used hexagonal holes cut within a circularpatchrepeatedlyovera FR4 substrate. It was CPW-fed, and the slot gap was optimised using parametric analysis. The antenna was also made from scratch. However, due to a lack of advanced equipment, measurements could not be carried out. REFERENCES 1. http://en.wikipedia.org/wiki/Antenna_(radio) 2. K. Fujimoto and J. James, Mobile Antenna Systems Handbook. Artech House, 1994 3. W. Beynon, “Marconi, Radio waves and the Ionosphere,” Radio Science, vol. vol.10, no.7,pp. 657–664, July, 1975. 4. Choukiker, Yogesh Kumar (2013) “Investigations on some compact wideband fractal antennas” PhD thesis 5. Agrawal, Sonu (2013) Design and Analysis of Hexagonal Shaped Fractal Antennas. MTech thesis 6. Zhi Ning Chen and Michael Y. W. Chia, “Broadband Planar Antennas, Design and Applications,” John Wiley & Sons, Ltd. 7. K. L. Wong, PlanarAntennasforWirelessCommunications. Wiley-Interscience, 2000 8. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. IEEE Press Series on Electromagnetic Wave Theory, 1997. 9. E. K. Miller, L. Medgyesi Mitschang, and E. H. Newman, Computational Electromagnetics: Frequency-Domain Method of Moments. IEEE Press, 1992 10. W. C. Chew, J. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, 2001 11. IE3D User Manual. Zeland Sofware Inc, 2003. 12. FEKO User‟s Manual, Suite 5.1. EM Software & Systems, South Africa
  • 6. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 09 Issue: 08 | Aug 2022 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 1743 13. User Manual for the CST. IMST GmbH, Germany, 2004. 14. User Manual for HFSS. Ansoft Corporation Pittsburg, PA, USA., 2000 15. J. Robinson and Y. Rahmat-Samii, “Particle Swarm Optimization In Electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 2, pp. 397–407,2004. 16. C. G. Christodoulou, M. Georgioipoulos, and A. H. E. Zooghby, Applications of Neural Networks in Smart Antennas for Mobile Communications. Applied Computational Intelligence, CRC Press, LLC, 2000. 17. C. Christodoulou, M.Georgiopoulos,andC.Christopoulos, Applications of Neural Networks in Electromagnetics. Artech House, 2001. 18. Y. Rahmat-Samii and E. Michielssen, Electromagnetic Optimization by Genetic Algorithms.NewYork:John Wiley& Sons, 1999. 19. D. S. Linden, Automated Design and Optimizationof Wire Antennas Using Genetic Algorithms. PhD thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1997. 20. D. T. Pham, A. Ghanbarzadeh, E. Ko¸ c, S. Otri, S. Rahim, and M. Zaidi, “The Bees Algorithm: A Novel Tool forComplex Optimisation Problems,” in Proc. 2nd Int. Virtual Conf. on Intelligent Production Machines and Systems (IPROMS 2006), 2006 21. E. K. P. Chong and S. H. Zak, An Introduction to Optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization, 2001. 22. C. Puente, J. Romeu, R. Bartoleme, and R. Pous, “Fractal multiband antenna based on Sierpinski gasket,” Electron. Lett., vol. 32, pp. 1-2, 1996. 23. C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Ant. Propagat., vol. 46, pp. 517524,1998. 24. N. Cohen, “Fractal antenna applications in wireless telecommunications,” in Professional Program Proc. of Electronics Industries Forum of New England, 1997, IEEE, pp. 43-49, 1997. 25. C. Puente-Baliarda, J. Romeu, R. Pous, J. Ramis, and A. Hijazo, “Small but long Koch fractal monopole,” Electron. Lett., vol. 34, pp. 9-10, 1998. 26. E. E. C. de Oliveira, P. H. da F. Silva, A. L. P. S. Campos, S. Gonc, A.D.Silva, “Overall Size Antenna Reduction using Fractal Geometry”, Microwave and Optical Technology Letters, vol. 51, no. 3, March 2009, pp. 671 -674. 27. B. B. Mandlebrot, The Fractal Geometry of Nature. W.H.Freeman and Company, 1983.