design and analysis of hexagonal shaped fractal Antennas

design and analysis of hexagonal shaped fractal Antennas
design and analysis of hexagonal shaped
fractal Antennas
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE
REQUIREMENT FOR THE DEGREE OF
MASTER OF TECHNOLGY
IN
COMMUNICATION AND SIGNAL PROCESSING
BY
SONU AGRAWAL
Roll. No. - 211EC4113
Department of Electronics and Communication Engineering
National Institute of Technology
Rourkela-769 008, India
2013
design and analysis of hexagonal shaped
fractal Antennas
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE
REQUIREMENT FOR THE DEGREE OF
MASTER OF TECHNOLGY
IN
COMMUNICATION AND SIGNAL PROCESSING
BY
SONU AGRAWAL
Roll. No. - 211EC4113
UNDER THE GUIDANCE OF
Prof. Santanu Kumar Behera
Department of Electronics and Communication Engineering
National Institute of Technology
Rourkela-769 008, India
2013
ACKNOWLEDGEMENT
It is my pleasure and privilege to thank many individuals who made this report possible. First
and foremost I offer my sincere gratitude towards my supervisor, Prof. Santanu Kumar
Behera, who has guided me through this work with his patience. A gentleman personified, in
true form and spirit, I consider it to be my good fortune to have been associated with him. I
thank Prof. Sukadev Meher, Head, Dept. of Electronics & Communication, NIT Rourkela,
for his constant support during the whole semester.
I would also like to thank all PhD scholars, especially to Mr. Ravi Dutt Gupta, and all
colleagues in the microwave laboratory to provide me their regular suggestions and
encouragements during the whole work.
Heartily thanks to Mr. Dayanand Singh, Scientist/Engineer-'SD', Mr. Venkata Sitaraman
Puram, Scientist/Engineer-'SC' and Ms. Sandhya Reddy B, Scientist/Engineer-'SC',
Communication System Group, ISRO Satellite Centre- Bangalore, India for providing
measurement facilities in their Laboratory.
Several people have impacted my career positively. I would also like to thank many of my
friends, especially Bijay, Mohit, Suyog, Ankit, Karthik and Ravi for their constant support
and inspiration in my quest for higher learning. It is a great pleasure to place on record my
gratitude towards all of them.
At last but not the least I am in debt to My Family to support me regularly during my hard
times.
Sonu Agrawal
Department of Electronics & Communication Engineering
National Institute of Technology Rourkela
CERTIFICATE
This is to certify that the thesis entitled, “Design and Analysis of Hexagonal Shaped
Fractal Antennas” submitted by Mr. Sonu Agrawal in partial fulfilment of the
requirements for the award of Master of Technology Degree in Electronics and
Communication Engineering with specialization in “Communication and Signal
Processing” during session 2011-13 at the National Institute of Technology, Rourkela
(Deemed University) is an authentic work carried out by him under my supervision and
guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to any
other University/Institute for the award of any degree or diploma.
Prof. S K Behera
Contents
Abstract
IV
List of figures
V
List of Tables
VII
1. Thesis Overview
1
1.1
Introduction
2
1.2
Thesis Motivation
6
1.3
Literature Review and Methodology
7
1.4
Thesis Outline
8
2. Microstrip Antenna
10
2.1 Microstrip Antenna (MSA)
11
2.1.1
Feeding Methods
13
2.1.2
Structural Analysis of MSA
18
2.1.2.1
18
2.1.3
Fringing Effects
Advantages and Disadvantages of MSA
21
2.1.3.1
Advantages
21
2.1.3.2
Disadvantages
22
2.2 Introduction – Finite Element Method
23
2.2.1
Finite Element Discretization
26
2.2.2
Element Governing Equations
27
2.3 Summary
30
3. Fractal Antenna
32
3.1 Introduction
3.1.1
33
Features of Fractal
I
34
3.1.2
Classes of Fractals
36
3.1.3
Fractal Dimensions
40
3.1.3.1
41
Similarity Dimension
3.1.4
Iterative Function System
42
3.1.5
Advantages and Disadvantages of using Fractals
43
3.1.5.1
Advantages
43
3.1.5.2
Disadvantages
44
3.2 Summary
44
4. Wideband Antenna Design
45
4.1
Introduction
46
4.2
Antenna Design
47
4.3
Anechoic Chamber
50
4.4
Simulated and Measured Results
52
4.5
Summary
58
5. Narrowband Antenna Design
59
5.1
Introduction
60
5.2
Design Parameters and Simulation Results
62
5.3
5.2.1
Antenna1: Design Parameters
62
5.2.2
Antenna1: Simulation Results
63
5.2.3
Antenna2: Design Parameters
65
5.2.4
Antenna2: Simulation Results
67
Measured Results
68
5.3.1
Return Loss
68
5.3.2
Radiation Patterns
70
II
5.4
Summary
72
6. Conclusion and Future Work
73
6.1
Conclusions
74
6.2
Suggestions for Future Work
75
Publications
76
References
77
III
ABSTRACT
In this report three antenna designs using fractals have been proposed. Fractal is a concept
which is being implemented in microstrip antenna to have better characteristics than
conventional microstrip antenna. In the first design, a hexagonal shaped monopole fractal
antenna for wideband application is designed. The proposed fractal-like geometry is
implemented on a microstrip fed planar hexagonal monopole antenna. The iterated hexagonal
fractal patch and modified ground plane are employed to achieve the desired wideband
characteristics. A notch is also achieved by introducing slits in ground plane.
In the second proposal, a new hexagonal shaped patch with modified hexagonal carpet
ground plane antenna for multiband application is proposed. Its structure is based on carpet
fractal geometry introduced in ground plane. The resonance frequency of a conventional
hexagonal patch with full ground is lowered by removing carpet of hexagonal elements from
the full ground plane. The antenna is optimized for a dual band operation.
The last antenna is the smallest of all the three antennas obtained by taking a hexagonal patch
of 8mm side on a fractal ground plane and whole dimension of 30x30mm 2. Firstly, full
ground plane is taken and studied. Then ground plane is modified by introducing and etching
out Symmetrical Vertical Pyramidal Structure (SVPS).
All antennas are simulated using CST Microwave Studio Suite 12. For all designs, low cost
and readily available FR-4 substrate of relative permittivity of 4.4 and height 1.6mm has been
used and fed with 50-ohm microstrip line. All antennas are measured to validate the
simulated results. The measured antenna parameters such as return loss, radiation patterns
and gain of the proposed antennas are found well matched to the simulated results.
IV
List of Figures
2.1
MSA configurations with its side view
12
2.2
Different shapes of microstrip patches
13
2.3
Microstrip line feed
14
2.4
Equivalent circuit of microstrip feed line
14
2.5
Coaxial line feed
14
2.6
Equivalent circuit of coax feed line
15
2.7
Aperture coupled feed
16
2.8
Equivalent circuit of aperture coupled feed
16
2.9
Proximity coupled feed
17
2.10
Equivalent circuit of proximity coupled feed
17
2.11
Microstrip line
18
2.12
Microstrip E-field lines and its effective dielectric constant
19
2.13
Typical finite elements: (a)-(c) Two-dimensional, (d) Three-dimensional
25
2.14
(a) Solution Region (b) Finite Element Discretization
26
2.15
Triangular element with node numbering anti-clockwise
29
3.1
Sierpinski Gasket with subsequent stages showing Initiator and generator
34
3.2
Classes of fractals
37
3.3.
Different fractal geometries (a) Koch curve, (b) Minkowski Loop,
(c) Sierpinski Gasket, (d) Fractal loop, (e) Cantor set and
(f) Hilbert Curve
39
4.1.
Geometry of the generator, 1st iteration and 2nd iteration
48
4.2.
The generator with simple ground plane
48
4.3.
The presented antenna with modified ground plane
49
4.4.
Fabricated Antenna Image (a) Radiating Patch (b) Ground Plane
50
V
4.5.
Anechoic Chamber Operation flowchart
51
4.6.
Return loss vs. level of iterations with simple ground plane
52
4.7.
Return loss variation in 2nd iteration with slot in simple ground plane
53
4.8.
Return loss variation with different lengths of slot
53
4.9.
Variation in notched band with length of slit
55
4.10. Measured vs. Simulated Return-Loss Characteristics
55
4.11. Measured Co-pol and Cross-pol field at (a) 4.6GHz
(b) 5.6GHz (c) 6.8GHz
57
4.12. Simulated gain of the proposed antenna
57
5.1.
Geometry of the radiating element of Antenna1
62
5.2.
The ground plane with removed hexagonal carpet
63
5.3.
The ground plane (at x=0) of dual band antenna
63
5.4.
Return loss variation with full and modified ground plane
64
5.5.
Return loss variation with gap(x)
64
5.6.
Return loss of final antenna at x=0
65
5.7.
Geometry of radiating patch of Antenna2
66
5.8.
Ground plane geometry of Antenna2
66
5.9.
Return loss variation with full and modified ground plane
67
5.10. Return loss variation with iteration in ground plane
67
5.11. Fabricated Antenna1 (a) Radiating Patch (b) Ground Plane
69
5.12. Measured vs. Simulated Return loss of Antenna1
69
5.13. Fabricated Antenna2 (a) Radiating Patch (b) Ground Plane
69
5.14. Measured vs. Simulated Return loss of Antenna2
70
5.13. Measured Normalised Radiation patterns of antennas, (a) & (b) for
Antenna1 and (c) for Antenna2, co-polarization (continuous-line), Crosspolarization (dash-line)
72
VI
List of Tables
1.1
Wireless communication system frequencies
5
3.1
Features of fractal antennas
35
3.2
Fractal vs. Euclidean geometry
36
4.1
Dimension of the presented antenna (in mm)
49
5.1
Antenna1 Characteristics
65
VII
CHAPTER 1
THESIS OVERVIEW
1
THESIS OVERVIEW
1.1
Introduction
Wireless communication is one of the most blooming areas in the communication field today.
It means the transfer of information between two or more points that are not connected by an
electrical conductor. Wireless operations allow facilities, such as distant communications,
that are tough or impractical to implement with the use of wires and it is costly too. In
numerous homes and offices, the mobile phones free us from the short leash of handheld
cords. Cell phones give us even more freedom such that we can communicate with each other
at any time and in any place. Wireless local area network (WLAN) technology provides us
access to the internet without suffering from managing yards of unsightly and expensive
cable. Information is transferred over both short and long distances. These wireless phones
use radio waves to enable their users to make phone calls from many locations worldwide.
Since 1960s, it has been a topic of study but the past decade has seen a downpour of
research activities in the area. This is due to a union of several factors. To start with, an
explosive increase in demand for tetherless connectivity is one of the major factors which are
driven so far mainly by cellular telephony. Second, the dramatic progress in VLSI technology
has enabled small-area and low-power implementation of sophisticated signal processing
algorithms and coding techniques. Also the need of compact and handy communication
systems is also one of prime reason behind this.
The maximum achievable data rate or capacity for the ideal band-limited additive
white Gaussian noise (AWGN) channel is related to the bandwidth and signal-to-noise ratio
(SNR) by Shannon-Nyquist criterion [1, 2], as shown in Eq. 1.1.
C = B log2 (1 + SNR)
2
(1.1)
where C denotes the channel capacity, B stands for the channel bandwidth.
Eq. 1.1 indicates that the total channel capacity can be increased by increasing the
bandwidth occupied by the signal or by increasing the transmission power of the signal.
However, the transmission power cannot be readily increased because many portable devices
are battery powered and the potential interference should also be avoided. Thus, to achieve
high data rate, a wide frequency bandwidth will be the only solution.
In 2002, Federal Communication Commission (FCC) allocated the bandwidth 3.l10.6GHz for commercial use and named it as UWB frequency band. The frequency band of
operation is based on the –10dB bandwidth of the UWB emission. Wireless communications
permits UWB technology to overlay already available services such as the Wi-MAX and the
IEEE 802.11 WLANs that coexist in the 3.1 to 10.6GHz. According to the FCC's rule, any
signal that occupies at least 500MHz spectrum or whose fractional bandwidth is greater than
0.25 can be used in UWB systems. It means that UWB is not restricted to impulse radio any
more. It is also applicable to all the technology that uses 500MHz spectrum and complies
with all other requirements for UWB [3]. The fractional bandwidth ‘B’ is given by the
formula
B=
where,
(1.2)
and f1 are upper and lower edge frequencies respectively whereas fc is central
frequency.
UWB technology offers noteworthy benefits for consumers, public safety, and
Government aided services. It is believed that the greatest potential use of UWB is in shortrange communications in the home or business, allowing equipment mobility and high data
rates to facilitate information sharing. UWB radio will supply the essential new wireless
bandwidth cheaply, without using any precious and limited radio frequencies. So it has a
3
significant role to play as an extension or complement to cellular technology in future mobile
systems.
These days, demand of seamless integration of cellular networks such as GSM & 3G
and WLAN & WPAN is increasing which is a strong indicator for the inclusion of high-speed
short range wireless in a broad picture of future wireless networks. The rapid development of
Wireless communication system is bringing about a wave of new wireless devices and
systems to meet the demands of multimedia applications. Cellular phones, wireless local area
networks (WLANs) and wireless personal area networks (WPANs) place several demands on
the small and multi-purpose antennas. Primarily, the antennas need to small dimension, high
gain, wide bandwidth, embedded installation, etc. In particular, the impedance bandwidths,
polarization or axial ratio, radiation patterns and gain are becoming the most important
factors that affect the application of antennas in contemporary and future wireless
communication systems [4].
Table 1.1 shows the operating frequencies of some of the most commonly used
wireless communication systems. The bandwidths vary from 7% to 13% for commercial
mobile communication systems, and reach up to 109% for ultra-wideband communications.
The antennas used must have the required performance over the relevant operating frequency
range. Antennas for fixed applications such as cellular base-stations and wireless access
points should have high gain and stable radiation coverage over the operating range.
Antennas for portable devices such as headphones, personal digital assistants (PDAs) and
laptop computers should be embedded, efficient in radiation and omnidirectional in coverage.
Most importantly, the antennas should be well impedance-matched over the operating
frequency range [4].
4
Table 1.1 Wireless communication system frequencies.
System
Operating frequency
Advanced Mobile Phone Service
Tx: 824–849MHz
Overall bandwidth
70 MHz (8.1 %)
(AMPS)
Rx: 869–894MHz
Global System for Mobile
Tx: 880–915MHz
80MHz (8.7 %)
Communications (GSM)
Rx: 925–960MHz
Personal Communications
Tx: 1710–1785MHz
170MHz (9.5 %)
Service (PCS)
Rx: 1805–1880MHz
Global System for Mobile
Tx: 1850–1910MHz
Communications (GSM)
Rx: 1930–1990MHz
Wideband Code Division Multiple
Tx: 1920–1980MHz
140MHz (7.3 %)
250MHz (12.2 %)
Access (WCDMA)
Universal Mobile
Rx: 2110–2170MHz
Tx: 1920–1980MHz
250MHz (10.2 %)
Telecommunication Systems
(UMTS)
Rx: 2110–2170MHz
Ultra-wideband (UWB)
3100–10 600MHz
communications and measurement
5
7500MHz (109 %)
1.2
Thesis Motivation
In recent years, modern telecommunication systems require antennas with wider bandwidth
and smaller dimension rather than conventional ones. Most importantly, the antennas should
be well impedance-matched over the operating frequency range. Narrowband operation of
antennas has become a necessity for many applications too. In recent wireless communication
systems, dual band as well as single band behaviour with good gain is the need for many
applications, such as GPS, GSM services operates at two different frequency bands. WLAN,
Wi-Fi systems require single band operation. In this wireless world, integration of many
applications is also required. So it requires same antenna to work for all of the integrated
applications.
Design of conventional microstrip patch with bandwidths as low as a few per cents,
wideband applications are very limited. Other disadvantages include low gain, low power
handling capability, high Q value and poor polarization purity. For over two decades,
researchers have proposed several methods to achieve miniaturization, improvement in
bandwidth in case of wideband behaviour and realizing narrowband characteristics using
planar microstrip antenna. Due to unique advantages such as small volume, low
manufacturing cost and easy integration into planar circuits, planar microstrip antennas are
ideal candidates.
Another method to have compact and small volume antenna is by using fractals in the
planar microstrip antenna geometry. Fractalisation of planar antenna will help in make
antenna more efficient. It will expand the bandwidth and reduce the dimensions of the
antenna [5]. Fractals will increase the total electrical length of the antenna keeping the total
area same. It helps in miniaturization of antenna. Size can be shrunk from two to four times
with surprising good performance. Multiband performance can be achieved at non-harmonic
frequencies.
6
1.3
Literature Review and Methodology
The invention of Microstrip patch antennas has been attributed to several authors, but it was
certainly dates in the 1960s with the first works published by Deschamps, Greig and
Engleman, and Lewin, among others. Since 1970, rigorous research publications came into
picture with the first design equations. Since then different authors started investigations on
Microstrip patch antennas like James Hall and David M. Pozar and many more who
contributed a lot. In high performance aircraft, spacecraft, satellite and missile applications,
where size, weight, cost, performance and ease of integration, low profile antenna are
required. To meet these requirements microstrip antenna can be used. The antennas discussed
earlier are 3-dimensional antennas which are bulky and need more space to be deployed.
MSA are the modern generation of antennas, having attractive features such as light weight,
low cost, small in size and ease of integration into arrays. These boastful features make them
ideal components of modern communications systems, particularly in cellular and WLAN
applications.
The main purpose of this thesis is to design antennas using fractal technique on
microstrip antenna to achieve miniaturization, thereby, achieving wideband as well as
narrowband characteristics using hexagonal structure. Different fractal techniques are
employed to get both the behaviour. Hexagonal gasket is used with partial ground plane to
achieve wideband behaviour whereas narrowband characteristics is realised by doing
employing fractal technique to modify full ground plane keeping same hexagonal patch of
smaller dimension.
Of all the quadrilaterals, hexagon forms the most compact geometry having area
coverage more than other basic shapes like circle and triangle. That is why shape of cell is
hexagonal in cellular network. By taking simple hexagonal patch itself will show good
behaviour. But to get desired characteristics with reduced dimension, some technique must be
7
employed. Therefore it is taken as a base structure for all the designs to realize all the
behaviour.
The term "fractal" was first used by mathematician Benoit Mandelbrot in 1975.
Rumsey, a well-known scientist, established that an antenna with shapes only defined by
angles would be frequency independent, since it would not have any characteristics size to be
scaled with wavelength. He was sometimes referred to as the father of fractal geometry, who
said, “I coined fractal from the Latin adjective fractus”. The word fractal is derived from the
Latin word “fractus” meaning broken, uneven, any of various extremely irregular curves or
shape that repeat themselves at any scale on which they are examined. Using fractal in
an antenna maximizes the length, or increase the perimeter (on any side of structure), of
material that can receive or transmit electromagnetic radiation within a given total surface
area or volume. There are different types of fractals which reveal that as you zoom in on the
image at finer and finer scales, the same pattern re-appears so that it is virtually impossible to
know at which level you are looking.
Fractal is a concept which is being implemented in microstrip antenna to have better
characteristics than microstrip antenna. In many fractal antennas, the self-similarity and
plane-filling nature of fractal geometries are often quantitatively linked to its frequency
characteristics. Fractals are self-similar geometrical shapes which repeat themselves at
different scales. The geometry of fractals is important because the effective length of the
fractal antennas can be increased while keeping the total area same.
1.4 Thesis Outline
The outline of this thesis is as follows.
Chapter 2: This chapter presents the basic theory of MSAs, including the basic microstrip
patch geometries, features, different feeding methods describing their characteristics, the
8
advantages and disadvantages of MSAs. Finally different calculations are shown to calculate
the feedline width and other dimensions of MSA. This chapter ends with the introductory part
of the numerical method, Finite Element Method (FEM), which is helpful to analyse any
complex geometry.
Chapter 3: This chapter deals about fractal geometry. Fractal antenna engineering represents
a relatively new field of research that combines attributes of fractal geometry with antenna
theory. Chapter presents basic theory of fractals describing its features, classes, and
dimensions and explained about Iterative function schemes (IFS). The performance of the
fractal antenna with respect to conventional Euclidean geometry has also been discussed. The
chapter ends by describing the advantages and disadvantages of using fractals in microstrip
antenna.
Chapter 4: This chapter describes the design of wideband antenna using CST Microwave
Studio Suite 12. The simulated and measured results are presented in terms of different
antenna parameters such as return loss, gain, radiation patterns measurements. The effect of
slots and slits in the partial ground plane are shown. Different parametric studies have also
been shown.
Chapter 5: In this chapter the narrowband antenna designs are described. The effect of
different ground planes is discussed. The different properties of antennas are studied and
simulated using CST Microwave Studio Suite 12. Finally comparison between the simulation
and theoretical results are presented..
Chapter 6: This chapter contains conclusion and scope of future work
9
CHAPTER 2
MICROSTRIP ANTENNA
10
MICROSTRIP ANTENNA
This chapter deals with the microstrip antennas which are small in size and much lighter than
the antennas discussed in the previous chapter. Though, the antennas already discussed are
also used, but planar antennas have their own advantages which will be discussed here. The
basic geometries, feeding techniques, features and applications of planar antennas are
illustrated here.
2.1 Microstrip Antenna (MSA)
The idea of microstrip antenna was traced in 1953 [6] and a patent in 1955 [7]. But it
received considerable attention in the start of 1970s. In high performance aircraft, spacecraft,
satellite and missile applications, where size, weight, cost, performance and ease of
integration, low profile antenna are required. To meet these requirements microstrip antenna
can be used [8]. The antennas discussed earlier are 3-dimensional antennas which are bulky
and need more space to be deployed. MSA are the modern generation of antennas having
attractive features as low profile, low cost, light weight and ease of integration into arrays.
These features make them ideal components of modern cellular and WLAN applications [9].
With increasing requirements for personal and hand-held mobile communications, the
demand for compact and low-cost antennas has brought the MSA to the forefront. A MSA in
its simplest form consists of a radiating patch on front side of a dielectric substrate and a
ground plane on the back side. The top and side views of a rectangular MSA (RMSA) are
shown in Fig. 2.1. Often microstrip antennas are also referred to as patch antennas. The
radiating elements and feed lines are usually photoetched on the dilelectric substrate. The
radiating patch may be square, circular, triangular, semi-circular, sectoral, and annular ring
shapes shown in Fig. 2.2.
11
Figure 2.1
MSA configurations with its side view
Also evaluation of the basic properties of microstrip patch antennas (MPA) has been
numerously discussed in literature [10], [11].
There are basically two types of radiator. One is broadside and other is end-fire
radiator. Broadside radiators are those whose maximum pattern is normal to the patch or axis
of the antenna whereas end-fire radiators are those whose maximum is along the axis of the
antenna. The microstrip patch is designed so that its pattern maximum is normal to the patch
i.e. it is generally behaves as broadside radiator. This is accomplished by properly choosing
the mode i.e. field configuration of the excitation beneath the patch. End-fire radiation can
also be possible by judicious mode selection. The strip and ground plane are separated by a
dielectric sheet as shown in Fig. 2.1.
There are several substrates that can be used for the design of microstrip antennas.
The dielectric constants are usually in the range of
12
. Most desirable for good
antenna performance is thick substrates whose dielectric constant is low because they provide
better efficiency, larger bandwidth, loosely bound fields for radiation into space, but it will
cost us in larger element size. Thin substrates with higher dielectric constants are also
Figure 2.2
Different shapes of microstrip patches
used for the microwave circuitry as they require tightly bound fields to minimize undesired
radiation and coupling which lead to smaller element sizes. However, they are less efficient
and have relatively smaller bandwidths on account of greater losses [12].
Since microstrip antennas are often integrated with other microwave circuitry, a
compromise has to be reached between good antenna performance and circuit design [8].
2.1.1 Feeding Methods
There are different feeding methods employed to feed the microstrip antennas. The most
popular techniques are microstrip line, coaxial probe, aperture coupling and proximity
coupling [8].
The microstrip feed line is also called conducting strip, generally of much smaller
width compared to the patch. The microstrip line feed is easy to fabricate and simple to match
13
by controlling the inset position and rather simple to model. However as the substrate
thickness increases surface waves and spurious feed radiation increase, which for practical
Figure 2.3
Figure 2.4
Microstrip line feed
Equivalent circuit of microstrip feed line
Figure 2.5
Coaxial line feed
14
Figure 2.6
Equivalent circuit of coax feed line
designs limit the bandwidth (typically 2-5%). A typical microstrip feed line and its equivalent
circuit are shown in Figs. 2.3 and 2.4, respectively.
Coaxial-line feeds, where the inner conductor of the coax is attached to the radiation
patch while the outer conductor is connected to the ground plane, are also widely used. The
coaxial probe feed is also easy to fabricate and match, and it has low spurious radiation.
However, it also has narrow bandwidth and it is more difficult to model, especially for thick
substrates. A typical coax feed and its equivalent circuit are also shown in Figs. 2.5 and 2.6,
respectively, where inner conductor is attached to the patch and outer to the ground plane.
Both the microstrip line and probe possess inherent asymmetries which generate
higher order modes which produce cross-polarized radiation. To overcome some of the
problems, non-contacting aperture coupling feeds have been introduced. The aperture
coupling is most difficult to fabricate. However, it is somewhat easier to model and has
moderate spurious radiation.
As shown in Fig. 2.7, aperture coupling consists of two substrates separated by a
ground plane. On the bottom side of the lower substrate, there is a microstrip feed line whose
energy is coupled to patch through a slot on the ground plane separating the two substrates.
Its equivalent circuit is described by Fig. 2.8. This arrangement allows independent
optimization of the feed mechanism and the radiating element. Typically a high dielectric
material is used for the bottom substrate, and thick low dielectric constant material for the top
15
substrate. The ground plane between the substrates also isolates the feed from the radiating
element and minimizes interferences of the spurious radiation for pattern formation and
polarization purity. For this design, the substrate electrical parameters, feed line width, and
slot size and position can be used to optimize the design. Typically matching is performed by
controlling the width of the feed and the length of the slot.
Figure 2.7
Figure 2.8
Aperture coupled feed
Equivalent circuit of aperture coupled feed
16
The most severe demerit of microstrip antennas is their small bandwidth. As
microstrip antennas are having small bandwidth, so there is need to have some mechanism to
increase its bandwidth. One of the most advantageous methods is by proximity coupling.
There are basically two types of bandwidths, one is impedance bandwidth (the bandwidth
over which the antenna remains matched to the feedline to some specified level, such as
(VSWR
), and the pattern bandwidth (the bandwidth over which the pattern remains, in
some sense, constant). The ideal broadband element will satisfy both the criteria.
Figure 2.9
Figure 2.10
Proximity coupled feed
Equivalent circuit of proximity coupled feed
17
The enhanced bandwidth is obtained by using a microstrip feed line proximity-coupled to a
patch antenna printed on a substrate above the feedline as shown in Fig.2.9 [13].
Its
equivalent circuit is shown in Fig.2.10.
2.1.2
Structural Analysis of MSA
There are different models of MSA. The simplest of all the models is transmission line
model. It is easiest but the disadvantage of using it is it yields less accurate results and it lacks
the versatility. Basically the transmission line model represents the microstrip antenna by two
slots separated by a low-impedance
transmission line of length L, width W and height H,
as shown in Fig.2.11.
Figure 2.11
Microstrip line
2.1.2.1 Fringing Effects
As the dimensions of the patch are finite along the length and width, the fields at the edges of
the patch undergo fringing. This is illustrated in Fig.3.12 for the two radiating slots of the
microstrip antenna. The amount of fringing is a function of the dimensions of the patch and
the height of substrate. For a microstrip line, typical electric field lines are shown in Fig.2.12.
This is a nonhomogenous line of two dielectrics; typically the substrate and air. As it can be
seen from the figure, most of the electric field lines reside in the substrate and parts of some
lines exist in air. As W/H
1 and
1, the electric field lines concentrate mostly on the
18
substrate. Fringing in this case makes the microstrip line look wider electrically compared to
its physical dimensions. Since some of the waves travel in the substrate and some in air, an
effective dielectric constant (EDC)
is introduced to account for fringing and the wave
propagation in the line [8].
For most applications, where the dielectric constant of the substrate is much greater
than unity (
constant
1), the value of
will be closer to the value of the actual dielectric
of the substrate. For a line with air above the substrate, the EDC has the values in
the range of 1
. EDC depends on frequency of operation too. As the operating
frequency increases, most of the electric field lines concentrate in the substrate [8].
Figure 2.12
Microstrip E-field lines and its effective dielectric constant
For low frequencies, EDC is nearly constant. At the intermediate frequencies its
values begin to increase slowly and ultimately approach the values of the dielectric constant
of the substrate. The initial or static value at low frequency of EDC is given by Eq. 2.1. This
value is valid for W/H
.
19
(
)
√
(2.1)
where W is width of feedline and ‘H’ is weight of the substrate.
The characteristics impedance
of the microstrip feed line also depends on the
width W of the feedline and height H of the substrate and it is having different values for
W/H
and W/H
as illustrated in the Eqs.2.2 and 2.3.
√
√
(
);
(2.2)
(
);
(2.3)
The width W of the line and height H of the substrate is decided by parameters A and
B which are dependent on the characterictics impedance of the line and dielectric constant of
the substrate as shown in Eqs.2.4, 2.5, 2.6 and 2.7.
;
(
[
)
(2.4)
{ (
)
}] ;
(2.5)
where
√
and
√
(
;
);
(2.6)
(2.7)
20
For the principal E-plane (xy-plane), fringing is a function of the ratio of the length of
the patch L to the height H of the substrate (L/H) and dielectric constant
For microstrip antenna,
of the substrate.
, so fringing is very less. But fringing must be reduced and
taken into account because it influences the resonant frequency of the antenna.
Generally, the characteristics impedance of the feedline is taken as 50Ω. The reason
behind choosing this are described below:

Practically, all available source ports are having 50Ω internal impedance. So by
Maximum Power Theorem, we have to select 50Ω as the characteristics impedance for
the feedline of the microstrip antenna to transfer maximum power from source to
load.

Theoretically, it has been found that 76Ω is required for minimum attenuation in the
line and 37Ω is needed for maximum power transfer from the line. So to compromise
between these two, we are selecting the average of the above two values and by
rounding off the average value, we will get 50Ω as the characteristics impedance for
the feedline.
2.1.3
Advantages and Disadvantages of MSA
Microstrip Patch antennas are widely used in today’s era. It is used in satellite
communication, military purposes, GPS, mobile, missile systems etc. Bearing in mind the
features of microstrip antenna, there are many advantages and disadvantages as well. Some of
them are discussed below.
2.1.3.1
Advantages
MSAs have several advantages compared to the conventional microwave antennas. The main
advantages of MSAs are listed as follows:
21
·
They are lightweight and have a small volume and a low-profile planar configuration.
·
They can be made conformal to the host surface.
·
Their ease of mass production using printed-circuit technology leads to a low
fabrication cost.
·
They are easier to integrate with other MICs on the same substrate.
·
They allow both linear polarization and circular polarization.
·
They can be made compact for use in personal mobile communication.
·
They allow for multi-frequency operations.
2.1.3.2
Disadvantages
MSAs suffer from some disadvantages as compared to conventional microwave antennas.
They are illustrated as follows:
·
They have narrow impedance bandwidth.
·
They are having low gain.
·
Extra radiation occurs from its feeds and junctions
·
Low power-handling capability
·
Their efficiency is very less.
·
Poor-polarization purity
·
High Q value
The quality factor is a figure-of-merit that is representative of the antenna losses. There are
different types of losses such as radiation, conduction, dielectric and surface wave losses. The
total quality factor Qt is influenced by all of these losses [14] and is, in general, given by Eq.
2.8.
22
(2.8)
where
Qt = total quality factor
Qrad = quality factor due to radiation (space wave) losses
Qc = quality factor due to conduction losses
Qd = quality factor due to dielectric losses
Qsw = quality factor due to surface waves
For very thin substrates, the losses due to surface waves are very small and can be neglected.
However, for thicker substrates they need to be taken into account.
The bandwidth is inversely proportional to the square root of the dielectric constant of
the substrate and Q value is inversely related to bandwidth. Generally, MSAs have narrow
bandwidth (BW), as a result of high Q value, typically 1–5%, which is the major limiting
factor for the widespread application of these antennas. Increasing the height of substrate
increases the BW but doing this will increase the fringing effect in MSAs [8], so this field has
been the major thrust of research, and broad BW up to 70% has been achieved.
2.2
Introduction – FINITE ELEMENT METHOD
Computer Simulation Technology (CST) which is an antenna design simulation tool offers
accurate, efficient computational solutions for electromagnetic design and analysis. It is userfriendly 3D EM simulation software enables us to choose the most appropriate method for the
design and optimization of devices operating in a wide range of frequencies. It is based on
Finite Element Method (FEM). FEM has its origin in the field of structural analysis. It is a
more powerful and adaptable numerical technique for handling programs involving complex
23
geometries. In mathematics, FEM is a numerical technique for finding approximate solutions
to boundary value problems. It uses variational methods (the Calculus of variations) to
decrease an error function and produce a steady solution. As we know that joining many tiny
straight lines can approximate a larger circle, FEM involves all the methods for connecting
many simple element equations over many small subdomains, named finite elements, to
approximate a more complex equation over a larger domain. FEM analysis of any problem
involves basically four steps [15]:

Discretizing the solution region into a finite number of sub-regions or elements.

Deriving governing equations of the typical element.

Assembling of all elements in the solution region.

Solving the system of equations obtained.
Typical steps mentioned above are followed for numerical analysis to analyse and solve any
complex structure. To represent any complex geometry, the geometry is sub-divided into
many small regions called finite elements and equations are obtained for each finite element.
After obtaining all the finite element’s equations, they are recombined to get the global
system of equations for final calculation of whole complex geometry. The global system of
equations has known solution techniques, and can be calculated from the initial values of the
original problem to obtain a numerical answer. The global system of equations has known
solution techniques, and can be calculated from the initial values of the original problem to
obtain a numerical answer. The sectoring of a total domain into smaller domains has several
advantages:

Complex geometry is represented exactly

Different material properties is also included
24

Total solution is easily represented

Internment of local effects
Including these advantages, another advantage of FEM is that it is numerically stable method
i.e. errors in the input and intermediate calculations do not accumulate, which avoids the
resulting output to become meaningless.
(a) Three-node Triangle
(b) Four-node Rectangle
(c) Four-node Trapezium
(d) Eight-node Hexahedron
Figure 2.13 Typical finite elements: (a)-(c) Two-dimensional, (d) Three-dimensional
The different finite elements are represented by different quadrilateral structures, few of them
are shown in Fig. 2.13.
These structures are used to divide solution region into smaller parts having different number
of nodes. In practical situations, however, it is preferred, for ease of computation, to have
elements of same type throughout the region. Also, in view of the fact that quadrilateral
elements do not conform to curved boundary as easily as triangular elements, we prefer to use
triangular elements throughout our analysis. As triangular elements are having minimum
25
number of nodes compared to other quadrilateral, so we prefer triangle than other
quadrilateral to have lesser complexity in calculation of potential at each nodes.
2.2.1 Finite Element Discretization
As an application to FEM to electrostatic problems, let us apply the four steps mentioned is
the process of FEM solution to solve Laplace equation,
.
y
(a) Solution
Region
x
y
7
6
5
8
6
11
5
(b) Finite Element Discretization
9
1
4
7
10
1
2
4
2
3
3
x
Figure 2.14 (a) Solution Region (b) Finite Element Discretization
Fig. 2.14(a) shows a region whose analysis has to be done by FEM. To obtain the potential
distribution V(x, y) for the two-dimensional solution region the solution region is divided into
many smaller sub-regions called finite-elements as shown in Fig. 2.14(b). The solution region
is divided into seven non-overlapping finite elements, one of them is five-node quadrilateral,
some are four-node quadrilaterals and rest are three-node triangles. In practical situations,
elements of same type throughout the region are preferred as it will ease the computation. In
view of the fact that quadrilateral elements do not conform to curved boundary as easily as
26
triangular elements, we prefer to use triangular elements throughout our analysis. So we will
split four-node quadrilateral to two three-node triangles, so we have twelve triangular regions
of the whole solution regions.
To find the potential of whole solution region V(x,y), we will start to find potential of each
node
(
) of each triangular element and then interrelate the potential distribution in
various elements such that the potential is continuous across inter-element boundaries. The
approximate solution for the whole region is [15]
∑
V(x,y)
(
)
(2.9)
where N is the number of triangular elements into which the solution region is divided. The
most common form of approximation for
within an element is polynomial approximation,
namely,
(
)
(2.10)
for triangular element and
(
)
(2.11)
for quadrilateral element. The constants a, b, c and d are to be determined. The potential
in
general is non-zero within element e but zero outside e.
(
)
(2.12)
2.2.2 Element Governing Equations
A typical triangular element is considered. The potentials
,
and
at node 1, 2 and 3,
respectively are obtained in [16] by using Eq. 2.10:
[
]=[
][ ]
27
(2.13)
The coefficients a, b and c are determined by above equation as
[ ]
[
]
(
=[
]
[
]
) (
[ (
(
)
)
)
(
(
∑
(2.14)
(
)
)
(
)
(
(
) ][
)
)
]
(2.15)
where
[(
)
(
)
(
) ],
(2.16a)
[(
)
(
)
(
) ]
(2.16b)
[(
)
(
)
(
) ]
(2.16c)
where A is area of the element
2A = [
=(
]
)
(
)
(
)
or,
A = [(
)(
)
(
)(
)]
(2.17)
If the nodes are numbered counter-clockwise then the value of A is positive as shown in Fig.
2.15.
28
y
Ve3(x3, y3)
3
2
1
Ve2(x2, y2)
Ve1(x1, y1)
x
Figure 2.15 Triangular element with node numbering anti-clockwise
Eq. 2.15 provides the potential at any point (x, y) within the element provided that the
potentials at the vertices are known.
Linear interpolation functions are given by
. They are called the element shape functions
and they have following properties [17]:
{
∑
(2.18a)
(
)
(2.18b)
The functional corresponding to Laplace’s equation is given by
We = ∫
|
|
= ∫
|
|
(2.19)
∑
(2.20)
Substituting Eq. 2.20 into Eq. 2.19 gives
We = ∑
∑
[∫
]
(2.21)
Now we define a term as
( )
∫
(2.22)
29
So Eq. 2.21 can be written in matrix form as
We =
[ ] [
( )
][ ]
(2.23)
where the subscript t denotes the transpose of a matrix,
[
The matrix [
( )
( )
]
[
( )
( )
( )
( )
( )
( )
( )
( )
( )
]
(2.24)
] is called as element coefficient matrix. The element
( )
of the coefficient
matrix is regarded as the coupling between nodes i and j; its value is obtained from Eqs. 2.16
& 2.22.
For example,
( )
[(
=
=
∫
)(
[(
)(
)
)
(
)(
(
)(
)] ∫
)]
(2.25)
Similarly, all the coefficients are obtained.
Also,
( )
2.3
( )
( )
( )
( )
( )
(2.26)
Summary
This chapter has discussed about the characteristics of microstrip antennas. This
chapter has also given insight of small and compact antennas with different feeding
mechanism that is required for wireless applications. The need of 50Ω transmission line has
also been discussed. It has deduced the complete theory behind the design of microstrip
30
antenna with their advantages and disadvantages. The structural analysis by FEM technique
has been briefly explained. A number of equations are analyzed to give insight into the
structural behavior of the microstrip antennas.
31
CHAPTER 3
FRACTAL ANTENNA
32
FRACTAL ANTENNA
3.1
Introduction
Fractal is a concept which is being implemented in microstrip antenna to have better
characteristics than microstrip antenna. The word fractal is derived from the Latin word
“fractus” meaning broken, uneven, any of various extremely irregular curves or shape that
repeat themselves at any scale on which they are examined. Using fractal in an antenna
maximizes the length, or increase the perimeter (on inside sections or the outer structure), of
material that can receive or transmit electromagnetic radiation within a given total surface
area or volume. Rumsey, a well-known scientist, established that an antenna with shapes only
defined by angles would be frequency independent, since it would not have any
characteristics size to be scaled with wavelength. The term "fractal" was first used by
mathematician Benoit Mandelbrot in 1975 [18]. He was sometimes referred to as the father of
fractal geometry, who said, “I coined fractal from the Latin adjective fractus”.
In many fractal antennas, the self-similarity and plane-filling nature of fractal
geometries are often quantitatively linked to its frequency characteristics. Fractals are
geometrical shapes, which are self-similar, repeating themselves at different scales. The
geometry of fractals is important because the effective length of the fractal antennas can be
increased while keeping the total area same. The shape of fractal antenna can be formed by
an iterative mathematical process called, Iterative Function Scheme (IFS) which will be
discussed later in this chapter. There are different types of fractals which reveal that as you
zoom in on the image at finer and finer scales, the same pattern re-appears so that it is
virtually impossible to know at which level you are looking.
33
The geometry of fractals is important because the effective length of the fractal
antenna can be increased while keeping the total area same. Fractal antenna design has two
things:
1) Initiator (0th stage): It is basic shape of the geometry. It can be any shape either
triangle, rectangle or any other quadrilateral.
th
0 stage
st
1 stage
nd
2 stage
Initiator
Figure 3.1
rd
3 stage
4th stage
Generator
Sierpinski Gasket with subsequent stages showing initiator and generator
2) Generator: It is the shape which is obtained by scaling the initiator and will be
repeated either inside or outside on the initiator to obtain subsequent stages to reach final
fractal geometry. Generator is obtained from the initiator itself.
In Fig. 3.1 showing one type of fractal geometry which is named as Sierpinski Gasket
which is derived by taking a triangular geometry as initiator and repeating a down-scaled
version of initiator called generator inside it to obtain subsequent stages of gasket.
3.1.1 Features of Fractal
There are many features of fractal antenna which make them useful for many applications.
Some of them are tabulated in Table 3.1.
34
Table 3.1
Features of fractal antennas
Self-Similarity
Useful in designing multi-band antenna.
Small Dimension
Useful to design electrically small antennas.
Space-Filling Ability
Useful for miniaturization of an antenna by increasing the electrical
length into a compact physical volume.
Increasing number of
Useful to decrease the resonant frequency while electrical length
Iterations
increases.
Sharp Edges, Corners
Helps to make antenna to radiate efficiently.
and Discontinuities
Other important factors that are differentiating it with microstrip antennas are:

Fractals are having no characteristics shape.

They have infinite range of scales within their structure, being composed of an infinite
number of clusters which are equal to the whole shape but to a smaller scale.

They are highly convoluted and having irregular shapes.

Since characteristic size has to be avoided to design a frequency independent antenna
or at least the antenna structure has to include many characteristics sizes to allow a
multi-wavelength operation and fractal antenna has this property to become a good
candidate for becoming frequency independent.
Fractals are structure of infinite complexity with a self-similar nature. It means that as the
structure is zoomed in upon, the structure repeats itself. This property could be used to design
antennas that can operate at several frequencies.
Fractal can fill the space occupied by the antenna in a more effective manner than the
traditional Euclidean geometry antenna. This can lead to more coupling of energy from
transmission lines to free space in less volume. It has a large number of irregularities, which
results in virtually infinite physical length. At higher frequencies, these antennas are naturally
35
broadband. The basic difference between traditional Euclidean geometry and fractals are
discussed in Table 3.2.
Table 3.2
Fractal vs. Euclidean geometry
Fractal geometry
Euclidean geometry
10-20 years old
years old
Defined by iterative rule
Defined by formula
Structure on many scales
Structure on one or few scales
Dilation or self-similarity property
No self-similarity
Fractional dimension possible
Finite dimension
Long range correlation
Variable correlation
Rough on most scales
Smooth on most scales
3.1.2
Classes of Fractals
There are different classes of fractals described in a flow chart form in Fig. 3.2. There are
basically two classes of it named as Deterministic and Non- Deterministic. Our point of
discussion in this chapter is Deterministic fractals which are again characterized as Linear
and Non-Linear geometry. Linear geometry is derived by using Iterative Function System
(IFS) which is main topic of discussion in this chapter. Under Linear geometry, there are
many curves so-called fractal curves such as Koch curve, Cantor curve, Minkowski curve,
Sierpinski gasket and many more. These are explained one by one below.

Koch curve: It is a good example of self-similar space-filling fractals which have
been used to develop wideband/multiband and/or miniaturized antennas [16]. The
features of the Koch geometry can overcome some of the limitation of small antennas
[20]. The expected benefit of using a fractal as a dipole antenna is to miniaturize the
total height of antenna at resonance. This is achieved by using Koch geometry. It does
36
not have piecewise continuous derivative. It is nowhere differentiable. Its shape is
highly rough and uneven. So works as a very efficient radiator as shown in Fig. 3.3(a).
Classes of Fractals
Not Deterministics
Deterministics
Linear (IFS)
Not Linear
- Fractal Brownian motion
- Diffusion limited
aggregation
- Cantor Curve
- Koch Curve
- Mandelbrot set
- Minkowski Curve
- Strange attractors
- Hilbert Curve
- Bifurcation diagrams
- Sierpinski Gasket
- Julia sets
Figure 3.2

Classes of fractals
Minkowski loop: It can be used to reduce the size of antenna by increasing the
efficiency with which fills up occupied volume with electrical length. It is analysed
where the perimeter is one wavelength. Several iterations are compared with a square
loop antenna to illustrate the benefits of using fractal antenna [21]. It is shown in Fig.
3.3(b). It is interesting to note that Minkowski fractal antennas are not only
broadband, but they also demonstrate multiband effects. This is due to the coupling
between the wires. As more contours and iterations of the fractal are added, the
coupling becomes more complicated and different segments of the wire resonate at
different frequencies. Minkowski island fractals can be used to achieve
37
miniaturization in antenna systems while keeping an identical electromagnetic
performance to the square loop antenna [22].

Sierpinski gasket: It was discovered by Polish mathematician Waclaw Sierpinski in
1916. The Sierpinski sieve of triangles possesses a certain multiband behavior owing
to its self-similar shape as shown in Fig. 3.3(c). A multiband fractal monopole
antenna [23], based on the Sierpinski gasket, was first introduced by Puente et al. [24].
The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows
from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.
The area of a Sierpinski triangle is zero. The area remaining after each iteration is
clearly 3/4 of the area from the previous iteration, and an infinite number of iterations
results in zero [25].

Fractal loops: Loop antennas are well understood and have been studied using a
variety of Euclidean geometry. Fractal loop antennas have shown improved
impedance and SWR performance in a reduced physical area when compared to nonfractal Euclidean geometries [26]. Resonant loop antennas require a large amount of
space and small loops have very low input impedance. A fractal island can be used as
a loop antenna to overcome these drawbacks. It has the property that the perimeter
increases to infinity while maintaining the volume occupied. For small loop this
increase in length improves the input resistance, thereby antenna can be more easily
matched to a feeding transmission line as shown in Fig. 3.3(d).

Cantor Set: The Cantor set is a set of points lying on a single line segment that has a
number of remarkable and deep properties. It was discovered by H. J. S. Smith in
1874 and introduced by German mathematician Georg Cantor in 1883. It is obtained
by taking out the one-third part of a unit length line (line can be of different
38
(a)
(b)
(c)
(d)
(e)
Figure 3.3
(f)
Different fractal geometries (a) Koch curve, (b) Minkowski Loop, (c)
Sierpinski Gasket, (d) Fractal loop, (e) Cantor set and (f) Hilbert Curve
dimensions) at each iterated occasion as described by Fig. 3.3(e). The different wideband
cantor set antenna has been proposed in [27, 28].
39

Hilbert Curve: The space-filling properties lead to curves that are electrically very
long, but fit into a compact physical space. This property leads to miniaturization of
antenna. Hilbert curve is one of the fractal curves which are having this property [29].
Because of this property it has become an attractive candidate for use in the design of
fractal antennas. The first little iteration of Hilbert curves are shown in Fig. 3.3(f). It
may be noticed that each successive stage consists of four copies of the previous,
connected with additional line segments. This geometry is a space-Filling curve, since
with a larger iteration, one may think of it as trying to fill the area it occupies.
Additionally the geometry also has the following properties: Self-Avoidance (as the
line segments do not intersect each other), Simplicity (since the curve can be drawn
with a single stroke of a pen) and Self-Similarity. Because of these properties, these
curves are often called as FASS curves [30]. The space-filling properties of the
Hilbert curve we investigated in [31, 32].
3.1.3
Fractal Dimensions
Generally, we can think of objects that are zero dimensional (0-D) i.e. points, 1-D i.e. lines,
2-D i.e. planes and 3-D i.e. solids. We are known with zero, one, two and three dimensions.
But for fractal antenna, we will talk about fractal dimensions i.e. non-integer dimensions,
such as 2.12D, 1.14D, 3.79D, etc. There are many fractal dimensions; some of them will be
discussed here.
Few of the fractal dimensions are Similarity dimension (DS), the Hausdorff
Dimension (DH), Box-counting dimension (DB), etc. We will mostly concentrate on
similarity dimension (DS), to characterize the construction of regular fractal objects. Fractals
are characterized by their dimension. It is the key structural parameter describing the fractal
and is defined by partitioning the volume where the fractal lies into boxes of side .
40
3.1.3.1
Similarity Dimension
The concept of dimension is closely associated with that of scaling. Consider a line is divided
into N smaller self-similar segments, each ‘’ in length, then  is in the scaling ratio. Thus,
For unit line
L = N = 1
(3.1)
For unit area
A = N = 1
(3.2)
For unit volume
V = N = 1
(3.3)
Therefore we see that the exponent of  in each case is a measure of the dimension of the
object. Thus
N
Therefore
=1
DS =
( )
(3.4)
(3.5)

where DS denotes the similarity dimension.
For Cantor Set, there are two such identical copies of the set contained within the set.
So, N = 2 and  = .
Hence
So, for Cantor Set, 0
DS =
DS
= 0.6309
(3.6)
1, that is it has a non-integer similarity dimension of 0.6309;
due to fractal structure of the object.
41
3.1.4
Iterative Function System
Iterative function schemes (IFS) represent an extremely versatile method for conveniently
generating a wide variety of useful fractal structures. These iterated function systems are
based on the application of a series of affine transformations, w, defined by [23]
w( )=(
)( )+( )
w (x, y) = (
or,
(3.7)
)
(3.8)
where a, b, c, d, e and f are real numbers. Hence, the affine transformations, w, is represented
by six parameters
| )
(
(3.9)
whereby a, b, c, an d control rotation and scaling, while e and f control linear translation [25].
Now suppose we consider
,
, ….,
as a set of affine linear transformations,
and let A be the initial geometry. Then a new geometry, produced by applying the set of
transformations to the original geometry, A, and collecting the results from
( )
( ),
( ), can be represented by
( )
( )
⋃
(3.10)
where W is known as the Hutchinson operator [33, 34].
A fractal geometry can be obtained by repeatedly applying W to the previous geometry. For
example, if the set
represents the initial geometry, then we will have
(
)
(
) ………;
42
(
)
(3.11)
An iterated function system generates a sequence that converges to a final image,
, in such
a way that
(
)
(3.12)
This image is called attractor of the iterated function system, and represents a “fixed point” of
W.
3.1.5
Advantages and Disadvantages of using Fractals
There are countless advantages and some disadvantages as well of using fractals in microstrip
antennas. They are discussed in detail in the subsections below.
3.1.5.1
Advantages
The advantages of using fractals in microstrip antenna are illustrated in here. Some of them
are:

Size can be shrunk from two to four times with surprising good performance.

Multiband performance is at non-harmonic frequencies.

Compressed resonant behaviour.

At higher frequencies the finite element antenna is naturally broadband.

Improved reliability

Reduced construction costs.

Polarisation and phasing of FEA also are possible.

Because FEA are self-loading, no antenna tuning coils or capacitors are necessary.

They do not require any matching components to achieve multiband or broadband
performance.
43
3.1.5.2
Disadvantages
With a number of advantages of using fractals in microstrip antenna, there are some
disadvantages associated with it too. They are as follows:

Low Gain

Too complex geometry

Numerical Limitations

Practically only few iterations are possible to design, after that benefits start to
diminish.
3.2
Summary
This chapter has discussed about fractal geometry. Fractal antenna engineering represents a
relatively new field of research that combines attributes of fractal geometry with antenna
theory. Fractals are space-filling geometries that can be used as antennas to effectively fit
long electrical lengths into small areas. Iterative function schemes (IFS) with different fractal
dimensions has been discussed. IFS represent an extremely versatile method for conveniently
generating a wide variety of usual fractal structures. The performance of the fractal antenna
with respect to conventional Euclidean geometry has also been discussed.
44
CHAPTER 4
WIDEBAND
ANTENNA DESIGN
45
WIDEBAND ANTENNA DESIGN
This chapter surveys a planar monopole antenna using the Hexagonal Gasket. The design
demonstrates details of fractal geometries developed to get wideband behaviour of patch
resonator antenna. Research on the performance of the antenna by creating iterated fractal
hexagons to increase the total perimeter (electrical length) of patch antenna is presented. The
behaviour of patch resonator for various incremental steps in fractions, results in significant
improvement in bandwidth. A Slot is created in the ground plane to increase the matching
and thus bandwidth further and slits are introduced to achieve a notch band at desired
frequency. The designed fractal-like geometry is realized on a FR4 substrate of relative
dielectric constant of 4.4 and 1.6mm of width with 50-ohm microstrip feedline for UWB
application. The simulated results show that the antenna has a good performance with 10dBreturn loss in the frequency range 2.64-6.96GHz that results in a fractional bandwidth (FBW)
of 90%. In addition, antenna performances such as radiation patterns and antenna gains over
the operating bands have been presented and compared with the measured results.
4.1
Introduction
In 2002, Federal Communication Commission (FCC) allocated the bandwidth 3.l-10.6GHz
for commercial use and named it as UWB frequency band. UWB technology offers
significant benefits for Government, public safety, businesses and consumers. The frequency
band of operation is based on the –10 dB bandwidth of the UWB emission. It is believed that
the greatest potential use of UWB is in short-range communications in the home or business,
allowing equipment mobility and high data rates to facilitate information sharing. Some of
UWB applications are ground penetrating radar (GPR) systems, wall-imaging systems,
46
automotive collision avoidance systems, radar level gauges used in storage tanks, and
communications systems measurement systems [4].
In recent years, modern telecommunication systems require compact and small
antennas with wider bandwidth rather than conventional ones. Many methods for the design
of antennas are used for improving their performances. One of these methods is fractal and it
is more efficient for antennas to expand the bandwidths and reduce the dimensions [35]. The
fractal antennas are preferred because of their lightweight, small dimension and also the fact
that they have extreme wideband characteristics [36]-[41]. Various antennas for wideband
operation have been studied [42]-[43]. Fractals are recursively generated object having a
fractional dimension. Fractals have space-filling property which leads to curves that are
electrically very long, but fit into compact physical space. This property leads to the
miniaturization of antenna elements. There are a variety of fractal shapes, such as Hilbert
Curve [44], Sierpinski-carpet [45], Minkowski [21], Koch curve [19] etc.
This chapter illustrates a microstrip-fed monopole hexagonal shaped fractal antenna for
UWB application. The design is implemented by doing fractal on base hexagonal patch till
second iteration. The simulation is done by using full wave EM simulation software. The
design process of proposed antenna is presented in the antenna design section. Following this
section, various antenna parameters such as return loss, radiation characteristics and gain are
discussed which is caused due to iterations on the patch and introduction of a slot and slits in
the ground plane. The simulated results are verified with the measured results. This paper
ends with a set of conclusions.
4.2
Antenna Design
The presented antenna consists of a hexagonal patch element mounted on a dielectric layer
over a ground plane. The low cost fiberglass dielectric substrate FR4 is used having 1.5 mm
47
of height and a relative permittivity of 4.4, and it is fed by a 50-ohm micro-strip line. The
radiating patch is planned by taking hexagon as a base structure called generator [25]. The
generator is downscaled by a factor of two which is added to each side of base structure such
that the center point of the smaller hexagon will coincide with the center point of the edge of
the previous structure.
Figure 4.1 Geometry of the generator, 1st iteration and 2nd iteration
Figure 4.2 The generator with simple ground plane
48
Figure 4.3 The presented antenna with modified ground plane
Later the hexagon formed inside the base structure because of this addition is removed to
get1st iterated structure. Fig.4.1 shows the basic element and the iterated structures. Again the
smaller hexagon is scaled down by 1/2 and the procedure is repeated to get 2nd and higher
iterated structures. This process can be repeated upto countless iteration but practically
infinite iterative structure is not possible because of fabrication constraints. The second
iterative fractal antenna has been finalized to design. The detailed dimensions of the base
antenna are as shown in Table 4.1.
Table 4.1: Dimension of the presented antenna (in mm)
R
H1
Hf
Wg
Hg
Ws
Ls
Wf
S
10
10
5.635
50
20
4.2
10
2.2
6.56
The ground plane has been modified by introducing a slot of dimension W s×Ls just beneath
the 50-ohm microstrip line, Fig.4.3. Later an L-shaped narrow slit is introduced on the either
side of the symmetry plane of the structure. The width of the slit is 0.5mm. The presented
antenna with the discussed dimensions is fabricated and shown in Fig.4.4.
49
(a)
(b)
Figure 4.4 Fabricated Antenna Image (a) Radiating Patch (b) Ground Plane
4.3
Anechoic Chamber
Anechoic Chamber is an antenna measurement chamber. It is a closed room having
pyramidal-like arrangement on the side walls with conical shape facing outside the wall. All
the walls of the room are coated with metals. This is done to avoid the outside radiation effect
on the measurement of the test antenna. The pyramidal like dome shape is made to make the
characteristic impedance to of atmosphere to match with the characteristic impedance of the
Antenna under Test (AUT).
Chamber is having a positioner to fix the test antenna and the reference antenna is
kept at other end having same polarization as that of the test antenna. The flowchart shown in
Fig. 4.5 describes the measurement operation to be done to test the characteristics of the
antenna. The source power is fed to the directional coupler which is distributed to amplifier
and mixer. The power received by the amplifier is amplified and is fed to the reference
antenna. This power will be radiated in the atmosphere inside the chamber and received by
50
the AUT. The power received by mixer from the directional coupler and AUT are compared
to the Local Oscillator (LO) frequency to produce same Intermediate Frequency (IF) that is
received by the receiver Rx. The positioner is connected to the positional controller that will
control the axis and position of the AUT and a system (Computer) is linked to it to calculate
the various results at different desired axis and position of the AUT.
There is basically four axis control system used for measurement. They are
Azimuthal, Slide Roll and Elevation axis control system. Out of these, the first three control
systems are used for main measurement and the last one is used for phase measurement.
Directional
Coupler
Source
Reference
Antenna
Amplifier
Mixer
LO
AUT
IF
Mixer
Anechoic
Chamber
Positioner
Rx
IF
Positional
Controller
Computer
AUT- Antenna Under Test
IF- Intermediate Frequency
Figure 4.5 Anechoic Chamber Operation flowchart
51
4.4
Simulated and Measured Results
The given antenna is simulated and optimized by using a full wave EM simulator CST
STUDIO SUITE. The simulated return loss against frequency for the proposed antenna is
shown in Figs.4.6 & 4.7. In Fig.4.6, it is observed that as the iteration is done on the basic
shape of patch antenna with simple ground plane, the whole band going downwards
indicating increase in bandwidth.
As it is known that the bandwidth is inversely related to the Q-factor and the resonant
frequency is directly related to the Q factor of the antenna. The Q of the antenna decreases
with increase in the iteration number [46], therefore, the bandwidth gets wider and the
resonant frequency decreases, shown in Fig. 4.6.
0
Reflection Coefficient (dB)
-2
-4
-6
-8
-10
-12
Basic shape
1 iteration
2 iteration
-14
-16
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Frequency (GHz)
Figure 4.6. Return loss vs. level of iterations with simple ground plane
52
7.5
0
Reflection Coefficient (dB)
-10
-20
-30
-40
with normal ground plane
with slot in ground plane
-50
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Frequency (GHz)
Figure 4.7 Return loss variation in 2nd iteration with slot in simple ground plane
0
Reflection Coefficient (dB)
-5
-10
-15
-20
-25
Ls=8
-30
Ls=9
-35
Ls=10
Ls=11
-40
-45
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Frequency (GHz)
Figure 4.8 Return loss variation with different lengths of slot
Slot is introduced in the ground plane of the final second iterated structure for further
improvement. The effect of the slot in the ground plane after the second iteration is illustrated
in Fig. 4.7. An improved impedance matching is achieved for the whole band and the
impedance bandwidth of the proposed antenna covers a wide operating band of 2.6453
6.96GHz with a FBW of 90% at the center frequency of 4.8GHz. The maximum return loss
achieved is 12.2dB at 4.62GHz and the minimum return loss is 42dB at 6.5GHz. A
parametric study has been done on lengths of slot from 8mm to 11mm with 1mm variation,
shown in Fig. 4.8, and best value of return loss is found out to be 42dB at 6.5GHz for
Ls=10mm which has been chosen for proposed design. Variation in width of slot is also done
and optimized for the above value.
Finally, An L-shaped narrow slit of width 0.5mm and length of C is introduced on the
either side of the symmetry plane of the structure to get a notched band characteristic. A
parametric study has been done with the length of the slit and the effect of the slit length C is
shown in Fig. 4.9. It can be seen that the notched band is tunable with C. As the length of the
slit is varied from 8.5mm to 11.5mm with 1mm variation, the notch band gets shifted to
lower frequency side as shown in Fig. 4.9. The relation between notched frequency and the
slit length is given in Eq. 4.1.
(
)
√
(4.1)
where,
v = velocity of light, m/s
C = length of slit in ground plane, mm
eff = effective dielectric constant of substrate
The slit length is taken as 9.5mm to get notched band between 4.1-4.5GHz. A comparison
has been shown for the gain of the antenna, Fig. 4.12, with and without slit. For the notched
type the gain is 2.84dB at 3.8GHz which reduces to 0.899dB at 4.2GHz showing a notched
band in that region. The maximum value of the gain is 5.2dB at 6.5GHz.
54
The measured result is compared with the simulated one and they are well matched as shown
in Fig. 4.10. The slight deviation is produced by the error in the manufacturing and
measurement. Fig. 4.11 displays the measured co-polarization and cross-polarization
radiation patterns at different frequencies. The antenna is having broadside radiation pattern
at all the operating frequencies as illustrated by Fig. 4.11.
0
Reflection Coefficient (dB)
-5
-10
-15
-20
-25
C=8.5
C=9.5
C=10.5
C=11.5
-30
-35
-40
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Frequency (GHz)
Figure 4.9 Variation in notched band with length of slit
Reflection Coefficient (dB)
0
-10
-20
-30
Measured
Simulated
-40
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Frequency (GHz)
Figure 4.10 Measured vs. Simulated Return-Loss Characteristics
55
0
0
330
30
-10
-20
300
60
-30
-40
-50
270
90
-40
-30
240
-20
120
-10
210
0
150
180
Co-pol at 4.6GHz
Cross-pol at 4.6GHz
(a)
0
0
330
30
-10
300
-20
60
-30
-40
270
90
-30
-20
240
120
-10
0
210
150
180
(b)
56
Co-pol at 5.6GHz
Cross-pol at 5.6GHz
0
0
330
30
-10
300
-20
60
-30
-40
270
90
-30
-20
240
120
-10
210
0
150
180
Co-pol at 6.8GHz
Cross-pol at 6.8GHz
(c)
Figure 4.11. Measured Co-pol and Cross-pol field at (a) 4.6GHz (b) 5.6GHz (c) 6.8GHz
6
5
Gain (dB)
4
3
2
1
with ground slit
without ground slit
0
2
3
4
5
6
7
8
Frequency (GHz)
Figure 4.12 Simulated gain of the proposed antenna
The lower band-edge frequency for wideband antenna is described in [20], and given by Eq.
4.2.
57
(
where L = √
,r=
)
(4.2)
and ‘H’ is side length of hexagon.
For commonly used FR4 substrate with
= 4.4 and h = 0.159 cm, the empirical value of k =
1.15, determines lower band-edge frequency within 10% [47]. For presented design, Eq. 4.1
validates the value of lower band-edge frequency which is 2.75GHz in comparison to
simulated and measured lower band-edge frequency of 2.64GHz, an error of 4%. The gain of
the antenna is found to be 2-5dBi in the whole band of operation having maximum gain of
5.2dBi at 6.5GHz as shown in Fig. 4.12.
4.5
Summary
A novel hexagonal shaped monopole fractal antenna for UWB application is designed and
presented in this chapter. As the second-iteration is used, the proposed antenna exhibits broad
impedance bandwidth (-10 dB) covering a wide operating band (2.64GHz-6.96GHz), while
maintaining the good radiation characteristics. The fabrication is done and the measured
results validate the simulated characteristics. The variation with ground slot and ground slit
are also simulated. It is observed that the impedance bandwidth drastically affected by ground
slot. A band notch can also be created at desired frequency by using ground slit, which is
tunable with the length of the slit, so that interference can be minimized in the desired band.
58
CHAPTER 5
NARROWBAND
ANTENNA DESIGN
59
NARROWBAND ANTENNA DESIGN
This chapter presents novel, small and compact planar antennas having hexagonal patch with
different fractal geometry in the ground plane. It has been found that modifying the ground
plane using fractals on hexagonal patch results in lowering of resonant frequency by 55% in
Antenna1 and improvement in impedance matching in Antenna2.Full ground plane is
reformed by removing hexagonal carpet in Antenna1 and etching out Symmetrical Vertical
Pyramidal Structure (SVPS) in Antenna2. Antenna1 is optimized for dual band operation and
achieves satisfactorily 10dB impedance bandwidth at 3.176GHz and 4.552GHz while
Antenna2 is having single band characteristic and resonate at 3.06GHz. Antnenna1 and
Antenna2 are having gain around 5dBi (at both bands) and 3.3dBi respectively. Performance
of the presented antennas is studied in terms of reflection coefficient (S11), radiation patterns,
and gain. The presented antennas show a broadside radiation pattern in agreement with the
conventional patch antennas. Both the presented geometry is fed by 50-ohm microstrip line.
They are simulated using EM Simulation Software, tested and verified by measurement
results. The measured results are well matched to the simulated output.
5.1 Introduction
The dramatic developments of a variety of wireless applications have remarkably increased
the demand of multiband/wideband antennas with smaller dimensions than conventionally
possible. Modern mobile devices need low-profile antennas [48]. The fact that different
wireless standards, such as UMTS, WLAN and WiMAX, use different operation bands push
the need for terminal antennas that are multiband and/or wideband [49]-[50]. The antennas
should also be compatible in terms of cost, size, radiation patterns, gain and ease of
integration in the printed circuit boards of communication devices. A number of antennas
have been suggested [51]–[53], often with sizes that may be too large to be used practically.
60
Some compact antennas [54]–[56], have also been proposed. There is an important relation
between antenna dimensions and wavelength. According to this relation, if antenna size is
less than λ/2, then it is not an efficient radiator because radiation resistance, gain and
bandwidth are reduced. So as size of antenna reduces, mismatch between antenna and source
increases. Fractal geometry is a very good solution for this problem.
A fractal is a self-repetitive curve whose different parts are scaled copies of the whole
geometry. Consequently, a radiator based on a fractal or self-similar geometry is expected to
operate similarly at multiple wavelengths [57]-[58]-[25] and might keep similar radiation
parameters through several bands. A multiband operation, in the 1-10GHz frequency range,
was attained in [58] through the use of the Sierpinski gasket fractal. Key benefits of using
fractal are reduced size and compactness. Fractals have space-filling property which leads to
curves that are electrically very long, but fit into compact physical space. This property leads
to the miniaturization of antenna elements. There are a variety of fractal shapes, such as
Hilbert Curve [29], Sierpinski-carpet [45], Minkowski [21], Koch curve [19] etc. Lowering of
resonant frequency and size reduction by using Sierpinski carpet is discussed in [59] where
frequency has been lowered by almost 19% by etching out carpet from the radiating patch.
In this chapter two new hexagonal patch antennas are presented. The ground plane of
Antenna1 is modified by etching out carpet fractal geometry which results in reduction of
resonant frequency by 55% and it is finally optimized for dual band characteristics. In
Antenna2, SVPS is introduced and removed from ground plane which maximizes the
impedance matching and finally optimized for single band operation. In the following
section, we discussed about the antennas geometries and the effects of modified ground
plane. The simulated and measured radiation characteristics with peak gain of the antennas
are also discussed. Finally conclusion is done in last section.
61
5.2 Design Parameters and Simulation Results
In this section the design consideration and corresponding results of both the antennas are
explained one by one.
5.2.1 Antenna1: Design Parameters
The presented antenna consists of a 50-ohm micro-strip line fed hexagonal patch element
mounted on a dielectric layer over a ground plane. This novel antenna has compact size of
50×50mm2 including substrate.The low cost fiberglass dielectric substrate FR-4 is used having
1.6 mm of height and a relative permittivity of 4.4.The radiating element is hexagon of 15mm
side length. In the beginning, patch with full ground plane is studied. Later a carpet of
hexagons is etched out from the ground plane. The dimension of hexagons in the carpet is
obtained by down-scaling the hexagonal patch to half of the whole dimension.
2.8
Figure 5.1 Geometry of the radiating element of Antenna1
The central element of the carpet is concentric with the patch while other elements are
placed around its edges forming hexagonal carpet geometry. The surrounding elements are
placed at a gap (x) from the central element as shown in Fig.5.2. Parametric study for x has
been done. The final geometry is obtained and tested as shown in Fig.5.3.
62
x
Figure 5.2 The ground plane with removed hexagonal carpet
Figure 5.3 The ground plane (at x=0) of dual band antenna
5.2.2 Antenna1: Simulation Results
Antenna1 was simulated and optimized by using full wave EM simulation software. The
simulated return loss against frequency for the presented antenna is shown in Fig. 5.4.
Initially a conventional hexagonal patch with full ground plane is studied and it was found
resonating at 5.8GHz. Later it has been observed that removing carpet of hexagonal elements
from the full ground plane by keeping the surrounding element at a gap of x=3, the antenna
63
resonates at 2.632GHz i.e. a reduction of 55% in resonating frequency is achieved by using
carpet fractal in ground plane.
REFLECTION COEFFICIENT (dB)
0
-5
-10
-15
-20
Full Ground Plane
x=3
-25
0
1
2
3
4
5
6
7
FREQUENCY (GHz)
Figure 5.4 Return loss variation with full and modified ground plane
0
REFLECTION COEFFICIENT (dB)
-5
-10
-15
-20
-25
x=3
x=2
x=1
x=0
-30
-35
-40
0
1
2
3
4
5
FREQUENCY (GHz)
Figure 5.5 Return loss variation with gap(x)
64
6
7
0
REFLECTION COEFFICIENT (dB)
-5
-10
-15
-20
-25
-30
Full Ground Plane
x=0
-35
0
1
2
3
4
5
6
7
FREQUENCY (GHz)
Figure 5.6 Return loss of final antenna at x=0
Table 5.1: Antenna1 Characteristics
Frequency (GHz)
3.176
4.552
Return loss (dB)
-28.51
-28.38
Bandwidth (%)
8.7
5.3
Gain (dBi)
4.88
5.71
Directivity (dBi)
5.08
6.41
Further, the resonance frequency vs. gap (x) is simulated and shown in Fig. 5.5, and
found that the resonating frequency is slightly increasing with falling x and a new resonating
band is observed for x=0, depicting a dual band characteristic. The antenna is optimized for a
dual band operation. This dual band antenna delivers a return loss better than 25dB and gain
of 4.88dBi and 5.71dBi at 3.176GHz and 4.552GHz, respectively. Table 5.1 summarizes the
key parameters of the proposed dual band antenna.
5.2.3 Antenna2: Design Parameters
Antenna2 is even smaller than Antenna1 and it has total dimension of only 30x30mm2
including substrate. It also consists of hexagonal radiating element but of smaller side length
65
of 8mm. Firstly, full ground plane is taken and studied. Then ground plane is modified by
introducing and etching out Symmetrical Vertical Pyramidal Structure (SVPS). SVPS is
obtained by taking two symmetrical horizontal rectangular geometries of 28mm length and
1mm width at the centre maintaining a gap of 1mm between them. Then the symmetrical
geometries were scaled along length by 0.75 keeping width length constant.
Figure 5.7 Geometry of radiating patch of Antenna2
Figure 5.8 Ground plane geometry of Antenna2
The scaled parts were added to both, at the centre, of the previous parts already present and
this process is iterated eight times to obtain final SVPS. For this design too, low cost and
readily available FR4 substrate of relative permittivity of 4.4 and height 1.6mm has been used
66
and fed with 50-ohm microstrip line. Antenna2 patch geometry and ground plane geometry
are shown in Figs.5.7 & 5.8.
5.2.4 Antenna2: Simulation Results
Antenna2 is simulated using EM Simulation Software. Initially antenna is simulated with full
ground plane.
REFLECTION COEFFICIENT (dB)
0
-10
-20
Full Ground Plane
Modified Ground Plane
-30
2.0
2.5
3.0
3.5
4.0
FREQUENCY (GHz)
Figure 5.9 Return loss variation with full and modified ground plane
REFLECTION COEFFIECIENT (dB)
0
-10
-20
Full Ground Plane
2nd Iteration
4th Iteration
6th Iteration
8th Iteration
-30
2.0
2.5
3.0
3.5
FREQUENCY (GHz)
Figure 5.10 Return loss variation with iteration in ground plane
67
4.0
Then the effect of removing rectangular structure is observed. It is done till we reach final
SVPS. The simulated results are shown in Figs. 5.9 & 5.10. Fig.5.9 shows the effect of even
number iteration done in the ground plane as we ignore to show the results of odd iterations
to present more clear results.
The simulated results show as we go on removing the rectangular structure, matching
goes on increasing and antenna has a good performance with 10dB-return loss in the
frequency range 2.9-3.17GHz that results in a fractional bandwidth (FBW) of 8.82%.
Fig.5.10 depicts the comparison between full and final modified ground plane. It gives a clear
view that matching has been improved too much at the desired frequency band by removing
SVPS from the ground plane in comparison to full ground plane. The gain of the presented
antenna is nearly 3.3dB.
5.3 Measured Results
In this section the antenna tested results are shown which is helpful to validate the simulated
results.
5.3.1 Return Loss
In order to show the improved performance of the antennas with the modified ground plane,
simulated results are compared through measurements in this section. Antennas are fabricated
and tested in the Anechoic Chamber. Fabricated Antenna1 is shown in Fig.5.11. Fig.5.12
shows the measured vs. simulated plot for Antenna1. It shows that measured result is nearly
matching with the simulated one. The simulated resonant frequency was at 3.176 GHZ &
4.552GHz and the measured resonant bands are found at 2.918GHz & 4.46GHz respectively.
This slight variation occurs due to the uncertainty of the relative permittivity of our low-cost
FR4 substrate for high frequencies.
68
(a)
(b)
Figure 5.11 Fabricated Antenna1 (a) Radiating Patch (b) Ground Plane
0
Reflection Coefficient (dB)
-5
-10
-15
-20
-25
-30
Simulated
Measured
-35
-40
1
2
3
4
5
6
Frequency (GHz)
Figure 5.12 Measured vs Simulated Return loss of Antenna1
(a)
(b)
Figure 5.13 Fabricated Antenna2 (a) Radiating Patch (b) Ground Plane
69
REFLECTION COEFFICIENT (dB)
0
-10
-20
Simulated
Measured
-30
2.0
2.5
3.0
3.5
4.0
FREQUENCY (GHz)
Figure 5.14 Measured vs Simulated Return loss of Antenna2
Similarly, Fabricated Antenna2 is shown in Fig.5.13. Fig. 5.14 describes the simulated vs.
measured plot of Antenna2. In this plot too, measured plot is nearly matching with the
simulated result. Simulation results show Antenna1 is resonating at 3.06GHz whereas it is
resonating at 2.95GHz on measurement. The small frequency drift is produced by the error in
the manufacturing and measurement.
5.3.2 Radiation Patterns
The radiation patterns of the antennas are measured in an anechoic chamber at 2.9185GHz
and 4.46GHz for Antenna1 and at 2.95GHz for Antenna2 in the principal cuts. At each
frequency, the radiation patterns in the E- and H-planes are normalized. Fig. 5.13(a) & (b)
presents the co-polarisation and cross polarisation of Antenna1 at 2.9185GHz and 4.46GHz
respectively and it is found that there a gap of around 15dBi between co and cross
polarisation at both the bands making it a useful device for S & C-band applications having
gain around 5dBi at both bands.
Fig. 5.13(c) shows co-polarisation and cross polarisation of Antenna2 at 2.95GHz.
There is difference of approx. 20dBi between co and cross polarisation which make it an
excellent gadget for S-band application having a gain of 3.3dBi.
70
0
0
330
30
-10
-20
300
60
-30
-40
270
90
-40
-30
-20
240
120
-10
210
0
150
180
Co-pol at 2.9185GHz
Cross-pol at 2.9185GHz
(a)
0
0
330
30
-10
300
-20
60
-30
-40
270
90
-30
-20
240
120
-10
0
210
150
180
(b)
71
Co-pol at 4.46GHz
Cross-pol at 4.46GHz
0
10
330
30
0
-10
300
-20
60
-30
-40
-50
270
90
-40
-30
-20
240
120
-10
0
10
210
150
180
Cross-pol at 2.95GHz
Co-pol at 2.95GHz
(c)
Figure 5.13 Measured Normalised Radiation patterns of antennas, (a) & (b) for
Antenna1 and (c) for Antenna2, copolarization (continuous line), cross-polarization (dash
line)
5.4
Summary
Two novel and compact hexagonal shaped patch with modified ground plane antenna are
designed and presented. Antenna1 has carpet fractal geometry which is introduced to lower
the resonant frequency. The resonance frequency of a conventional hexagonal patch with full
ground is lowered by almost 55% by removing carpet of hexagonal elements from the full
ground plane while maintaining the good radiation characteristics. A dual band characteristic
is obtained by optimizing the gap (x). This antenna is optimized for S & C-band operation
having a decent gain at both the bands. Antenna2 has SVPS removed from ground plane
which improves the matching. It is optimized for S-band operation. It is having good gain of
3.3dBi at resonating point. The presented antennas show a broadside radiation pattern in
agreement with the conventional patch antennas. The measurement results are also shown
and found to be well matched to the simulated results.
72
CHAPTER 6
CONCLUSIONS AND
FUTURE WORK
73
CONCLUSIONS AND FUTURE WORK
This chapter sums up the results and highlights the achievements of the research work carried
out. This is followed by few suggestions for future work. The results presented in the thesis
have been published by the author in different international journals and conferences.
6.1
Conclusions
In this work, fractal geometries are designed and implemented. For this, three antennas are
designed using fractals. In fractal antennas, the self-similarity and plane-filling nature of
fractal geometries are linked to its frequency characteristics. Fractals are geometrical shapes,
which are self-similar, repeating themselves at different scales. Using fractal in an antenna
maximizes the length, or increase the perimeter of material that can receive or
transmit electromagnetic radiation within a given total surface area or volume.
Each design has specific characteristics and operates at different bands. The
conclusions are as follows:
a) Both the characteristics i.e. Wideband and Multiband behavior of the antenna
using fractals in hexagonal geometry have been successfully achieved.
b) Significant improvement in bandwidth is achieved by creating iterated fractal
hexagons to increase the total perimeter (electrical length) of patch antenna to
have wideband behaviour.
c) Fractional bandwidth greater than 90% is achieved for wideband antenna.
d) A controlled band notch is created in wideband characteristics to avoid
interference at desired frequency.
e) With modification in the ground plane, narrowband characteristics have been
successfully achieved with reduced dimension.
74
f) Reduction by almost 55% in resonant frequency is achieved by removing
hexagonal carpet from the ground plane.
g) Modifying ground plane by etching out Symmetrical Vertical Pyramidal Structure
(SVPS) helps to design an smaller antenna for S-band application.
h) The theoretical and simulated different characteristics of antennas such as return
loss, radiation pattern, gain, etc. are verified by measuring those antennas.
i) All measured results are found well matched to simulated results.
All the presented designs are simulated using CST Microwave Studio Suite12. Designs are
made using FR4 substrate having  value 4.4 and height of 1.6mm which is a low cost
material and easily available in the market. Microstrip feed line of 50 is used in every case.
Measurement of all the antennas is done using the lab facility of ISAC-Bangalore. The small
frequency drift seen in measurement results is produced by the error in the manufacturing and
measurement.
6.2
Suggestions for Future Work
The following are some of the prospects for future work:
a) The whole band of UWB (i.e. 3.2GHz - 10.6GHz) is not covered in wideband
antenna. New techniques can be employed in future to increase the matching i.e.
fractional bandwidth of antenna.
b) The gain of the narrow band antennas designed is low, so in future other techniques
can be employed to increase the gain of these antennas.
c) FEM can be employed to solve and implement all the designs.
75
Publications
International Conferences
[1] Sonu Agrawal, R. D. Gupta and S. K. Behera, “A New Dual Band Antenna with
Hexagonal Carpet in Ground Plane,” 8th International Conference on Microwaves,
Antenna Propagation and Remote Sensing (ICMARS), Jodhpur, Rajasthan, India, pp.
415-418, Dec 2012.
[2] Sonu Agrawal, R. D. Gupta and S. K. Behera, "A Hexagonal Shaped Fractal Antenna
for UWB Application", IEEE 2012 International Conference on Communications,
Devices and Intelligent Systems (CODIS), ISBN 978-1-4673-4700-6/12, Kolkata,
India, pp. 535-538, Dec 2012.
National Conference
[1] R. D. Gupta, Sonu Agrawal and S. K. Behera, “Design of a Compact Reconfigurable
RDRA,” 19th National Conference on Communication (NCC), 978-1-4673-5952-8/13,
IIT Delhi, India, Feb 2013.
International Journals
[1] Sonu Agrawal and S. K. Behera, “On Design of Different Fractal Ground Geometries
on Hexagonal Patch Antenna,” International Journal of RF and Microwave ComputerAided Engineering, Wiley (Communicated)
[2] Sonu Agrawal, R. D. Gupta and S. K. Behera, “Design of Wideband Planar
Hexagonal Fractal Antenna Having Notch-Band Characteristics,” Journal of
Electromagnetic Waves and Applications, Taylor & Francis. (Communicated)
76
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