Planar Fractal Antennas for UWB Apllications

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: [email protected]

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)


IIT (BHU), Varanasi


Indian Institute of Technology

(Banaras Hindu University)

Varanasi 221005, INDIA

Phone: 0542-2307010 Fax: 0542-2366758 E-mail: [email protected]

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

v

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

Chapter-1

IIT (BHU) Varanasi Page 1

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

Chapter-1


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

Chapter-1


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-

Chapter-1


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].

Chapter-1


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

Chapter-1


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

Chapter-1


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]

Chapter-1


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

Chapter-1


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]

Chapter-1


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

Chapter-1


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

Chapter-1


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

Chapter-1


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.

Chapter-1


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Chapter-1


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[14] R.Kumar, Y.B.Thakre and M.Bhattacharya, "Novel Design of Star Shaped Circular Microstrip

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[15] A.Azari and J.Rowhani, "Ultra Wide Band Fractal Microstrip Antenna Design", IEEE

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[16] A.Ramadan and K.Y.Kabalan, "Compact Sierpinski Carpet Based Patch Antenna for UWB

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[17] A.Ramadan, K.Y.Kabalan and M.A.Husseini, "Design Using FEM and MoM of an Ultra-

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National Radio Science Conference, New Cairo, Egypt, pp.1-6, 2009.

[18] M.A.Husseini and A.Ramadan, "Design of a Compact and Low-Cost Fractal-Based UWB

PCB Antenna", In Proceedings of 26th National Radio Science Conference, New Cairo, Egypt,

pp.1-8, 2009.

[19] R.Kumar and A.Tiwari, "Design of Appollian Like Gasket Fractal Antenna with CPW-Fed",

Microwave and Optical Technology Letters, Vol. 51, No. 12, pp.2836-2839, 2009.

[20] A.Azari, "Super Wideband Fractal Antenna Design", In Proceedings of 3rd IEEE

International Symposium on Microwave, Antenna, Propagation and EMC Technologies for

Wireless Communications, Beijing, pp.242-245, Oct. 2009.

[21] A.Falahati and M.N.Jahromi, "Dual Band Notch CPW Ground Fed UWB Antenna by

Fractal Binary Tree Slot", In Proceedings of Fifth IEEE International Conference on Wireless

and Mobile Communications, Cannes, La Bocca, pp.385 - 390, 2009.

[22] S.S.Lee and J.N.Lee, "The Design of Fractal Antenna for UWB Applications", IEEE

International Symposium on Antennas and Propagation, Bangkok, Thailand pp.492-49, 2009.

[23] A.Azari, "A New Ultra Wideband Fractal Antenna", In Proceedings of URSI International

Symposium in Electromagnetic Theory, Berlin, pp. 424-427, 2010.

[24] J.Rahani and A.Azari, Koch Fractal Antenna for UWB Applications", In Proceedings of

IEEE Progress in Electromagnetic Research Symposium, Cambridge, USA, pp. 889-891,

2010.

[25] Y.B.Thakare and R.Kumar, "Design of Fractal Patch Antenna for Size and Radar Cross-

Section Reduction", IEEE IET Microwave, Antennas & Propagation, Vol. 4, No.2, pp.175

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Chapter-1


[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

No.2, pp.89-93, March 2010.

[27] R.Kumar and K.K.Sawant, "Design of CPW -Fed Fourth Iterative UWB Fractal Antenna",

International Journal of Microwave and Optical Technology, Vol.5, No.6, 2010.

[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

Geometry", In Proceedings of ITU-T Kaleidoscope Academic Conference, Pune, pp.1-5, 2010.

[30] D.Soren, R.K.Mishra, R.Ghatak and D.R.Poddar, "A Monopole Type Sierpinski Carpet

Fractal Patterned Rectangular Dielectric Resonator Antenna for UWB Application", IEEE

Indian Antenna Week (IAW), Kolkata, pp.1-5, 2011.

[31] A.Karmakar, R.Ghatak and D.R.Poddar, "Dual Band Notched Fractal Ultra-Wideband

Antenna", IEEE Indian Antenna Week (IAW), Kolkata, pp.1-5, 2011.

[32] A.Karmakar,P. Chakraborty, R.Ghatak and D.R.Poddar, "Compact UWB Antenna With Open

Ended Quarter Wave Length Slot For Notch Characteristic", In Proceedings of Annual IEEE

India Conference (INDICON), Hyderabad, pp.1-4, 2011.

[33] R.Ghatak, A.Karmakar and D.R.Poddar, "A Circular Shaped Sierpinski Carpet Fractal UWB

Monopole Antenna with Band Rejection Capability", Progress In Electromagnetics Research

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[34] A.Azari, "A New Fractal Antenna for Ultra Wide- And Multi-Band Applications", In

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[37] R.Kumar and S.Hake, "Design of Modified Ground Square-Shaped Fractal Antenna for UWB

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Chapter-1


[39] R.Kumar and P.N.Chaubey, "On the Design of CPW-Fed Pentagonal-Cut UWB Fractal

Antenna, International Journal of Microwave and Optical Technology, Vol.6, No.5 pp. 249-

254, 2011.

[40] R.Kumar and P.N.Chaubey, "On The Design of CPW-Fed Pentagonal-Cut UWB Fractal

Antenna, Microwave and Optical Technology Letters, Vol.53, No.12, pp.2828-2830, 2011.

[41] R.Kumar, D.Magar and K.K.Sawant, "On The Design of Inscribed Triangle Circular Fractal

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Communications(AEU), Vol.66, No.1 pp.68-75, 2011.

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No.5, pp.1150-1153, 2011.

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Band, Miniaturized Monopole Antenna Design for UWB Wireless Applications",

In Proceedings of IEEE-APS Topical Conference on Antennas and Propagation in Wireless

Communications (APWC), Torino, pp.584-587, 2011.

[44] L.Ghanbari, S.Nikmehr and M.Rezvani, "A Novel Small UWB Antenna Using New Fractal-

like Geometry", In Proceedings of IEEE Applied Electromagnetics Conference (AEMC),

Kolkata, pp.1-4, 2011.

[45] Y.S.Li, X.D.Yang, C.Y.Liu, and T.Jiang, "Analysis and Investigation of a Cantor Set Fractal

UWB Antenna with a Notch-Band Characteristic", Progress in Electromagnetics Research B,

Vol. 33, pp. 99-114, 2011.

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[47] J.Pourahmadazar, C.Ghobadi, and J.Nourinia, "Novel Modified Pythagorean Tree Fractal

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Letters, Vol. 10, pp. 484-487, 2011.

[48] Y.Li, W.Li, C.Liu and T.Jiang, "Cantor Set Fractal Antennas for Switchable Ultra Wideband

Communication Applications", In Proceedings of IEEE International Conference on

Microwave and Millimeter Wave Technology (ICMMT), Shenzhen, Vol.3, pp.1-4, 2012.

[49] Y.Li, W.Li, C.Liu and T.Jiang, A Printed Diversity Cantor Set Fractal antenna for Ultra

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Symposium on Antennas, Propagation & EM Theory (ISAPE), Xian, pp.34-38, 2012.

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12, pp.1366-1373, 2012.

Chapter-1


[51] K.K.Sawant, R.Kumar and A.N.Gaikwad, "A Novel CPW-Fed Circular Square-Corner

Fractal Antenna With Varying Notch-Band For UWB Applications", In Proceedings of IEEE

International Conference on Communication, Information & Computing Technology

(ICCICT), Mumbai, pp.1-6, 2012.

[52] R.Ghatak, A.Karmakar, B.Biswas and D.R.Poddar, "Inscribed Gasket Fractal Circular

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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

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(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


[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

Chapter-2


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

Chapter-2


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]

Chapter-2


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]

Chapter-2


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]

Chapter-2


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

Chapter-2


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

Chapter-2


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

Chapter-2


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

Chapter-2


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

Chapter-2


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.

Chapter-2


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

Chapter-2


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

Chapter-2


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.

Chapter-2


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

Planar Fractal Antennas for UWB Apllications

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