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Planar Tree Shaped Fractal Antennas for UWB Applications
A Dissertation Submitted in partial fulfillment of the requirements
For the award of the degree of
Master of Technology In
Electronics Engineering (Microwave Engineering)
Submitted By
Tushar Goel
Under the Supervision of
Dr. Amit Kumar Singh
Department of Electronics Engineering Indian Institute of Technology
(Banaras Hindu University) Varanasi 221005, INDIA
July, 2014 Roll No: 12305EN002
i
Ref: IIT/ECE/. Date: ..
CERTIFICATE
This is to certify that the dissertation entitled Planar Tree Shaped Fractal Antennas For
UWB Applications submitted by Mr. Tushar Goel ( Roll No: 12305EN002), to the
Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University),
Varanasi, in partial fulfillment of the requirements for the award of the degree of Master of
Technology in Electronics Engineering (Microwave Engineering) is an authentic work carried
out at Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu
University), Varanasi by him under my supervision and guidance.
(Dr. Amit Kumar Singh) (Prof. P.K Jain)
Supervisor Head of the Department
Department of Electronics Engineering
Indian Institute of Technology
(Banaras Hindu University)
Varanasi 221005, INDIA
Phone: 0542-2307010 Fax: 0542-2366758 E-mail: head.ece@iitbhu.ac.in
ii
Ref: IIT/ECE/. Date: ..
CANDIDATES DECLARATION
I hereby declare that the work presented in this dissertation titled Planar Tree Shaped
Fractal Antennas For UWB Applications is an authentic record of my own work carried
out at Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu
University), Varanasi as requirements for the award of degree of Master of Technology in
Electronics Engineering (Microwave Engineering), submitted in the Indian Institute of Technology,
(Banaras Hindu University), Varanasi (U.P) under the supervision of Dr. Amit Kumar Singh,
Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University),
Varanasi. It does not contain any part of the work, which has been submitted for the award of any
degree either in this Institute or in other University/Deemed University without proper citation.
Tushar Goel
Roll No: 12305EN002
M.tech. (Microwave Engineering)
Department of Electronics Engineering
IIT (BHU), Varanasi
Department of Electronics Engineering
Indian Institute of Technology
(Banaras Hindu University)
Varanasi 221005, INDIA
Phone: 0542-2307010 Fax: 0542-2366758 E-mail: head.ece@iitbhu.ac.in
iii
Dedicated To
My Family& Friends
iv
ACKNOWLEDGEMENTS
First and foremost, I would like to express my hearty thanks and indebtedness to my
supervisor Dr. Amit Kumar Singh, Department of Electronics Engineering, Indian Institute of
Technology (Banaras Hindu University), Varanasi for his enormous help and encouragement
throughout the course of this dissertation. His vast technical knowledge and insight have given me
an excellent background in the field of my work. His excellent guidance, perseverance, invaluable
suggestions made this work possible and complete.
My profound gratitude to Prof. P. K. Jain, Head, Department of Electronics Engineering,
Indian Institute of Technology (BHU), Varanasi for providing necessary facilities and for
connecting me with CRMT laboratory in order to perform necessary measurements on network
analyser.
I would also like to thank Dr. M. K. Meshram for the valuable suggestions for success of
this work. A special acknowledgement goes to Dr. Bhogendra Jha for his help in measurement of
antenna parameters. I would also like to thanks all the faculty members and the librarians for their
kind cooperation and encouragement during the course of work.
I am also grateful to Jairam Sir, Bahadur Sir for all his technical and experimental
assistance throughout my post graduate program, and to all of the technical and non-technical
staffs for all the instances in which their assistance helped me along the way.
I would like also to acknowledge Ph.D. scholars Soni mam, Situ mam, Swati mam, Gargi
mam, Sarthak sir, Madan sir, Harishankar sir, Gaurav sir and Bharti sir without them this project
work could not have seen the daylight and helped me with their constant support, involvement and
encouragement during my project.
Above all, it was my family and friends named Mr. Darab Singh Meena, Mr. Praveen verma,
Mr. Pankaj Kumar, Mr. Ravi Paudel, Mr. Sachin Kalraiya and Mr. Abhijeet Singh, who gave me
endless support and provided me with an opportunity to reach this far with my studies. Their
constant encouragement has always helped me to walk over all the hurdles. Its just not possible to
express my gratitude and indebtedness towards them in words.
Last but not least, I thank almighty Lord Vishwanath for providing me strength and
courage in completing the work
Tushar Goel
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ABSTRACT
Now a days operators are looking for systems which can perform over several frequency
bands because the number of wireless communication applications have increased steadily,
leading to the competition for currently allocated frequency bands. Thus authorities around the
world are pressurized to permit communications in higher and wider frequency ranges to achieve
higher wireless data rate capacity. The federal communication commission (FCC) in USA has
unleashed the band 3.1-10.6 GHz for ultra-wideband (UWB) communications. In the past few
years, new designs of UWB antenna have been investigated for wireless devices because of their
wider impedance bandwidth and high data rate capacity. Requirement of UWB has initiated
antenna research in various directions, one of which is fractal shaped antenna elements. Fractal
plays a prominent role for size reduction and wide band requirements. Fractal antenna is a
geometric shape that has the property of self-similarity. Fractal antennas have ability to add
more electrical length in less volume. Main focus of this dissertation is tree shaped fractal
antenna for UWB applications. Authors objective in this dissertation is to design planar tree
shaped UWB fractal antennas having more than 50% size reduction. This dissertation examines
two compact structures based on tree shaped fractal geometry operating in UWB frequency band.
In the first design a compact hexagonal tree shaped fractal antenna for UWB applications is
proposed. By using tree shaped fractal geometry approximately 69% size reduction has been
achieved. The size of antenna is 30mm40mm.The bandwidth has been enhanced by using
modified feedline and semicircular ground plane. It has an impedance bandwidth of 2.44-16 GHz
(147%).The proposed second iteration fractal antenna has nearly omnidirectional patterns at its
resonance frequencies. Prototype of proposed design is developed by fabrication and experimental
measurement has been carried out. It is found that measured response of built up prototype is in
very good agreement with the simulated results.
In the second design, a CPW-Fed inner tapered tree shaped fractal antenna is proposed to meet
the requirement of miniaturized UWB antenna. In this design, 95% size reduction is achieved. The
dimension of proposed structure is 18.5mm9.2mm. The bandwidth is enhanced by using CPW
ground plane technique and increasing the number of iterations. An impedance bandwidth of 4.58-
15.60 GHz (109%) is achieved. Both of the structures have been designed with the help of
Ansoft HFSS simulator on a FR-4 epoxy substrate having a dielectric constant of 4.4 and a
thickness of 1.6 mm.
vi
CONTENTS
Acknowledgements iv
Abstract v
List of Figures viii
List of Tables xi
Chapter 1
Introduction
1.1 Introduction. 1
1.2 Historical Review ... 2
References 14
Chapter 2
Analysis of UWB Fractal Antenna
2.1 Ultra Wide Band. 20
2.1.1 UWB application 20
2.2 Fractal 21
2.2.1 Fractal in Nature.. 22
2.2.2 Fractal Antenna 23
2.2.3 Fractal Antenna Geometries 23
2.2.3.a Sierpinski Carpet Geometry.. 24
2.2.3.b Sierpinski Gasket Geometry.. 24
2.2.3.c Nested type triangular fractal antenna.. 25
2.2.3.d Hilbert Curves Geometry. 26
2.2.3.e Circular Fractal Geometries 27
2.2.3.f Giusepe Peano Fractal Geometry. 28
2.2.3.g Koch Curve Fractal Geometry. 28
2.2.3.h Pythagorean Tree Fractal Geometry 30
2.3.2.i Tree Shaped Fractal Geometry. 31
vii
2.2.3.j Fractal Binary tree 32
2.2.4 General Applications of Fractal.. 33
2.2.5 Advantages of Fractal antenna 34
References 35
Chapter 3
Design & Analysis of Tree Shaped UWB Fractal Antenna 38
3.1 Design1: Hexagonal Tree Shaped Fractal Antenna For UWB Applications. 39
3.1.1 Antenna design 39
3.1.2 Results and Discussion .. 45
3.2 Design 2: CPW-Fed Inner tapered tree shaped UWB fractal antenna 57
3.2.1 Antenna Design 57
3.2.2 Results and discussion .. 60
References . 71
Chapter 4
Conclusion And Future Work
4.1 Conclusion 73
4.2 Future scope of work .. 74
List of Publications
viii
LIST OF FIGURES
Figure No. Figure name Page No.
Figure.2.1 Examples of fractals that can be found in nature 22
Figure 2.2 Four stages in construction of Sierpinski carpet geometry.. 24
Figure 2.3 Sierpinski gasket for zeroth, first, second iterations 25
Figure 2.4 Nested triangle fractal antenna structure 25
Figure 2.5 Four stages in construction of Hilbert curves. 26
Figure 2.6 Different iterations of Circular microstrip patch fractal antenna. 27
Figure 2.7 Initiator and generator of the Giusepe Peano fractal Geometry..... 28
Figure 2.8 Zeroth, first, second iterations of Giusepe Peano fractal geometry 28
Figure 2.9 Geometry of the square slot and Koch fractals for four iterations with =90o 29
Figure 2.10 Step of construction of Koch curves geometries with = 60o 29
Figure 2.11 Illustration of the first four iterations for Pythagorean tree fractal 31
Figure 2.12 fabricated first five iterations for Pythagorean tree fractal monopole antenna 31
Figure 2.13 Illustration of first three iterations of tree shaped fractal geometry.. 31
Figure 2.14 Various iterations of fractal Binary tree. 32
Figure 2.15 3rd iterated fractal Binary tree with different branching angles 32
Figure 3.1 Antenna structures (a) Antenna I: Rectangular Patch with Rectangular
ground plane, (b) Antenna II: Rectangular Initiator with Semicircular
ground plane and (c) Antenna III: Hexagonal Initiator..
41
Figure 3.2 Three iterations of the proposed antenna structure (a) Zeroth iteration,
(b) First Iteration (c) Second Iteration
43
Figure 3.3 Proposed second iteration Hexagonal tree shaped fractal antenna
structure (a) Radiating patch (b) Ground plane..
44
Figure 3.4 The prototype of proposed hexagonal tree shaped fractal UWB antenna. 45
Figure 3.5 Comparison of return loss characteristics for Antenna I, Antenna II and
Antenna III
46
Figure 3.6 Return loss versus frequency plot for three iterations of the proposed
second iteration hexagonal tree shaped fractal antenna
47
Figure 3.7 Comparison of the return loss versus frequency plot by HFSS and CST for
second iteration hexagonal fractal antenna..
48
Figure 3.8 VSWR versus frequency plot for three iterations of the proposed second
Iteration hexagonal tree shaped fractal antenna..
49
Figure 3.9 Comparison of the VSWR versus frequency plot by HFSS and CST for
second iteration hexagonal fractal antenna.. 50
Figure 3.10 Real and Imaginary part of input impedance versus frequency plot for
second iteration hexagonal fractal antenna..
50
ix
Figure 3.11 Radiation pattern of second iteration hexagonal fractal antenna at different
Frequencies.
51
Figure 3.12 The peak realized gain Vs. frequency plot for second iteration hexagonal
Fractal antenna..
52
Figure 3.13 Simulated surface current distribution at resonance frequencies.. 53
Figure 3.14 Total and radiation efficiency Vs. frequency plot for the proposed antenna
structure
54
Figure 3.15 Time Domain analysis of the proposed antenna structure 55
Figure 3.16 Simulated phase (S21) response of proposed antenna.. 56
Figure 3.17 Transfer function (S21) versus frequency plot for the proposed
antenna
56
Figure 3.18 Four iterations of the proposed antenna structure (a) Zeroth iteration,
(b) First Iteration (c) Second Iteration (d) Third Iteration.
58
Figure 3.19 (a)Proposed third iteration inner tapered tree shaped fractal UWB antenna
Structure (b) prototype of proposed structure....
59
Figure 3.20 Return loss versus frequency plot for all four iterations of the proposed
Third Iteration Inner tapered tree shaped fractal antenna.
60
Figure 3.21 Comparison of HFSS, CST and measured return loss 61
Figure 3.22 VSWR versus frequency plot for all four iterations of the proposed third
iteration inner tapered tree shaped fractal antenna.
62
Figure 3.23 Comparison of return loss versus frequency of HFSS, CST and measured
results... 63
Figure 3.24 Real and Imaginary part of input impedance versus frequency plot for third
iteration inner tapered tree shaped fractal antenna..
63
Figure 3.25 Peak realized gain versus frequency plot for third iteration inner tapered tree
shaped fractal antenna
64
Figure 3.26 Radiation pattern of third iteration inner tapered tree shaped fractal antenna
at resonance frequencies 64
Figure 3.27 Co-Polar and Cross-Polar Radiation patterns of third iteration inner tapered
tree shaped fractal antenna at resonance frequencies
65
Figure 3.28 Surface current distribution for the proposed third iteration inner tapered tree
shaped fractal antenna structure.
67
Figure 3.29 Total and radiation efficiency versus frequency plot for the proposed
antenna structure
68
Figure 3.30 Time Domain analysis of the proposed antenna structure 69
x
Figure 3.31 Group delay versus frequency plot for the proposed third iteration inner
tapered tree shaped fractal antenna
69
Figure 3.32 Simulated phase (S21) response of proposed antenna. 70
Figure 3.33 Transfer function (S21) versus frequency plot for the proposed antenna. 70
xi
LIST OF TABLES
Table no. Table Name Page no.
Table 2.1 Feature advantages and benefits of fractal 34
Table 3.1 Calculated Dimensions of Radiating Patch for Zeroth iteration
40
Table 3.2 Optimized Dimensions of the Proposed Antenna...
42
Table 3.3 Size Reduction Calculation for Different Iterations.. 42
Table 3.4 Effects of Initial Structure Modification
47
Table 3.5 Lower and Higher Edge of the Bandwidth for Three Iterations
48
Table 3.6 Comparison of Bandwidth of Proposed Antenna Using HFSS and CST..
49
Table 3.7 Fidelity Factor for Two Configurations.
55
Table 3.8 Size reduction calculations for different iterations . 58
Table 3.9 Optimized dimensions of the proposed antenna. 59
Table 3.10 Comparison of all four iterations of the proposed antenna structure. 61
Table 3.11 Effects of transition from zeroth to first iteration.. 61
Table 3.12 Bandwidth Comparison of return loss using HFSS, CST and Measured
results 62
Table 3.13 Fidelity Factor for Two Configurations.. 68
Chapter 1
Introduction
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Introduction
1.1 Introduction
An antenna is a transducer that converts guided electromagnetic energy in a transmission line
to radiated electromagnetic energy in free space. It may also be viewed as an impedance
transformer, coupling between an input or line impedance, and the impedance of free space.
For many years, lots of research work has been carried out on various antennas for wideband
operation for communications and radar systems. It has been a hot topic throughout the years, with
various parameters in focus in order to further enhance system performance. Wireless data transfer
capacity is an important issue in modern wireless communications. The imminent wide spread
commercial deployment of ultra-wideband (UWB) systems has sparked renewed interest in the
subject of high wireless data transfer capacity. According to Federal communication commission
(FCC) definition the frequency band of 3.1 to 10.6 GHz is referred as UWB spectrum. UWB
Microstrip patch antennas are gaining popularity for use in wireless communication, in high-
performance aircraft, spacecraft, satellite and missile applications where size, weight, cost,
performance, ease to installation, and aerodynamic profile are constraints.
Applications in present wireless communication systems usually require conformal smaller
antenna as well as high data rate with low cost implementation. Thus size reduction and wide-band
operation are becoming major design considerations for practical application of microstrip patch
antennas. UWB offers several advantages including low power consumption, high date rate, high
time resolution, low-cost implementation, obstacle penetration, resistance to interference, covert
transmission, co-existence with narrowband systems and so on. Such advantages enable a wide
range of applications of UWB microstrip patch antennas to communications, radar, imaging and
positioning etc.
Several methods exist to reduce the size and to increase the bandwidth of the UWB microstrip
patch antennas but mainly four types of UWB antennas are investigated for this purpose and those
are dipole antenna, monopole antenna, fractal antenna, Vivaldi antenna. Fractal UWB antennas
are suitable candidates due to their small size, multiband and wideband operation at wide range of
microwave frequency. Fractal structure is known for its space filling property that means the size
of fractal structure becomes large at the same area as the number of iterations increases. Because
of this property fractal geometries have been applied to antenna design not only to achieve
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multiband and broadband operation but also to miniaturize the size of antenna.
UWB microstrip patch antenna is very much useful especially in fixed mobile applications,
radio astronomy, defense systems, Radar and navigation systems, wireless communication
systems, fixed satellites, broadcasting satellites etc.
In the light of the above it was thought useful to take up the topic on microstrip patch UWB
fractal antenna for investigations emphasizing mainly on microstrip patch tree shaped fractal UWB
antenna. Therefore the author has endeavored to achieve ultra-wide band by using several methods
like incorporating the slots on the radiating patch, tapering the feed line, changing the shape of
ground plane. Consequently simulation and experimental investigations have been carried out
which are given in the following chapters that embody the present dissertation.
Before going to the actual problem an effort has been made to study the available literature
under the topic and consequently a brief historical in the following section.
1.2 Historical review:
The term fractal firstly was proposed by the French mathematician B.B. Mandelbrot during
1970s after his pioneering research on several naturally occurring irregular and fragmented
geometries not contained within the realms of conventional Euclidian geometry. These geometries
were generally discarded as formless, but Mandelbrot discovered that certain special features could
be associated with them. Many of these curves were recognized well before him, and were often
associated with mathematicians of yesteryears. But Mandelbrots research was path-breaking: It
was discovered that a common element in many of these seemingly irregular geometries and
formulated theories based on his findings.[1]-[2]
In 1999, C.T.P. Song et. al. presented fractal stacked monopole antenna with very wide
bandwidth. They introduced a parallel feed stacked fractal antenna using the square Sierpinski and
diamond Sierpinski carpet .They achieved a good input impedance match throughout the passband
(1-20GHz) below -5dB return loss. They used four strip dipoles having their arms printed on the
two sides of an electrically thin dielectric substrate [4]. Since FCC defined UWB criteria in 2002
according to which return loss should be below -10dB and hence this antenna cannot be considered
as UWB antenna. [3]
In 2003, for the very first time Nathan Cohen et. al. introduced fractal wideband antennas for
software defined radio, UWB, and multiple platform applications. They introduced IIFA (Invariant
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impedance fractal), FIFA (Frequency invariant fractal), and wide band array as an examples of
extremely wideband devised from fractal Antenna technology [5].
In 2005, W.J. Lui et. al. proposed frequency notched ultra-wideband microstrip slot antenna
with fractal tuning stub. This antenna was similar to conventional microstrip slot antenna. The
frequency notched function was achieved by introducing a fractal tuning stub. They used a
Substrate having dielectric constant equal to 2.65 with thickness 1mm and the size of antenna was
48mm41 mm with this configuration they achieved operational bandwidth from 2.66 to 10.76
GHz in which a frequency notched band from 4.95 to 5.85 GHz had been achieved [6].
In the same year M.Jamshidifar et. al. presented miniaturized wideband fractal patch antenna
and by introducing fractal geometry they achieved 68% size reduction in comparison of
conventional square patch antenna. Dimension of antenna was 64.5mm64.5mm and 13%
bandwidth for 3rd iteration was obtained at center frequency of 1.7GHz [7].
While on the other hand Y.M Madany et. al. demonstrated the analysis of ultra-wideband like
fractal microstrip patch antenna using non-uniform photonic bandgap substrate structure. This
antenna was sensitive to the PBG with periodic patch structure and had operational bandwidth in
the range of 4 GHz to 20 GHz. They observed that PBGs enhance some modes and weaken others,
which had been used to control the antenna bandwidth. They used FR-4 epoxy substrate of
thickness 1.6 mm with relative permittivity 4.4. [8]
In 2006, W. J. Lui et. al. presented compact frequency notched ultra-wideband fractal printed
slot antenna. By introducing Koch fractal slot in conventional microstrip antenna, the size of the
antenna was reduced significantly and also frequency notched function was achieved. Size of the
antenna was 28mm24mm1mm and antenna was fabricated on a thin dielectric substrate with
low relative permittivity equal to 2.65.The operational bandwidth of the antenna was from 2.85 to
12 GHz, in which a frequency notched band from 4.65 to 6.40 GHz was achieved. [9]
In the same year M.Ding et. al. proposed design of a CPW-fed ultra-wideband crown circular
fractal antenna. They used Teflon substrate with thickness of 1mm and relative permittivity of 2.2.
They used circular patch antenna as a basic structure. The size of antenna was 39.6mm43.5mm
1.03mm and with this dimension they achieved frequency bandwidth from 2.28 GHz to above
12GHz. [10]
After that S.V.Krupenin et. al. presented the irregular-shaped fractal for ultra-wideband radio
systems using two dimensional fractal clusters. They studied multiband behavior of the fractal-
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cluster based by means of numerical analysis. In comparison to regular shaped fractal more
frequency bands and better matching are achieved. As a multiband antenna they achieved more
than ten frequency bands of various width and matching in the range of 0.1-20 GHz.[11]
In 2007, Hyo-Won Song et. al. demonstrated design of the tree-shaped UWB antenna using
fractal concept. They used the partial ground plane technique and the fractal concept to achieve an
ultra-wideband impedance matching. They observed that as the number of iteration was increased,
the lower-edge of the impedance bandwidth was moved to the low frequency and the level of the
impedance matching over the operating frequency band (3.1-4.8 GHz) was improved. They used
FR-4 proxy as a substrate with antenna size of 30mm20mm1.6mm. The basic structure was
rectangular patch antenna and then two iterations were applied on it in order to achieve good
impedance bandwidth. They tapered the same structure to increase the electrical length travelled
by current that further improved the impedance bandwidth. The operational bandwidth from final
structure was achieved from 2.7 to 6.4 GHz. They achieved required bandwidth by varying angles
in trapezoidal shape, and gap between patch and ground. [12]-[13].
In 2008, R.Kumar et. al. represented a design of star shaped circular microstrip fractal antenna.
They designed that antenna on substrate having relative permittivity 4.3 and thickness 1.53 mm.
Their main purpose was to reduce the size of antenna by shifting the first resonant frequency
towards lower side. [14]
In the same year, A.Azari et. al proposed an Ultra wide band fractal antenna design that was
a fractal structure on hexagonal patch and several iterations were applied on initial shape. They
showed if antenna size is less than /4 then antenna is not efficient because radiation resistance,
gain, bandwidth is reduced hence antenna size has to be large. Fractal geometry was used to
miniaturize the size of antenna, and by using fractal geometry antenna was reduced upto
70cm70cm .With this antenna configuration operational bandwidth from 0.1GHz to 24GHz was
achieved.[15]
In 2009, A. Ramadan et. al. presented compact (30mm20mm) Sierpinski Carpet based patch
antenna for UWB applications. To perform good impedance matching incorporating dual slots on
rectangular patch, they introduced a tapered connection between patch and feed line that is 'I'
shaped feed line. This feed line always gives very good impedance matching. They used Isola
Gigaver substrate of thickness 1.83mm and achieved impedance bandwidth from 3.4GHz to 11.75
GHz.[16].
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Subsequently A.Ramadan et. al. represented another modified Sierpinski carpet antenna for
UWB applications, antenna was designed using FEM and MOM techniques in which they titled
the carpet by 45% while feed remains the same. In this design patch width was selected smaller
than its length to keep better omnidirectional properties at high frequency. They observed as the
width of planar monopole antenna decreases, it operates more similar to a printed thin monopole
antenna and thus it improves the ability to retain the omnidirectional horizontal patterns over its
band of operation. The size of antenna was kept 30mm20mm and FR-4 proxy substrate having
thickness 1.6mm was used and this time 3.0 GHz to 11.3 GHz bandwidth was achieved. [17]
Following it, M.A Husseini et. al. illustrated another antenna for UWB applications using
Sierpinski carpet gasket fractal concept. This time also they used FR-4 proxy substrate of thickness
1.6mm while size of antenna was reduced to 25mm20mm. They used tapered microstrip feed line
and ground plane consisted of rectangular and semicircular part. Patch was designed by rounding
the corners of rectangular patch and using fractal geometry. By rounding the corners of patch and
using tapered feed line led to bandwidth enhancement and 3.15-14GHz bandwidth was achieved.
[18]
Later on in same year, R.Kumar et. al. proposed appollian like Gasket fractal multiband
antenna with CPW-Fed. The antenna had been designed on FR-4 substrate having dielectric
constant of 4.3, with a thickness of 1.53 mm. The shift in first resonant frequency of antenna
revealed the size reduction in comparison of solid equilateral triangular patch of 40 mm. Proposed
antenna showed the multiband behavior with the center frequencies of 1.265, 4.66, and 7.8 GHz
with impedance bandwidth of 50%, 17.5%, and 15%, respectively. [19]
In same year, A.Azari demonstrated a super wide band fractal antenna having 40GHz
bandwidth with frequency range from 20GHz to 60GHz. Fractal geometry was applied to square
loop antenna. The proposed design was a loaded 3rd iteration of Tee fractal antenna and an
appropriate location was selected for feeding. The proposed structure had a small dimensions of
3.5cm3.5 cm. [20].
Afterwards in same year, A. Falahati et. al. proposed dual band notch CPW ground Fed Fractal
Binary tree slot UWB antenna that was capable of reducing interference at WLAN by eliminating
4.95-6.05GHz band. The size of antenna was very compact, it was just 16mm22mm. They used
four iterations with 1200 branch splitting angles and 1.0 arm to stem was employed. Fractal shape
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was subtracted from original patch. Fractal geometry introduced 2nd resonance at 10.2 GHz that
could not be achieved by simple structure. [21]
In the end of 2009, S.S. Lee et. al. represented fractal trapezoidal ultra-wideband antenna.
Trapezoidal patch was used for omnidirectional pattern. This antenna was on Sierpinski Gasket
fractal antenna and bandwidth achieved was about 6GHz by increasing the electrical length using
fractal antenna .They observed that to evaluate the dispersion, group delay and path loss distance
between two UWB antennas should be at least 30cm. [22]
In 2010, Abofazl Azari presented a new ultra wideband fractal antenna. It was the modified
version of the antenna that was presented in 2009,[20] in which he had achieved super wide band.
This time size of antenna was 6.2cm6.2cm. By simply modifying the previous structure dual band
7.5-14.5GHz & 17.5-37.5GHz was achieved. [23]
After that in same year, A.Azari et. al. proposed another design of Koch Fractal antenna for
UWB applications. This time by tilting the square loop to 450, operating bandwidth from 100MHz
to 10GHz was achieved. [24]
Following that, Raj Kumar et. al presented several designs based on circular patch antennas.
For fractal shape they used triangular square, rotated square, overlapped triangular etc. Firstly they
proposed Triangular wheel shaped Fractal antenna that was a conventional circular microstrip
patch antenna (CCMPA) with full ground plane. The size of antenna was 80mm77.4mm and
hence almost 50% size reduction was achieved. It was found that increase in number of fractal
iterations reduced backscattering RCS at multiband compared to the conventional patch antenna.
The antenna could be tuned for low backscattering by variation in the substrate dielectric constant
and thickness and the superstrate dielectric constant and thickness. This antenna covered
operational bandwidth from 0.85GHZ to 4GHz. [25]
After that in same antenna they used CPW feeding technique and achieved excellent
bandwidth from 0.86 GHz to 11.49 GHz. This antenna had been designed on dielectric substrate
r = 4.3 and thickness h = 1.53 mm with radius a=40mm.They observed that effect of fractal
geometry shifts the resonant frequency because of removal of metallization. It is because current
is mainly distributed along the circumference of antenna hence low current density is present in
the middle area of antenna. Therefore if the middle of area of antenna is slotted, the current in that
area would not get affected. By slotting the area of antenna, effective path of surface current is
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increased thus first resonance frequency would be decreased and antenna size would be reduced.
[26]
In same year, R.Kumar et. al. illustrated design of CPW -Fed Fourth Iterative UWB Fractal
Antenna based on inscribed square circular fractal structure. In which they used FR-4 substrate
with dielectric constant 4.3 and thickness 1.53mm. They presented two different design as follows.
Firstly they proposed an antenna without notch band and design size of antenna was
117mm140mm, with this size they achieved impedance bandwidth ranging from .88 to 15 GHz.
They observed that CPW (Co-Planar waveguide) fed was advantageous for less dispersion at high
frequency, broader matching, easy fabrication & integration with MMIC and also improves
impedance bandwidth. [27]
They redesigned same antenna by adjustable band notch characteristics. In this design size of
antenna was reduced to 40mm45mm and adjustable U shaped notch in feedline was used to
reduce interference with the frequency bands of worldwide interoperability for microwave access
(WiMAX) ranging from 3.3GHz to 3.7 GHz. They achieved bandwidth range from 3.1 to 15 GHz.
They observed that the resonant frequency of notch band is defined by the effective length of slot
and notched frequency bandwidth is defined by width of slot. [28]
In the same year, H.E Zadeh et. al. represented a compact circular multifractal monopole
antenna with 22mm33mm size. The design was made by 3 co-centric circles with decreasing
radii. The design was repeated such that every design was at 1200 angle to each other and created
a new design. Because of asymmetry in structure the feed line was not in the middle of substrate.
They achieved frequency band ranging from 3GHz to 12.5GHz.[29]
In 2011, R.Ghatak et. al. firstly demonstrated a monopole type Sierpinski carpet fractal
patterned regular dielectric resonator antenna for UWB applications with microstrip feed line.
They observed that a solid rectangular dielectric resonator mounted on a vertical ground plane
edge with a micro strip line feed monopole arrangement which reduced the total size of antenna
as compared to horizontal ground plane. This antenna offered 87.86% impedance bandwidth. [30]
Later on, they presented a Dual band notched fractal UWB antenna based on Sierpinski carpet
fractal geometry which significantly reduced the size of antenna & increased bandwidth. This
antenna had volume 63mm63mm0.8mm. They modified same design as they used in previous
DRA by cutting U shaped slot at ground plane to create notch band. Notch band for WIMAX
3.1GHz to 3.7GHz and 5.15-5.825 GHz for IEEE 802.11a & HIPERLAN was achieved. [31]
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Subsequently they proposed the modified version of previous antenna, it was very compact
antenna having volume (27mm24.5mm1.6mm). They used partial ground plane which was
given the shape of modified Von Koch curve. Length of slots were taken almost quarter of guided
wavelength at center frequency 5.5GHz. Bandwidth achieved was from 3.1GHz to11 GHz with
5.15 to 5.825 GHz band was rejected. Radiation pattern achieved was almost omnidirectional. [32]
Later on, for the very first time they represented Sierpinski Fractal shaped antenna with
circular boundary before this all Sierpinski based antenna were rectangular shaped. They cut the
slots having meander type shape on radiator. The meander geometry provides sufficient
miniaturization and does not affect radiation characteristics. Antenna size was 40mm38mm while
bandwidth achieved was 3GHz to 12GHz with band notched for HiperLAN 2, 5.15-5.825 GHz.
[33]
A.Azari proposed two antennas based on novel Koch fractal geometry in the same year. Firstly
their design was based on rotated square having dimension 40mm40mm. Impedance bandwidth
achieved was from 5-30GHz. The design was based on 2nd iteration of new generator to a square
loop antenna. Maximum bandwidth was achieved by replacing feed location. [34]
Later on, in the same year A.Azari presented another monopole antenna with Koch fractal
structure that was based on same generator presented previously and achieved bandwidth from 6
to 30 GHz. Fractal antenna was made by copper and vertically installed above a ground plane
which was aluminum metal with physical dimension of 32mm16mm. [35]
After that, in same year R.Kumar et.al. demonstrated in six different papers in which few of
them were modified and rest were new designs. Firstly they presented inscribed square circular
fractal antenna that was the same shape as that they presented in 2010 with also band notch.[27]
This time they modified it and presented compact fractal antenna on same shape with size
24mm37mm while last time size was 40mm45mm. This time also they used CPW fed and
achieved 3.01 to 15 GHz operating band. [36]
Later on, with same shape R.Kumar et. al. illustrated modified ground plane but this time they
took larger antenna having size 50mm71.80mm. They used four iterations on that design instead
of three as they used last time. Ground plane was modified by inserting three circles of different
radius in CPW fed to improve bandwidth. They achieved 2.235 to 15 GHz operating band. [37]
R.Kumar et al. proposed basic shape of inscribed triangle circular fractal antenna in 2010,
[28] and then in 2011, modified L shaped CPW fed UWB fractal antenna was proposed with
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volume of 51mm50mm1.53mm. Dielectric medium was the same as before with dielectric
constant 4.3 and from 2.465 to 15GHz operating bandwidth was achieved by using L shaped CPW
fed. [38]
After that, Raj Kumar et. al. represented CPW fed Pentagonal cut UWB fractal antenna. In
this design they used twelve dimensional pentagonal structure with side length of 1.837mm .This
twelve dimensional pentagonal structure was fit between outer circle and inner circle hence by
four iterations they got 4.69 GHz to 15GHz bandwidth that is upper UWB mainly for DS-CDMA
5.825GHz to 10.6 GHz. They used CPW fed and volume of antenna was taken
31mm32mm1.53mm.[39]
Again in same year, they presented modified version of same antenna with circular cut at CPW
fed. By increasing the size of antenna upto 52.45mm58mm, they achieved impedance bandwidth
from 2.5 to 15 GHz. [40]
After that in the same year Raj Kumar et. al. proposed triangular wheel shaped antenna. They
modified their own design represented in 2010,[26] with different size and different frequency
band. This time antenna size was 62mm55mm. They achieved omnidirectional radiation pattern
in whole operating frequency band i,e from 2.25 GHz to 15GHz.[41]
Subsequently in same year Hai-Yang Xu et. al. demonstrated an ultra-wideband fractal slot
antenna based on Koch curve with low backscattering cross section. Antenna volume was
63mm63mm0.8mm and they achieved operating band from 2.5 GHz to 15GHz. They observed
that RCS of antenna includes two category RCS of structural mode and antenna mode because of
Koch shaped and subtracting metal from patch the structural mode become lower whereas
radiation characteristic & UWB width was favorable.[42]
Later on, A. Kaka et. al. represented a fractal geometry, multiband, miniaturized monopole
antenna design for UWB wireless applications. Minikowski fractal was applied to the lines of
square and then Sierpinski carpet was formed on it. The antenna size was 45mm45mm.They
achieved multiband characteristics with 80% radiation efficiency and 4-6dBi antenna gain. [43]
Afterwards L. Ghanbari et. al. proposed a novel small UWB antenna using new fractal like
geometry which was implemented on a planar circular disk monopole antenna. They achieved
operational bandwidth from 2.57GHz to 12.15 GHz. They observed that disk radius plays
important role in deciding resonant frequency. [44]
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Later in the same year Y. S. Li et. al. analyzed and investigated a cantor set fractal UWB
antenna with a notch-band characteristics. Antenna size was 26mm21mm. The operational
bandwidth was broadened by setting two symmetrical triangular tapered corners at the bottom of
the wide slot. Notched band characteristics was achieved by employing a T shaped tuning stub at
the top of the wide slot. They achieved operating frequency range from 2.8GHz to 11GHz except
for band frequency 5.0 GHz to 6.3GHz.[45].
After that M. Naghshvarian Jahromi et. al. discussed application of fractal binary tree slot and
constructed a dual band-notch CPW-ground-fed ultra-wideband antenna. Antenna size was
16mm22mn. They created the notch band for WLAN bands. They used fractal binary tree to
achieve the desired stop band characteristics. They used a tree with four Iterations, it had 1200
branch splitting angles and a 1.0 arm to stem method. This fractal structure is subtracted from
radiating patch. The maximum suppression obtained for the stops at 5.65 and 9.9 GHz were -13.1
and 7.2 dB, respectively. [46].
Afterwards, J. Pourahmadazar et. al. presented novel modified Pythagorean tree fractal
monopole antennas for UWB applications. The size of antenna was very compact 25mm25mm
1mm. By inserting a modified Pythagorean tree fractal in conventional T-patch they achieved
much wider impedance bandwidth from 2.6 GHz to 11.12GHz. They used semi elliptical ground
plane as an impedance matching circuit.[47]
In 2012, Yingsong Li et. al. illustrated cantor set fractal antennas for switchable ultra-
wideband communication applications. The notch functions were achieved using a U-shaped slot
etched in the coplanar waveguide (CPW) ground plane and a T-shaped stub inserted in the inner
of wide slot, respectively. The switchable characteristics were obtained using switches in the
middle of the U shaped slot and the T-shaped stub. The notch band was able to reduce the potential
interference between UWB and wireless local area network (WLAN). The size of the antenna was
32mm24mm. To broaden the bandwidth of the proposed antenna, circular and triangular tapered
corner were used in the designs.[48]
After that in same year, Yingsong Li et. al. proposed another printed cantor set fractal antenna
for ultra-wideband applications. The size of antenna was 25mm48mm. The antenna consisted of
two identical wide slot antennas and the radiation patches were designed by using Cantor set fractal
technology. The proposed antenna operated over a wide band spanning from 4.5 GHz to 10.6 GHz.
The diversity antenna had a high isolation over 20dB. The high isolation was obtained using
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multiple slots etched in its CPW ground plane. The diversity performance of the antenna was
assessed by isolation and radiation patterns. The results showed that the proposed antenna provided
stable patterns diversity, which enabled the designed antenna to combat multi-path in wireless
channels used in UWB systems [49]
Later on, B. S. Cook et. al. presented the smallest reported Inkjet-Printed UWB antenna on
paper substrate utilizing a novel fractal matching network. The antenna was inkjet-printed on a
paper substrate to demonstrate the ability to produce small and low-cost UWB antennas with
inkjet-printing technology which could enable compact, low-cost, and environmentally friendly
wireless sensor network. The antenna was based on the microstrip monopole with a tapered
Sierpinski Gasket fractal geometry. [50]
In the same year Kailas K. Sawant et. al. demonstrated a novel CPW-fed circular square-
corner fractal antenna with varying notch-band for UWB applications. The size of antenna was
52.4mm50.8mm. This was the same structure that was presented in 2011, [36] except this time
they used N shaped slot in the CPW fed to create band notch. This notch was adjustable to over
the entire operating band. They achieved operational bandwidth from 3.1 to 15 GHz. The band-
notch characteristic between 5GHz to 6GHz frequencies was observed. [51]
Later on, Rowdra Ghatak et. al. illustrated CPW Fed inscribed gasket fractal circular
monopole antenna for UWB application as they presented in 2011.[33] Size reduction of the
antenna was done by Sierpinski gasket fractal concept which offered 24% thinning. The size of
antenna was 48mm 60mm.This antenna provided excellent bandwidth having span from 2.44 to
14.31 GHz. The band-rejection operation achieved at the WLAN (5.155.85GHz) band by adding
defected ground structure (DGS) or slit in the ground plane. [52]
Following it in same year, Abhik Gorai et. al. presented Sierpinski fractal binomial tapered
planar monopole antenna for UWB communication. Size of antenna was 33.24mm30mm. First
iteration of the Sierpinski fractal was achieved by etching out the center rectangle of Area A from
the patch. The second iteration was achieved by etching out eight similar rectangles of area A/3
from the patch. Patch was slightly tapered circularly at its corners. This antenna covered 3.1 GHz
to 10.6 GHz UWB band. [53]
Afterwards in same year, Ramavath Ashok Kumar et. al. represented design of hybrid fractal
antenna for UWB application. The proposed antenna was designed by combination of Giusepe
Peano and Sierpinski Carpet fractal geometries. They used elliptical ground plane and microstrip
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line feed circuit. The size of antenna was 30mm25 mm and with this antenna configuration they
achieved operational bandwidth from 3.1 GHz to 10.6 GHz [54]
In 2013, Anirban Karmakar et. al. proposed design and analysis of fractal based monopole
antenna with impedance steps and fractal slots in the ground plane that contributed to ultra-wide
band characteristics. The size of the antenna was 30mm35mm. They showed that impedance
steps as well as fractal technique was adopted to improve the bandwidth of the antenna in
comparison to its non-fractal counterpart. With that structure they achieved operating frequency
range from 2.7GHz to 10.9GHz which provides 120% impedance bandwidth. [55]
Later on, M.N.Moghadasi et. al. demonstrated UWB CPW-Fed fractal patch antenna with
band-notched function employing folded T-shaped element (FTSE). The antenna had dimensions
of 14mm18mm1 mm. The impedance match of the antenna was determined by the number of
fractal unit cells, and the necessary band-notch functionality was provided by the FTSE. The
filtering property was tuned finely by controlling of length of FTSE. Antenna operated over a
frequency band between 2.9411.17 GHz with fractional bandwidth of 117% for, except at the
notch band between 3.34.2 GHz. [56]
After that in same year, H.Fallahi et. al. represented study of a class of UWB CPW-Fed
monopole Antenna with Fractal elements. They added six small hexagonal shaped fractal
resonating elements at the corners of a hexagonal radiator. Antenna dimensions were only
25mm25 mm. They investigated a multi-resonance technique and achieved standard UWB
characteristics in a CPW-fed monopole antenna. Fidelity factor of the antenna was greater than
0.92 in both elevation and azimuth planes. [57]
Following it, A.S.Abd El-Hameed et. al. proposed Fractal quasi-self-complimentary
miniaturized with Koch fractal boundary for UWB applications. The proposed antenna had a total
size of 16mm13mm1.5 mm .The microstrip feed line was tapered for impedance matching. A
semi-circular Koch fractal radiating element and its complementary magnetic counterpart were
etched on opposite sides of the dielectric substrate. Two rectangular cut were also inserted on the
ground plane in order to improve the impedance matching. Antenna was covering the operating
frequency range from 3.313.5GHz..[58]
Later on, G.Wang et. al presented an UWB antenna using modified Sierpinski-carpet Fractal
antenna. The size of the antenna was 88.7mm76.3mm1.6mm. The proposed antenna consisted
of a patch element mounted on a dielectric isotropic layer over a ground plane. The radiating
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IIT (BHU) Varanasi Page 13
element was a square which was applied by modified Sierpinski-carpet fractal geometry. There
were four resonant frequencies between 1GHz-20GHz and the lower band bandwidth was covered
from 1.1GHz-10.8GHz.[59].
Subsequently, S.Tripathi et. al. proposed a novel multi band notched octagonal shaped Fractal
UWB antenna. This antenna was designed using Minkowski like fractal geometry. The size of
antenna was just 16.5mm 13.5mm. They observed that multiple notches helped not only to obtain
the desired bandwidth but also provided an additional resonant frequency in higher operating
range. Entire UWB operating range from 3.1 GHz to 10.6 GHz with two distinct resonant
frequencies at 4.2 GHz, and 9.4 GHz was achieved. [60]
In 2014, Y. K.Choukiker et. al. presented a microstrip line feed modified Sierpinski square
fractal antenna for ultra-wide band (UWB) with band notch characteristics. UWB operation (3.1
10.6 GHz) was achieved by increasing the numbers of iterations and rectangular grooved ground
plane. The band rejection characteristic was realized by a -slot in the feed line. The proposed
antenna had a volume 34mm34mm1.6 mm with a square shape structure and showed
omnidirectional radiation patterns. The antenna offered UWB operation and a notch at 5.5 GHz
(56 GHz) which covered the wireless local area network band. [61]
In the same year, T.Sedghi et. al. proposed a compact printed monopole antenna consisting
of a fractal radiating patch, which was excited with a coplanar waveguide. The miniaturized
antenna had a total size of 14mm18mm1mm. It was shown that with the inclusion of two pairs
of notches in the ground plane, the antennas performance for UWB applications could be
extended. The antennas patch was composed of a definite number of fractal rectangular unit cells.
The antenna operated over a frequency band from 2.95 to 12.81 GHz with fractional bandwidth of
125%. [62]
From the above literature review, it can be deduced that Fractal antenna can be a better
tool for applications at UWB and radar application and hence complete analysis of UWB fractal
antenna is presented in the next chapter.
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IIT (BHU) Varanasi Page 14
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[14] R.Kumar, Y.B.Thakre and M.Bhattacharya, "Novel Design of Star Shaped Circular Microstrip
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[22] S.S.Lee and J.N.Lee, "The Design of Fractal Antenna for UWB Applications", IEEE
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[26] R.Kumar and P.Malathi, "On the Design of CPW-Fed Ultra Wideband Triangular Wheel
Shape Fractal Antenna", International Journal of Microwave and Optical Technology, Vol.5
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[27] R.Kumar and K.K.Sawant, "Design of CPW -Fed Fourth Iterative UWB Fractal Antenna",
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[28] R.Kumar, K.K.Sawant and J.Pai, "Design of Inscribed Square Circular Fractal Antenna with
Adjustable Notch-Band Characteristics", In Proceedings of ITU-T Kaleidoscope Academic
Conference, Pune, pp.1-5, 2010.
[29] R.Kumar and P.Bansode, "On the Design of Ultra Wide Band Antenna Based On Fractal
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[30] D.Soren, R.K.Mishra, R.Ghatak and D.R.Poddar, "A Monopole Type Sierpinski Carpet
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[51] K.K.Sawant, R.Kumar and A.N.Gaikwad, "A Novel CPW-Fed Circular Square-Corner
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Emerging Technology Trends in Electronics, Communication and Networking, Surat, pp.1-4,
2012.
[53] A.Gorai, A.Karmakar, S.Verma and R.Ghatak, "Sierpinski Fractal Binomial Tapered Planar
Monopole Antenna for UWB Communication", In Proceedings of 5th IEEE International
Conference on Computer and Devices for Communications (CODEC), Kolkata, pp.1-3, 2012.
[54] R.A.Kumar, Y.K.Choukiker and S.K.Behera, "Design of Hybrid Fractal Antenna For UWB
Application", In Proceedings of International Conference on Computing, Electronics and
Electrical Technologies, Kumaracoil, pp.691-693, 2012.
[55] A.Karmakar, U.Banerjee, R.Ghatak and D.R.Poddar, "Design and Analysis of Fractal Based
UWB Monopole Antenna", In Proceedings of National Conference on Communications
(NCC), New Delhi, pp.1-5, 2013.
[56] M.N.Moghadasi, R.A.Sadeghzadeh, T.Sedghi, T.Aribi, and B.S.Virdee, UWB CPW-Fed
Fractal Patch Antenna With Band-Notched Function Employing Folded T-Shaped Element",
IEEE Antennas and Wireless Propagation Letters, Vol. 12, pp.504-507, 2013.
[57] H.Fallahi and Z.Atlasbaf, "Study of a Class of UWB CPW-Fed Monopole Antenna with
Fractal Elements", IEEE Antennas and Wireless Propagation Letters, Vol. 12, pp.1484-1487,
2013.
[58] A.S.Abd El-Hameed, D.A.Salem, E.A.Abdallah and E.A.Hashish, "Fractal Quasi-Self
Complimentary Miniaturized UWB Antenna", Progress in Electromagnetic Research B,
Vol.56, pp.185-201, 2013.
[59] G.Wang, D.Shen and X.Zhang, "An UWB Antenna Using Modified Sierpinski-Carpet Fractal
Antenna", In Proceedings of Antennas and Propagation Society International Symposium
(APSURSI), Orlando, pp. 216 - 217, 2013.
[60] S.Tripathi, S.Yadav, V.Vijay, A.Dixit and A.Mohan, "A Novel Multi band notched Octagonal
Shaped Fractal UWB Antenna, International Conference on Signal Processing and
Communication (ICSC), Noida, pp.167-169, 2013.
[61] Y.K.Choukiker and S.K.Behera, Modified Sierpinski Square Fractal Antenna Covering
Ultra-Wide Band Application With Band Notch Characteristics, Microwaves, Antennas & Propagation, IET, Vol.8, No.7, pp.506-512, 2014.
Chapter-1
IIT (BHU) Varanasi Page 19
[62] T.Sedghi and M.Jalali, Very Compact UWB CPW-Fed Fractal Antenna Using Modify
Ground Plane And Unit Cells, Microwave and Optical Technology Letters, Vol.56, No.
4, pp.851-854, 2014.
Chapter 2
Analysis of UWB Fractal
Antenna
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IIT (BHU) Varanasi Page 20
Analysis of UWB Fractal Antenna
2.1 Ultra Wide Band (UWB)
UWB signals are pulse-based waveforms compressed in time, instead of sinusoidal
waveforms compressed in frequency. It refers to systems with very large bandwidth that is
generally larger than 500MHz. There are following 2 criteria available for Identifying UWB.
First criteria was set up by Defense Advance Research Agency (DARPA), according to this,
system having more than 25% fractional bandwidth refers to UWB system.
Where, Fractional Bandwidth = 2 (FH-FL)/(FH+FL)
FH ..Higher cutoff Frequency of band
FL .. Lower cutoff Frequency of band
Second criteria was set up by Federal Communication Commission (FCC) in 2002. According
to FCC system having more than 20% fractional bandwidth refers to UWB system. FCC unleased
the frequency band from 3.1GHz to 10.6GHz i.e. bandwidth of 7.5GHz with power emission
level of -41.3dBm/MHz for UWB systems.[1]
UWB systems requires extremely low transmission energy less than 1mW, so these systems
are digitally compatible. Because of low power consumption, UWB systems are small in size and
possess nearly all-digital architecture ideal for micro miniaturization into a chipset. The biggest
advantage of UWB systems is that they offer very high data rate (500Mbps) due to large
bandwidth for short range communication (10m).Wideband nature of the UWB signal reduces
time varying amplitude fluctuations. These signals are relatively immune to multipath
cancellation effects because path delay for UWB signals is approximately equal to 1ns that is
greater than pulse duration. UWB systems offer frequency diversity with minimal hardware
modifications that increases the immunity to fading. Such advantages enable a wide range of
applications of UWB to communications, radar, imaging and positioning etc.
2.1.1 UWB applications
UWB systems are being used in following applications.
Desktop and Laptop PCs
-High resolution printers, scanners, storage devices, etc. Connectivity to mobile and
Consumer Electronics devices
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Mobile Devices
-Multimedia files, MP3, games, video,personal connectivity
Consumer Electronics Devices
-Cameras, DVD, PVR, HDTV, personal connectivity.
Positioning, Geolocation, Localization
-High Multipath Environments, Obscured Environments
Communications
- High Multipath Environments, Short Range High Data Rate, Low Probability of
Intercept/ Interference
Radar/Sensor
-MIR (motion detector, range-finder, etc.): Military and Commercial: Asset Protection,
Anti-Terrorist/Law Enforcement Rescue Applications.
Several methods exist to reduce the size and to increase the bandwidth of the UWB microstrip
patch antennas but mainly four types of UWB antennas are investigated for this purpose and
those are dipole antenna, monopole antenna, fractal antenna, Vivaldi antenna. Among them
UWB fractal antennas are suitable candidates due to their small size, multiband and wideband
operation at wide range of microwave frequency
2.2 Fractal
According to Webster's Dictionary a fractal is defined as being "Derived from the Latin
' fractus' meaning broken, uneven. The term fractal was originally coined by Mandelbrot to describe
a family of complex shapes that possess self-similarity or self-affinity in their geometrical structure.
Mandelbrot offered the following definition: A fractal is a shape made of parts similar to the
whole in some way. According to the Mandelbrot, fractal can be defined by traditional
geometrical or statistical geometry that possess self-similarity property. Self-similarity means each
part of the shape is a smaller version of the whole shape.
Another property of fractal is space filling that means the size of fractal structure becomes
large in the same area as the number of iterations increase. Because of this property fractal
geometries have been applied to antenna design to make multiband and broadband operational
antenna.[2]-[3]
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2.2.1 Fractal in Nature
Any of various extremely irregular curves or shapes that repeat themselves at any scale on
which they are examined can be considered as a fractal. Fractals permeate our lives, appearing in
places as tiny as the membrane of a cell and as majestic as the solar system. Fractals are the
unique, irregular patterns left behind by the unpredictable movements of the chaotic world at
work. In universe, everything existent is a fractal for example:
The leaves in trees,
The veins in a hand,
Waters swirling and twisting out of a tap,
A puffy cumulus cloud,
Tiny oxygen molecule, or the DNA molecule,[33]
Figure.2.1 Examples of fractals that can be found in nature.[33]
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2.2.2 Fractal Antenna
Fractals are used as an antenna elements due to having following property.
Fractals as Space-filling Geometries
Space-filling properties lead to curves that are electrically very long, but fit into a compact
physical space and can lead to the miniaturization of antenna elements.
Fractals as Miniaturized
A fractal can fill the space occupied by the antenna in a more effective manner than the
traditional Euclidean antenna. This leads to more effective coupling of energy from feeding
transmission lines to free space in less volume.
Fractals as Multiband
Fractal antenna represents a class of electromagnetic radiators where the overall structure is
comprised of a series of repetition of a single geometry and where repetition is at different
scale. In order to enable more operating bands within lower spectrum, a higher scaling factor
is required.[33]
2.2.3 Fractal Antenna Geometries
Iterated function system (IFS) is the general method to describe the fractal structure, it creates
a series of self-affine on the basis of transformation W, the W can be formulated as:
f
e
y
x
dc
ba
y
xW (2.1)
Where the a, b, c, d, e and f are real numbers. The a, b, c and d control the rotation and scale
transformation; the e and f control of linear shift. Assume w1, w2wn are a series of linear affine
transformation and the A represents the initial graph. By application transform of A, it can be
expressed as follow:
AwAWN
n
n1
(2.2)
The W is called Hutchinson operator. Using the W fractal geometry is formed. Iterated function
system fractal is a powerful tool in antenna design. It provides a description, classification and
operation of the general method of fractal. There are many fractal geometries those have been
discovered and investigated to be useful in developing new and innovative designs for antennas.
Some of unique geometries are being discussed below.[12]
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2.2.3.a Sierpinski Carpet Geometry
Sierpinski Carpet fractal antenna is realized by successive iterations applied on a simple
square patch as shown in Figure2.2 (a), which can be termed as the zeroth order iteration. A
square of dimension equal to one third of the main patch is subtracted from the center of the
patch to retrieve first order iteration, as shown in Figure 2.2(b). The next step is to etch squares
which are nine times and twenty seven times smaller than the main patch as demonstrated in
Fig.2.2 (c) and 2.2 (d) respectively. The second and third order iterations are carried out eight
times and sixty four times respectively on the main patch. [4]-[11]
(a)Zeroth iteration (b) First iteration
(c) Second iteration (d) Forth Iteration Figure 2.2 Four stages in construction of Sierpinski carpet geometry
2.2.3.b Sierpinski Gasket Geometry
Sierpinski gasket geometry is the most widely studied fractal geometry for antenna
applications. Sierpinski gaskets have been investigated extensively for monopole and dipole
antenna configurations. An equilateral (gasket) triangle patch antenna may be designed as
shown in Figure 2.3.The process is continuously removed the small inverted triangle in the
center of the original triangle. This process will produce 3k smaller triangle, and the area is (3/4)k
, where k is the number of iterations. The side length of the triangle of each level is half of the
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IIT (BHU) Varanasi Page 25
side length of the top grade triangle. The iterated function system is as follows: [12]-[13]
yxyxyxyx ,,,, 321 (2.3)
Where,
yxyx
2
1,
2
1,1
4
3
2
1,
4
1
2
1,2 yxyx
4
3
2
1,
4
1
2
1,3 yxyx
Figure 2.3 Sierpinski gasket for zeroth, first, second iterations
2.2.3.c Nested type triangular fractal Geometry
Nested type triangular fractal antenna consists of different isosceles triangles with
different open angular size and different height and common vertex as shown in Figure 2.4.
The shaded area is the antenna entity and the vacuum area is empty area. Adopting ideal
conductor infinite floor and discrete port feed, the feed distance is d=1mm.
Figure 2.4 Nested triangle fractal antenna structure
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The number of nested triangles is set n, the corresponding height of the triangle is h1,
h2,...,hn. Due to the nested type triangular fractal antenna contains the triangular elements of
different sizes, and the multi-band reflection coefficient of the results appears. The factors
affected the passband center frequency and bandwidth are the height of the nesting triangle,
the angle value of the same vertices and the number of nested triangles.[12]
2.2.3.d. Hilbert Curves Geometry
Figure2.5 shows the first few iterations of Hilbert curves. It is noticed that each
successive stage consists of four copies of the previous, connected with additional line
segments. This geometry is a space-filling curve, which is trying to fill the occupied area with
a larger iteration. The sum S of all the line segments is given by (2.4).
S = (22n -1) d = (2n +1) L (2.4)
12
n
Ld (2.5)
Here L is the side dimension of the Hilbert-curve, d is the length of each line segment,
and n indicates the order of iteration. [14]-[16]
Initiator n=0
n=1
n=2
n=3
Figure 2.5 Four stages in construction of Hilbert curves
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2.2.3.e. Circular Fractal Geometries
First, a circular metallic patch is designed, as shown in figure 2.6(a). Then a point star
shaped fractal geometry with some sharpness factor and dimension is subtracted from circular
patch, as shown in Figure 2.6(b), to create first fractal iteration. Proper care has been taken to
maintain electrical connectivity throughout the circular boundary. Such four electrically
interactive iterations are included in the antenna geometry to design the final fractal geometry
as shown in Figure 2.6(e). The design expression of simple circular microstrip antenna for
calculating the resonant frequency is given below,
effeff
or
r
vf
2
841.1 (2.6)
Where, vo is the velocity of light. The effective radius reff can be calculated by following
expression.
reff = ro[1+2h/r0r{ln(r0 /2h)+(1.41 r +1.77) +h/ r0 (0.268 r +1.65)]1/2 (2.7)
Where, h is thickness of substrate, r is dielectric constant of substrate and r0 is actual radius
of circular patch.[17]-[23]
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2.6 Different iterations of Circular microstrip patch fractal antenna
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2.2.3.f. Giusepe Peano Fractal Geometry
In 1890, Giuseppe Peano introduced a fractal function for space filling property of a
structure known as Giuseppe Peano fractal geometry. This concept of Giuseppe Peano fractal
structure has been introduced in antenna engineering for miniaturization purpose. The recursive
procedure of the Giusepe Peano fractal is shown in Figure 2.7, which is applied to the edges
of the square patch up to the second iteration as depicted in Figure 2.8. [9]-[10]
Figure 2.7 Initiator and generator of the Giusepe Peano fractal Geometry
Figure 2.8 zeroth, first, second iterations of Giusepe Peano fractal geometry
2.2.3.g. Koch Curve Fractal Geometry
The geometric construction of the standard Koch curve is fairly simple. It starts with a
straight line as an initiator as shown in Figure 2.10. This is partitioned in to four equal parts, and
the two centric segments are replaced with four others of the same length with the indentation
angle = 60o or 90o. This is the first iterated version of the geometry and is called the generator.
The process is reused in the generation of higher iterations.
At each new iteration n, the curve of each Koch island increases, as a result of which
the area of the slot also increases as shown in Figure 2.9. Let An be the area of the slot at
iteration n, then the area of the next iteration can be computed as (2.8):
2
1
1223
2
8
3aAA
n
nn
(2.8)
aaln
n 2222
3 (2.9)
Where a is the side of the initial square slot that has an area A0 = a2, the overall
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perimeter for iteration n is given by (2.9).
n=0
n=1
n=2
n=3
Figure 2.9 Geometry of the square slot and Koch fractals for four iterations with =90o
Figure 2.10 Step of construction of Koch curves geometries with = 60o
Each segment in the first iteration (generator) is the length of the initiator. There are
six such segments. Thus for nth iteration, length of the curve is (6/4)n.
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The transformations to achieve the segments of the generator with = 60o are:
100
04
10
004
1
1W
100
060cos4
160sin
4
1
4
160sin
4
160cos
4
1
00
00
2W
100
60sin4
160cos
4
160sin
4
1
8
360sin
4
160cos
4
1
000
00
3W
100
060cos4
160sin
4
1
2
160sin
4
160cos
4
1
00
00
4W
100
60sin4
160cos
4
160sin
4
1
8
560sin
4
160cos
4
1
000
00
5W
100
04
10
4
30
4
1
6W
The generator is then achieved as:
AWAWAWAWAWAWAW 654321 (2.10)
This process can be repeated for higher iterations of this fractal geometry. Also, the similarity
dimension of this geometry can be calculated as: [24]-[27]
29248.18log
6logD (2.11)
2.2.3.h. Pythagorean Tree Fractal Geometry
Unmodified Pythagoras tree fractal (UPTF) was invented by the Dutch mathematician
Albert E. Bosman, in 1942.The Pythagoras tree is a 2-D fractal constructed from squares. It is
named after the ancient Greek mathematician Pythagoras because each triple of touching squares
encloses a right triangle based on configuration traditionally used to depict the Pythagorean
Theorem. If the largest square has a size of LL, the entire Pythagoras tree fits snugly inside a
box of size 6L 4L. The construction of the Pythagoras tree begins with a square. Two other
squares are constructed upon this square, each scaled down by a linear factor of (1/2)2 such that
the corners of the squares coincide pairwise. The same procedure is then applied recursively to
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the two smaller squares, this process is repeated upto infinity as shown in Figure 2.11. Iteration
n adds 2n squares of size ((1/2)2)n in the construction, for a total area of 1. Thus, the area of
the tree fractal might seem to grow without boundary n .[28] Figure 2.12 shows an
illustration of the first five iterations in the construction process of fractal antenna based on
Pythagorean fractal geometry.
Order 0 Order 1 Order 2 Order 3
Figure 2.11 Illustration of the first four iterations for Pythagorean tree fractal
(a) n=0 (b) n=1 (c)n=2 (d) n=3 (e) n=4
Figure 2.12 fabricated first five iterations for Pythagorean tree fractal monopole antenna
2.3.2.i. Tree Shaped Fractal Geometry
Basic structure for tree shaped fractal geometry is simple rectangular patch antenna.
Then rectangular initiator is scaled down and repeated up to second iteration. All three
iterations were connected to achieve the final tree shaped fractal antenna as show in Figure
2.13. [29]-[30]
(a) Zeroth Iteration (b) First iteration (c) Second iteration
Figure 2.13 Illustration of first three iterations of tree shaped fractal geometry
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2.2.3.j. Fractal Binary tree Geometry
A binary fractal tree is defined recursively by symmetrical binary branching. Here, the
approach taken for the generation of trees is somewhat different from conventional fractal
shapes. One starts with a stem and allows one of its ends to branch off in two directions. In
the next stage of iteration, each of these branches is allowed to branch out again, and this
process can be continued infinitely as shown in Figure 2.14. Figure 2.15 shows 3rd iterated
fractal binary tree with different branching angles.[31]-[32]
Figure 2.14 Various iterations of fractal Binary tree.
Figure 2.15 3rd iterated fractal Binary tree with different branching angles.
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2.2.4 General Applications of Fractal
2.2.4.a. Astronomy
Fractals will may be revolutionize the way that the universe is seen. Cosmologists
usually assume that matter is spread uniformly across space. But observation shows that this is
not true. Astronomers agree with that assumption on "small" scales, but most of them