Post on 24-Oct-2014
Chapter 1
Introduction
1.1Microstrip patch antenna
Antennas are a very important component of communication systems. By definition,
an antenna is a device used to transform an RF signal, traveling on a conductor, into
an electromagnetic wave in free space. Antennas demonstrate a property known as
reciprocity, which means that an antenna will maintain the same characteristics
regardless if it is transmitting or receiving. Most antennas are resonant devices, which
operate efficiently over a relatively narrow frequency band. An antenna must be
tuned to the same frequency band of the radio system to which it is connected;
otherwise the reception and the transmission will be impaired. When a signal is fed
into an antenna, the antenna will emit radiation distributed in space in a certain way.
A graphical representation of the relative distribution of the radiated power in space
is called a radiation pattern [1].
Microstrip antennas are attractive due to their light weight, conformability and low
cost. These antennas can be integrated with printed strip-line feed networks and
active devices. This is a relatively new area of antenna engineering. The radiation
properties of micro strip structures have been known since the mid 1950’s. The
application of this type of antennas started in early 1970’s when conformal antennas
were required for missiles. Rectangular and circular micro strip resonant patches have
been used extensively in a variety of array configurations. A major contributing
factor for recent advances of microstrip antennas is the current revolution in
electronic circuit miniaturization brought about by developments in large scale
integration. As conventional antennas are often bulky and costly part of an electronic
system, micro strip antennas based on photolithographic technology are seen as an
engineering breakthrough.
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However, one of main disadvantages of micro-strip antenna is their narrow band
width. It is well known that the multilayer structure is useful method to improve these
problems. The researchers have investigated their basic characteristics and extensive
efforts have also been developed to design of electromagnetically coupled two layer
microstrip stacked antenna stacked square patch antenna for Bluetooth application
and analysis of stacked rectangular microstrip antenna . Microstrip patch antenna
elements with a single feed are used in many popular for various radar and
communication system such as synthetics aperture radar (SAR), dual-band, multi-
band, mobile communication system and Global Positing Systems (GPS) . It may be
mentioned that the bandwidth can also be improved by stacking a parasitic patch on
the fed patch . By using two stacked patches with the wall at edges between the two
patches, one can obtained enhance impedance bandwidth.
1.2Rectangular Patch Antenna
In its most fundamental form, a Microstrip Patch antenna consists of a radiating patch
on one side of a dielectric substrate which has a ground plane on the other side as
shown in Figure 1.1. The patch is generally made of conducting material such as
copper or gold and can take any possible shape. The radiating patch and the feed lines
are usually photo etched on the dielectric substrate.
Figure 1.1 Structure of a Microstrip Patch Antenna
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For a rectangular patch, the length L of the patch is usually 0.3333λo< L < 0.5 λo,
where λo is the free-space wavelength. The patch is selected to be very thin such that
t << λo (where t is the patch thickness). The height h of the dielectric substrate is
usually 0.003 λo ≤h ≤0.05 λo. The dielectric constant of the substrate (εr) is typically
in the range 2.2 ≤ εr ≤ 12.
Microstrip patch antennas radiate primarily because of the fringing fields between the
patch edge and the ground plane. For good antenna performance, a thick dielectric
substrate having a low dielectric constant is desirable since this provides better
efficiency, larger bandwidth and better radiation. However, such a configuration
leads to a larger antenna size. In order to design a compact microstrip patch antenna,
substrates with higher dielectric constants must be used which are less efficient and
result in narrower bandwidth. Hence a trade-off must be realized between the antenna
dimensions and antenna performance.
1.3Advantages and Disadvantages
Microstrip patch antennas are increasing in popularity for use in wireless applications
due to their low-profile structure. Therefore they are extremely compatible for
embedded antennas in handheld wireless devices such as cellular phones, pagers
etc.The telemetry and communication antennas on missiles need to be thin and
conformal and are often in the form of microstrip patch antennas. Another area where
they have been used successfully is in Satellite communication.
Some of their principal advantages are given below:
• Light weight and low volume.
• Low profile planar configuration which can be easily made conformal to host surface.
• Low fabrication cost, hence can be manufactured in large quantities.
• Supports both, linear as well as circular polarization.
• Can be easily integrated with microwave integrated circuits (MICs).
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• Capable of dual and triple frequency operations.
• Mechanically robust when mounted on rigid surfaces.
Microstrip patch antennas suffer from more drawbacks as compared to conventional antennas.
Some of their major disadvantages discussed are given below:
• Narrow bandwidth
• Low efficiency
• Low Gain
• Extraneous radiation from feeds and junctions
• Poor end fire radiator except tapered slot antennas
• Low power handling capacity.
• Surface wave excitation
Microstrip patch antennas have a very high antenna quality factor (Q). It represents
the losses associated with the antenna where a large Q leads to narrow bandwidth and
low efficiency. Q can be reduced by increasing the thickness of the dielectric
substrate. But as the thickness increases, an increasing fraction of the total power
delivered by the source goes into a surface wave. This surface wave contribution can
be counted as an unwanted power loss since it is ultimately scattered at the dielectric
bends and causes degradation of the antenna characteristics. Other problems such as
lower gain and lower power handling capacity can be overcome by using an array
configuration for the elements.
1.4Basic Concepts in Antenna Engineering
1.4.1 Input Impedance
For an efficient transfer of energy, the impedance of the radio, of the antenna and of
the transmission cable connecting them must be the same. Transceivers and their
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transmission lines are typically designed for 50ohms impedance. If the antenna has
impedance different from 50 then there is a mismatch and an impedance matching
circuit is required [1].An antenna's impedance relates the voltage to the current at the
input to the antenna. An antenna with a real input impedance (zero imaginary part) is
said to be resonant. An antenna's impedance will vary with frequency.
1.4.2 Return loss
The return loss is another way of expressing mismatch. It is a logarithmic ratio
measured in dB that compares the power reflected by the antenna to the power that is
fed into the antenna from the transmission line. The relationship between SWR and
return loss is the following:
1.4.3 Bandwidth
The bandwidth of an antenna refers to the range of frequencies over which the
antenna can operate correctly. The antenna's bandwidth is the number of Hz for
which the antenna will
exhibit an SWR less than 2:1. The bandwidth can also be described in terms of
percentage of the center frequency of the band., is the highest frequency in the
band, is the lowest frequency in the band, and is the center frequency in the band.
In this way, bandwidth is constant relative to frequency. If bandwidth was expressed
in absolute units of frequency, it would be different depending upon the center
frequency. Different types of antennas have different bandwidth limitations.
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1.4.4 Directivity and Gain
Directivity is the ability of an antenna to focus energy in a particular direction when
transmitting, or to receive energy better from a particular direction when receiving. In
a static situation, it is possible to use the antenna directivity to concentrate the
radiation beam in the wanted direction. However in a dynamic system where the
transceiver is not fixed, the antenna should radiate equally in all directions, and this is
known as an omni-directional antenna.
Where is radiation intensity and is power radiated. Gain is not a quantity which can
be defined in terms of a physical quantity such as the Watt or the Ohm, but it is a
dimensionless ratio.
Gain is given in reference to a standard antenna. The two most common reference
antennas are the isotropic antenna and the resonant half-wave dipole antenna. The
isotropic antenna radiates equally well in all directions. Real isotropic antennas do
not exist, but they provide useful and simple theoretical antenna patterns with which
to compare real antennas. Any real antenna will radiate more energy in some
directions than in others. Since it cannot create energy, the total power radiated is the
same as an isotropic antenna, so in other directions it must radiate less energy. The
gain of an antenna in a given direction is the amount of energy radiated in that
direction compared to the energy an isotropic antenna would radiate in the same
direction when driven with the same input power. Usually we are only interested in
the maximum gain, which is the gain in the direction in which the antenna is radiating
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most of the power. An antenna gain of compared to an isotropic antenna would
be written as 3dBi.
1.4.5 Beam width
An antenna's beam width is usually understood to mean the half-power beam width.
The peak radiation intensity is found and then the points on either side of the peak
which represent half the power of the peak intensity are located. The angular distance
between the half power points is defined as the beam width. Half the power
expressed in decibels is 3db,so the half power beam width is sometimes
referred to as the beam width. Both horizontal and vertical beam widths are usually
considered. Assuming that most of the radiated power is not divided into sidelobes,
then the directive gain is inversely proportional to the beam width: as the beam width
decreases, the directive gain increases.
1.4.6 Radiation Pattern
The radiation or antenna pattern describes the relative strength of the radiated field in
various directions from the antenna, at a constant distance. The radiation pattern is a
reception pattern as well, since it also describes the receiving properties of the
antenna. The radiation pattern is three-dimensional, but usually the measured
radiation patterns are a two dimensional slice of the three-dimensional pattern, in the
horizontal or vertical planes. These pattern measurements are presented in either a
rectangular or a polar format. Figure 1.1 shows a rectangular plot presentation of a
typical element Yagi.
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Fig1.2: Radiation pattern of a Yagi antenna
1.4.7 Side lobes
No antenna is able to radiate all the energy in one preferred direction. Some is
inevitably radiated in other directions. The peaks are referred to as sidelobes,
commonly specified in dB down from the main lobe.
1.4.8 Nulls
In an antenna radiation pattern, a null is a zone in which the effective radiated power
is at a minimum. A null often has a narrow directivity angle compared to that of the
main beam. Thus, the null is useful for several purposes, such as suppression of
interfering signals in a given direction.
1.4.9 Polarization
Polarization is defined as the orientation of the electric field of an electromagnetic
wave. Polarization is in general described by an ellipse. Two special cases of
elliptical polarization are linear polarization and circular polarization. The initial
polarization of a radio wave is determined by the antenna. With linear polarization
the electric field vector stays in the same plane all the time. Vertically polarized
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radiation is somewhat less affected by reflections over the transmission path. Omni
directional antennas always have vertical polarization. With horizontal polarization,
such reflections cause variations in received signal strength. Horizontal antennas are
less likely to pick up man-made interference, which ordinarily is vertically polarized.
In circular polarization the electric field vector appears to be rotating with circular
motion about the direction of propagation, making one full turn for each RF cycle.
This rotation may be right hand or left hand. Choice of polarization is one of the
design choices available to the RF system designer.
1.4.10 Polarization Mismatch
In order to transfer maximum power between a transmit and a receive antenna, both
antennas must have the same spatial orientation, the same polarization sense and the
same axial ratio. When the antennas are not aligned or do not have the same
polarization, there will be a reduction in power transfer between the two antennas.
This reduction in power transfer will reduce the overall system efficiency and
performance. When the transmit and receive antennas are both linearly polarized,
physical antenna misalignment will result in a polarization mismatch loss which can
be determined using the following formula:
where is the misalignment angle between the two antennas. For we have a
loss of for we have, for we have and for we have an infinite loss. The actual
mismatch loss between a circularly polarized antenna and a linearly polarized antenna
will vary depending upon the axial ratio of the circularly polarized antenna. If
polarizations are coincident no attenuation occurs due to coupling mismatch between
field and antenna, while if they are not, then the communication can't even take place.
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1.5Feed Techniques
Microstrip patch antennas can be fed by a variety of methods. These methods can be
classified into two categories: contacting and non-contacting. In the contacting
method, the RF power is fed directly to the radiating patch using a connecting
element such as a microstrip line. In the non-contacting scheme, electromagnetic field
coupling is done to transfer power between the microstrip line and the radiating patch
1.5.1Coaxial Feed
The Coaxial feed or probe feed is a very common technique used for feeding
microstrip patch antennas. As seen from Figure 1.3, the inner conductor of the coaxial
connector extends through the dielectric and is soldered to the radiating patch, while
the outer conductor is connected to the ground plane.
Figure 1.3 Probe feed microstrip patch antennas
The main advantage of this type of feeding scheme is that the feed can be placed at
any desired location inside the patch in order to match with its input impedance. This
feed method is easy to fabricate and has low spurious radiation. However, a major
disadvantage is that it provides narrow bandwidth and is difficult to model since a
hole has to be drilled in the substrate and the connector protrudes outside the ground
plane, thus not making it completely planar for thick substrates (h > 0.02λo). Also,
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for thicker substrates, the increased probe length makes the input impedance more
inductive, leading to matching problems. It is seen above that for a thick dielectric
substrate, which provides broad bandwidth, the microstrip line feed and the coaxial
feed suffer from numerous disadvantages.
1.5.2Transformer Feed
The microstrip antenna can be matched to transmission line of characteristic
impedance Z0 using a quarter wavelength transmission line of characteristic
impedance Z1.
Fig1.4: Patch antenna with quarter wave matching section.
The goal is to match the input impedance (Zin) to the transmission line (Z0).If the
impedance of the antenna is Za, the input impedance viewed from the beginning of
the quarter wavelength line becomes
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This input impedance Zin can be altered by Z1, so that Zin=Zo and the antenna is
impedance matched.The parameter Z1 can be altered by changing the width of the
quarter wavelengths strip.The wider the wavelength strip,the lower the Z0 is for that
line.
1.6 Methods of Analysis
The preferred models for the analysis of microstrip patch antennas are the
transmission line model, cavity model, and full wave model (which include primarily
integral equations/Moment Method).
The transmission line model is the simplest of all and it gives good physical insight
but it is less accurate. The cavity model is more accurate and gives good physical
insight but is complex in nature. The full wave models are extremely accurate,
versatile and can treat single elements, finite and infinite arrays, stacked elements,
arbitrary shaped elements and coupling. These give less insight as compared to the
two models mentioned above and are far more complex in nature. Transmission
model is most widely used and discussed below.
1.6.1Transmission Line Model
This model represents the microstrip antenna by two slots of width W and height h,
separated by a transmission line of length L. The microstrip is essentially a non-
homogeneous line of two dielectrics, typically the substrate and air.
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Figure1.5 Microstrip Line Figure 1.6 Electric Field Lines
Hence, as seen from Figure 3.6, most of the electric field lines reside in the substrate
and parts of some lines in air. As a result, this transmission line cannot support pure
transverse-electromagnetic (TEM) mode of transmission, since the phase velocities
would be different in the air and the substrate. Instead, the dominant mode of
propagation would be the quasi-TEM mode. Hence, an effective dielectric constant
(εreff) must be obtained in order to account for the fringing and the wave propagation
in the line. The value of εreff is slightly less then εr because the fringing fields around
the periphery of the patch are not confined in the dielectric substrate but are also
spread in the air as shown in Figure 3.8 above.
The expression for εreff is given by as:
…eq. (1)
where
εreff = Effective dielectric constant13
εr = Dielectric constant of substrate
h = Height of dielectric substrate
W = Width of the patch
Consider Figure1.6 below, which shows a rectangular microstrip patch antenna of
length L, width W resting on a substrate of height h. The co-ordinate axis is selected
such that the length is along the x direction, width is along the y direction and the
height is along the z direction.
Figure 1.7 Microstrip patch antenna
In order to operate in the fundamental TM10 mode, the length of the patch must be
slightly less than λ/2 where λ is the wavelength in the dielectric medium and is equal
to λo/√εreff where λo is the free space wavelength. The TM10 mode implies that the
field varies one λ/2 cycle along the length, and there is no variation along the width
of the patch. In the Figure 2.10 shown below, the microstrip patch antenna is
represented by two slots, separated by a transmission line of length L and open
circuited at both the ends. Along the width of the patch, the voltage is maximum and
current is minimum due to the open ends. The fields at the edges can be resolved into
normal and tangential components with respect to the ground plan.
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Figure 1.8 Top view of antenna Figure 1.9 Side view of antenna
It is seen from Figure4.9 that the normal components of the electric field at the two
edges along the width are in opposite directions and thus out of phase since the patch
is λ/2 long and hence they cancel each other in the broadside direction. The tangential
components (seen in Figure 4.8), which are in phase, means that the resulting fields
combine to give maximum radiated field normal to the surface of the structure. Hence
the edges along the width can be represented as two radiating slots, which are λ/2
apart and excited in phase and radiating in the half space above the ground plane. The
fringing fields along the width can be modeled as radiating slots and electrically the
patch of the microstrip antenna looks greater than its physical dimensions. The
dimensions of the patch along its length have now been extended on each end by a
distance ΔL, which is given empirically as:
…eq(2)
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…eq(3)
…eq(4)1.7Modern Antennas
There has been an ever growing demand, in both the military as well as the
commercial sectors, for antenna design that possesses the following highly desirable
attributes:
• Compact size
• Low profile
• Conformal
• Multi- band or broadband
To increase the gain and impedance bandwidth of a simple patch antenna can be done
using a parasitic patch.
For obtaining an antenna for frequency hopping pattern and multiple bands along
with low profile we use fractals. These provide much higher gain and bandwidth than
simple technique like stacking. Fractal antenna and its concept are discussed further
in detail in next chapter.
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Chapter 2
Fractal Antenna
2.1Basics of Fractal Geometry
Several fractal geometries have been explored for antennas with special
characteristics, in the context of both antenna elements and spatial distribution
functions for elements in antenna arrays. The fractal geometry has been behind an
enormous change in the way scientists and engineers perceive, and subsequently
model, the world in which we live [9]. Many of the ideas within fractal geometry
have been in existence for a long time; however, it took the arrival of the computer,
with its capacity to accurately and quickly carry out large repetitive calculations, to
provide the tool necessary for the in-depth exploration of these subject areas. The
word ―fractal was coined by Benoit Mandelbrot, sometimes referred to as the father
of fractal geometry, who said, I coined fractal from the Latin adjective fractus. The
corresponding Latin verb frangere means to break ‘to create irregular fragments.
Figure 2.1:Classes of Fractals.
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A fractal is by definition a set for which the Hausdorff dimension strictly exceeds the
topological dimension, which he later retracted and replaced with: ―A fractal is a
shape made of parts similar to the whole in some way.
But here are five properties that most fractals have:
• Fractals have details on arbitrarily small scales.
• Fractals are usually defined by simple recursive processes.
• Fractals are too irregular to be described in traditional geometric language.
• Fractals have some sort of self-similarity.
• Fractals have fractal dimension.
2.2 Random Fractals
The exact structure of regular fractals is repeated within each small fraction of the
whole (i.e., they are exactly self-similar). There is, however, another group of
fractals, known as random fractals, which contain random or statistical elements.
These fractals are not exactly self-similar, but rather statistically self-similar. Each
small part of a random fractal has the same statistical properties as the whole.
Random fractals are particularly useful in describing the properties of many natural
objects and processes.
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Table 1.1: General comparison of Euclidian and fractal geometry
A simple way to generate a fractal with an element of randomness is to add some
probabilistic element to the construction process of a regular fractal. While such
random fractals do not have the self-similarity of their nonrandom counterparts, their
non uniform appearance is often rather closer to natural phenomena such as
coastlines, topographical surfaces, or cloud boundaries. A random fractal worthy of
the name should display randomness at all scales, so it is appropriate to introduce a
random element at each stage of the construction. By relating the size of the random
variations to the scale, we can arrange for the fractal to be statistically self-similar in
the sense that enlargements of small parts have the same statistical distribution as the
whole set. This compares with (nonrandom) self-similar sets where enlargements of
small parts are identical to the whole.
2.3Significance of Fractals in Nature
The original inspiration for the development of fractal geometry came largely from an
in-depth study of the patterns of nature. For instance, fractals have been successfully
used to model such complex natural objects as galaxies, cloud boundaries, mountain
ranges, coastlines, snowflakes, trees, leaves, ferns, and much more.
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Figure 2.2: (a) a fern leaf looks almost identical to the entire fern (b), a tree branch
looks similar to the entire tree
Mandelbrot realized that it is very often impossible to describe nature using only
Euclidean geometry that is in terms of straight lines, circles, cubes, and so forth. He
proposed that fractals and fractal geometry could be used to describe real objects,
such as trees, lightning, river meanders, and coastlines, to name but a few [10].
Many more examples could be introduced to prove the fractal nature of universe.
Therefore, there is a need for a geometry that handles these complex situations better
than Euclidean geometry.
Figure 2..3: A uniform cantor Fractal set
2.4 Prefractals: Truncating a Fractal to Useable Complexity
There is some terminology that should be established to understand fractals and how
they can be applied to practical applications [11]. From the scale of human
perception, a cloud does seem to be infinitely complex in larger and smaller scales.
The resulting geometry after truncating the complexity is called a prefractal [12]. A
prefractal drops the intricacies that are not distinguishable in the particular
applications. In Figure 1.5, the fifth iteration is indistinguishable from the Cantor set
obtained at higher iterations.
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This problem occurs due to the limit of the finite detail our eyes (or the printer we use
to plot the image) can resolve. Thus, to illustrate the set, it is sufficient to repeat the
generation process only by the number of steps necessary to fool the eye, and not an
infinite number of times. This is true for all illustrations of fractal objects. However,
make no mistake, only after an infinite number of iterations do we obtain the Cantor
set. For a finite number of iterations the object produced is merely a collection of line
segments with finite measurable length. These objects formed en route to the fractal
object are termed prefractals.
2.5Limitations on Small Antennas
With fast growing development of wireless communication systems there has been an
increasing need for more compact and portable communications systems. There is a
need to evolve small sized, high-performance and low cost antenna designs which are
capable of adjusting frequency of operation for integration of multiple wireless
technologies and decrease in overall size. However when the size of the classical
antenna (designed using Euclidean geometry) is made much smaller than the
operating wavelength it becomes highly inefficient because radiation efficiency and
impedance bandwidth decrease with the size of the antennas because these effects are
accompanied by high currents in the conductors, high ohmic losses and large values
of energy stored in the antenna near field.
An antenna is said to be small when it can be enclosed into a radian sphere, i.e. a
sphere with Radius a, where a = λ/2π, where. Due to the variations of the current
inside, the radian sphere the field outside the radian sphere can be described as a set
of orthogonal spherical vector waves.
Here is described according to the stored electric energy, magnetic energy,
Frequency and average radiated power as:
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An infinitesimally small antenna radiates only a or spherical mode that depends
on the electric size of the antenna given by , whereis the wave number at resonance
and is the radius of the smallest sphere that encloses the antenna. In general the of an
antenna is inversely proportional to its bandwidth thus implying narrow bandwidth
for antennas with high values of. Narrow bandwidth antennas are not usually
preferred because of the difficulty of matching. Achieving a low antenna basically
depends on how efficiently it uses the available volume inside the radian sphere. Thus
the high currents in the conductors, high ohmic losses, large values of the stored
energy is the antenna near field and high values make the performance of
small antennas inefficient.
2.6Fractals as Antennas and Space- Filling Geometries
While Euclidean geometries are limited to points, lines, sheets, and volumes, fractals
include the geometries that fall between these distinctions. Therefore, a fractal can be
a line that approaches a sheet. The line can meander in such a way as to effectively
almost fill the entire sheet. These space-filling properties lead to curves that are
electrically very long, but fit into a compact physical space. This property can lead to
the miniaturization of antenna elements. In the previous section, it was mentioned
that prefractals drop the complexity in the geometry of a fractal that is not
distinguishable for a particular application. For antennas, this can mean that the
intricacies that are much, much smaller than a wavelength in the band of useable
frequencies can be dropped out [10]. This now makes this infinitely complex
structure, which could only be analyzed mathematically, but may not be possible to
be manufactured. It will be shown that the band of generating iterations required to
reap the benefits of miniaturization is only a few before the additional complexities 22
become indistinguishable. There have been many interesting works that have looked
at this emerging field of fractal electrodynamics.
i = 0 i = 1
i = 2 i = 3
Fig 2..4: Generation of four iterations of Hilbert curves. The segments used to
connect the geometry of the previous iteration are shown in dashed lines.
Much of the pioneering work in this area has been documented in. These works
include fundamentals about the mathematics as well as studies in fractal antennas and
reflections from fractal surfaces. The space-filling properties of the Hilbert curve and
related curves (e.g., Peano fractal) make them attractive candidates for use in the
design of fractal antennas. The space-filling properties of the Hilbert curve were
investigated in as an effective method for designing compact resonant antennas. The
first four steps in the construction of the Hilbert curve are shown in Figure 1.6.
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The Hilbert curve is an example of a space-filling fractal curve that is self voiding
(i.e., has no intersection points). In the antenna engineering it can be used as dipole
(fed in the center), monopole (fed on one side) antenna, as well as meandered
structure of microstrip patch antenna.
2.7 Fractals Defined by Transformations—Self-Similar
2.7.1 Iterated Function Schemes: Fractal geometries are generated in an
iterative fashion, leading to self-similar structures. This iterative generating technique
can best be conveyed pictorially, as in Figure 1.7. The starting geometry of the
fractal, called the initiator, depends of final fractal shape: each of the straight
segments of the starting structure is replaced with the generator, which is shown on
the left of Figure 1.7.
Figure 2..5: (a) The first stages in the construction of the standard the Sierpinski
fractal the fractal tree via an iterated function system (IFS) approach.
The first few stages in the construction of the Sierpinski fractal are shown in Figure
1.5 (a.) The procedure for geometrically constructing this fractal begins with an
equilateral triangle contained in the plane, as illustrated in stage i=0 of Figure 1.7(a).
The next step in the construction process (see stage i=1) is to remove the central
triangle with vertices that are located at the midpoints of the sides of the original
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triangle, shown in stage i=0. This process is then repeated for the three remaining
triangles, as illustrated in stage i=2 of Figure 1.5 (a). The next two stages (i.e., i=3
and 4) in the construction of the Sierpinski fractal are also shown in Figure 1.5(a).
The Sierpinski-fractal fractal is generated by carrying out this iterative process an
infinite number of times. It is easy to see from this definition that the Sierpinski
fractal is an example of a self-similar fractal.
The fractal tree, shown in Figure 1.5 (a), is similar to a real tree, in that the top of
every branch splits into more branches. The planar version of the tree has the top
third of every branch split into two sections. The three-dimensional version (this use
of the term is only meant to imply that the structure cannot be contained in a plane)
has the top third of each branch split into four segments that are each one-third in
length. All the branches split with 60° between them. The length of each path remains
the same, in that a path walked from the base of the tree to the tip of a branch would
be the same length as the initiator. Finding the fractal dimension of these structures is
not as easy as it is to find the dimension of the self-similar fractals that were
previously observed. This is because the tree fractal is not necessarily self-similar.
Mandelbrot suggests that depending on the constructing geometry, the shape may not
truly be fractal in the entire structure.
This iterative generating procedure continues for an infinite number of times. The
final result is a curve or area with an infinitely intricate underlying structure that is
not differentiable at any point. The iterative generation process creates a geometry
that has intricate details on an ever-shrinking scale. In a fractal, no matter how closely
the structure is studied, there never comes a point where the fundamental building
blocks can be observed. The reason for this intricacy is that the fundamental building
blocks of fractals are scaled versions of the fractal shape. This can be compared to it
not being possible to see the ending reflection when standing between two mirrors.
Closer inspection only reveals another mirror with an infinite number of mirrors
reflected inside.
2.8Deterministic Fractals as Antennas
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Having seen the geometric properties of fractal geometry, it is interesting to explain
what benefits are derived when such geometry is applied to the antenna field [16].
Fractals are abstract objects that cannot be physically implemented. Nevertheless,
some related geometries can be used to approach an ideal fractal that are useful in
constructing antennas. Usually, these geometries are called prefractals or truncated
fractals. In other cases, other geometries such as multi triangular or multilevel
configurations can be used to build antennas that might approach fractal shapes and
extract some of the advantages that can theoretically be obtained from the
mathematical abstractions. In general, the term fractal antenna technology is used to
describe those antenna engineering techniques that are based on such mathematical
concepts that enable one to obtain a new generation of antennas.
One can summarize the benefits of fractal technology in the following way:
• Self-similarity is useful in designing multi-frequency antennas, as, for instance, in
the examples based on the Sierpinski fractal, and has been applied in designing of
multiband arrays.
• Fractal dimension is useful to design electrically small antennas, such as the Hilbert,
Minkowski, and Koch monopoles or loops, and fractal shaped micro strip patch
antennas.
• Mass fractals and boundary fractals are useful in obtaining high-directivity
elements, under sampled arrays, and low - sidelobes arrays.
2.9Fractal Arrays
The term fractal antenna array was originally coined by Kim and Jaggard in 1986 to
denote a geometrical arrangement of antenna elements that is fractal. The main
advantage of this technique is that it yields sparse arrays that possess relatively low
side lobes. While this is a feature typically associated with periodic arrays, it is not so
for random arrays. Another advantage of the technique is that it is also robust, which
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in turn is a feature typically associated with random arrays, but not with periodic
arrays.
2.10Fractals as Antenna Elements
The classical small antennas suffer from inefficient performance. Fractal geometry
provides the solution by designing compact and multiband antennas in a most
efficient and sophisticated way. The general concepts of fractals can be applied to
develop various antenna elements. The properties of these fractal designed antennas
allows for smaller, resonant antennas that are multiband and may be optimized for
gain. When antenna elements or arrays are designed with the concept of self-
similarity for most fractals, they can achieve multiple frequency bands because
different parts of the antenna are similar to each other at different scales. Application
of the fractional dimension of fractal structure leads to the gain optimization of wire
antenna and the self-similarity makes it possible to design antennas with very
wideband performance.
Fractal geometry can be employed to design self resonant small antennas in which
effective reduction in the resonant frequency can be obtained. It should be noted
though applying fractal geometry to reduce the size of the wire antenna a reduction in
resonant frequency is obtained.
2.11Fractals as Multiband Antennas
It has been found that for an antenna, to work well for all frequencies i.e. show a
wideband or multiband behavior, it should be:
• Symmetrical: This means that the figure looks the same as its mirror image.
• Self-similar: This means that parts of the figure are small copies of the whole figure.
These two properties are very common for fractals and thus make fractals ideal
candidates for design of wideband /multiband antennas.
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Figure 2.6: Four antennas (with a wave cartoon) intended to be used for four discrete
frequency bands.
Figure 2.7: One antenna intended to be used as a four-band antenna using the
fractal geometry of Sierpinski fractal.
Traditionally a wideband/multiband antenna in the low frequency wireless band can
only be achieved with heavily loaded wire antennas which usually imply that
different antennas are needed for different frequency bands. Recent progresses in the
fractal antennas suggest solution for using a single small antenna operating in several
frequency bands. The self similarity properties of the fractal structures are translated
into the electromagnetic behavior when used as antenna. This multiband behavior can
be explained with the help of a Sierpinski triangle (fractal) antenna employing
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Sierpinski fractal geometry with a self similar structure. Figure 2.2 show a typical
antenna system in which a single antenna is used for each application that is intended
for each different frequency band (four bands in this figure).
2.12 Cost Effectiveness of Fractal Antennas
One practical benefit of fractal antenna is that it is resonant antenna in a small space
thereby excluding the need of attaching discrete components to achieve resonance.
Usually at UHF and microwave antenna the cost for such parts for the
transceivers can become more expensive than the antenna. Further the addition of
parts produces reliability issues and breakage/return problems. In most of applications
fractal antennas are small bendable etched circuit boards or fractal etchings on mother
boards and contain no discrete components. This makes design of fractal antennas a
cost effective technique.
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Chapter 3
Stacked patch antenna
3.1Introduction
A stacked antenna is of compact, low profile construction, with stacked patch
elements operating at separate frequency bands. A patch element that is directly fed
by a coaxial feed has its ground plane connected to a portion of the coaxial feed that
is referenced to ground. The stacked patch element lacks inherent isolation of its
operating band of frequencies due to the use of a common feed. Accordingly, the
patch elements of a stacked patch antenna are poorly isolated, which increases the
complexities of tuning and frequency band separation by adding circuit components.
3.2Brief background
In the past, a known method of feeding the radiating patch is to connect the inner
conductor of the coaxial feed to the patch at a natural feed point of the patch. The
natural feed point of the radiating patch is the point at which it presents apparent fifty
ohm impedance when a conductor is coupled at that point. This locus of points
typically is offset from the geometric center of the radiating patch.
Stacked patch antennas are known in which two patch antennas are stacked on top of
each other. The individual antennas in a stacked patched antenna assembly will be
referred to as patch antennas or simply antennas. The top conductive pattern of a
patch antenna will be termed the radiating patch of the patch antenna and the bottom
conductive pattern, if included, will be termed the ground patch of the patch antenna.
The entire stacked patch antenna assembly comprising multiple patch antennas will
be referred to as a stacked patch antenna assembly.
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A stacked patch antenna assembly is suitable for the aforementioned two band GPS
type application. Conventional stacked patch antenna assemblies typically have used
one of two types of feed arrangements. In one arrangement, only one patch antenna is
directly fed while the other is parasitically coupled to the first patch antenna. In the
other type of feed arrangement, each patch antenna is directly fed. In the type of feed
arrangement where each patch antenna is directly fed, each feed, which comprises a
coaxial cable with an inner and an outer conductor, has the outer conductor shorted to
the ground patch at some non-centered point on the patch antenna.
In both of these types of feed arrangements, the amount of isolation achieved between
the operating frequencies of the two (or more) patch antennas is quite limited. In the
former type, in which one of the patch antennas is parasitically coupled to a directly
fed patch antenna, coupling between the bands is intentionally induced. In the latter
case, in which each patch antenna is directly and separately fed, coupling arises from
the existence of non-zero surface currents on the radiating patch of the lower patch
antenna or antennas at the point or points where the outer conductor of the coaxial
feed for the upper patch antenna contacts the radiating patch of the lower patch
antenna.
3.3Stacked patch antenna
The demand for application of microstrip antenna in various communication systems
has been increasing rapidly due to its lightweight, low cost, small size, ease of
integration with other microwave components [2-5]. Microstrip antenna gained in
popularity and become a major research topic in both theoretically and
experimentally. However one of main disadvantages of micro-strip antenna is their
narrow band width. It is well known that the multilayer structure is useful method to
improve these problems. The researcher have investigated their basic characteristics
and extensive efforts have also been developed to design of electromagnetically
coupled two layer elliptical microstrip stacked antenna [6], stacked square patch
antenna for Bluetooth application and analysis of stacked microstrip rectangular
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microstrip antenna. Several methods have been presented in the last years to improve
its such as: thicker substrate reactive matching network, and stacked patches [7–8].
Microstrip patch antenna elements with a single feed are used in many popular for
various radar and communication system such as synthetics aperture radar (SAR),
dual-band, multi-band, mobile communication system and Global Positing Systems
(GPS). It may be mentioned that the bandwidth can also be improved by stacking a
parasitic patch on the fed patch. Therefore in this present paper, we observed on an
electromagnetically stacked rectangular microstrip antenna.
3.4Parasitic patch
In general, the impedance bandwidth of a patch antenna is proportional to the antenna
volume measured in wavelengths. However, by using two stacked patches with the
walls at the edges between the two patches, one can obtain enhanced impedance band
width. There has recently been considerable interest in the two layer probe fed patch
antenna consisting of a driven patch in the bottom and a parasitic patch on a
microstrip patch antenna, the antenna with high gain or wide bandwidth can be
realized. These characteristics of stacked microstrip antenna depend on the distance
between a fed patch and a parasitic patch.
Fig3.1:Stacking of patch antenna and parasitic antenna
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By stacking a parasitic patch on a microstrip patch antenna, an
antenna with high gain or wide bandwidth can be realized. These
characteristics of stacked microstrip antenna depend on the
distance between a fed patch and a parasitic patch. When the
distance is about 0.1λ (operating wavelength), the stacked
microstrip antenna has a wide bandwidth [8].
33
Chapter 4
Design specifications
4.1 Sierpinski fractal antenna
In this chapter, the procedure for designing a sierpinski fractal antenna is explained.
The results are obtained from the simulations are demonstrated.
The three essential parameters for the design of a sierpinski fractal antenna:
Frequency of operation (fo): The resonant frequency of the antenna must
be selected appropriately. The mobile systems uses the frequency range from
5 -30GHz. Hence the antenna designed must be able to operate in this frequency
range.
Dielectric constant of the substrate (εr): The dielectric material selected for our
design is RT Duroid which has a dielectric constant of 3.2. A substrate with a
high dielectric constant has been selected since it reduces the dimensions of
the antenna.
Height of dielectric substrate (h): For the sierpinski gasket antenna to be
used in Wifi, it is essential that the antenna is not bulky. Hence, the height of the
dielectric substrate is selected as 0.798 mm.
Hence, the essential parameters for the design are:
• fo = 5 GHz
• εr = 3.2
• h = 0.798 mm
Step 1: Calculation of triangle side
34
a= 2 c
2 f r2√ϵr
Step 2: Calculation of effective dielectric constant
Step 3: Calculation of antenna height2√32
a
Step 4: Design using IE3D Software.
Step 5 : Simulation and optimization.
4.2 Stacked patch antenna
The following essential parameters for the design of a rectangular microstrip patch
antenna with stacking:
Frequency of operation (fo): The resonant frequency of the antenna must
be selected appropriately. The Mobile Communication Systems uses the
frequency range from 2100-5600 MHz. Hence the antenna designed must be
able to operate in this frequency range. The resonant frequency selected for my
design is 2.4 GHz which belongs to C-band.
Dielectric constant of the substrate (εr): The dielectric material selected for our
design is cellophane which has a dielectric constant of 4.4.A substrate with a
high dielectric constant has been selected since it reduces the dimensions of
the antenna.
35
Height of dielectric substrate (h): Height selected is same as that of
normal patch antenna, so that comaparisons can be
made.Thus height selected is 1.588mm.
Distance between the parasitic patch and active patch(d): The
antenna is made of two stacked patches, two layers and a
vertical probe connected to the lower patch. The lower patch,
with width W and length L is supported by a low dielectric
substrate with dielectric permittivity ε1 and thickness h1.The
upper patch with the same width and length as lower patch is
stacked at the height h2 above the lower substrate and
supported by another air-filled layer with permittivity ε1 and
thickness h2.
Hence, the essential parameters for the design are:
fo = 2.4 GHz
εr = 4.4
h = 1.588 mm
0.05 λ < d < λ as per variations done.
36
Chapter 5
5.1 Serpeinski fractal antenna
Antenna parameters :
€r = 3.2
h = 0.798mm
f = 5Ghz
side (a) = 22.00mm
height = 19.052mm
Iteration 0
Iteration 0 consists of a
sierpinski antenna designed
for a frequency of 5 Ghz
Figure 5. 1 s h o w i n g i t e r a t i o n 0
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The current distribution pattern showing
the movement of current on the antenna
surface.
Figure 5. 2 : C u r r e n t d i s t r i b u t i o n p a t t e r n
Radiation pattern showing a single lobe with a gain of 4.6dB.
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Figure 5. 3 Radiation pattern for iteration 0
Figure 5. 4 VSWR for iteration 0
S-parameter plot showing resonant frequency
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Figure 5. 5 S-parameter for iteration 0
40
Smith chart showing points of resonance between capacitance and reactance.
Figure 5.6 Smith chart for iteration 0
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Iteration 1
The first iteration consists of a single fractal
hole dug right at the centre of the antenna.
The resonant frequencies obtained are :8.31
Ghz, 15.63Ghz and 17.57 Ghz.
Figure 5. 7 showing iteration 1
The current distribution pattern showing
the spreading of current on the antennae
surface.
Figure 5. 8 showing current distribution
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Radiation pattern showing a single lobe with a gain of 6.96 dB.
Figure 5. 9 Radiation pattern for iteration 1
Figure 5. 1 0 VSWR for iteration 1
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Return loss showing 3 Bands with return loss less than 10dB.
Figure 5. 1 1 S-parameter plot showing resonant frequencies
Smith chart showing points of resonance between capacitance and reactance.
Figure 5.12: smith chart
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Iteration 2
The second iteration consists of nine
independent radiating elements as shown
in figure.
The resonant frequencies obtained are at
13.90 Ghz, 15.0 Ghz and 19.84 Ghz.
Figure 5. 1 3 showing iteration 2
The current distribution pattern
showing the spreading of current
on the antennae surface.
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Figure 5. 1 4 Current distribution pattern
Radiation pattern showing a single lobe a gain of 5.53 dB.
Figure 5. 1 5 Radiation pattern for iteration 2
46
The resonant frequencies obtained are: 8.31 Ghz, 15.63 Ghz and 17.57 Ghz.
Figure 5. 1 6 VSWR for iteration 2
Return loss showing 3 Bands with return loss less than 10dB.
Figure 5. 1 7 S-parameter for iteration 2
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Smith chart showing points of resonance between capacitance and reactance.
Figure 5. 1 8 Smith chart for
iteration 2
48
Iteration 3
Iteration 3 consists of 27 independent
radiating elements fed with truncated
transformer feed as shown in figure.
Figure 5. 1 9 showing iteration 3
The current distribution
pattern showing the spreading
of current on the antennae
surface.
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Figure 5. 2 0 Current distribution pattern for iteration 3
Radiation pattern showing a single lobe a gain of 5.52 dB.
FIgure 5. 2 1 Radiation pattern for iteration 3
The resonant frequencies obtained are: 20 GHz and 25.1 GHz.
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Figure 5. 2 2 VSWR for iteration 3
Return loss showing 2 Bands with return loss less than 10dB.
Figure 5. 2 3 S-parameter display for iteration 3
Smith chart showing points of resonance between capacitance and reactance.
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Figure 5. 2 4 Smith chart for iteration 3
Iteration 3 (modified)
Modified iteration 3 consists of 27
independent radiating elements fed with
transformer feed as shown in figure.
Figure 5. 2 5 showing modified iteration 3
The current distribution
pattern showing the spreading
of current on the antennae
surface.
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Figure 5. 2 6 Current distribution for modified iteration 3
Radiation pattern showing a single lobe a gain of 1.94 dB.
Figure 5. 2 7 Radiation pattern for modified iteration 3
53
The resonant frequencies obtained are: 8.31 Ghz, 15.63 Ghz and 17.57 Ghz.
Figure 5. 2 8 VSWR for modified iteration 3
Return loss showing 4 Bands with return loss less than 10dB.
54
Figure 5. 2 9 S-parameter for modified iteration 3
Smith chart showing points of resonance between capacitance and reactance.
Figure 5. 3 0 Smith chart for
modified iteration 3
5.2: Patch antenna without stacking
Patch antenna with coaxial feed:
L=28.837mm W=37.26mm
55
Fig 5.31: Patch antenna
Fig 5.32: VSWR =1.7
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Fig 5.33: S-parameter= -17.8 dB
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5.3: Patch antenna with stacking
Case1: Distance between stacks, d =0.1λ
Fig 5.34: VSWR=1.7
Fig 5.35 :Gain versus frequency curve, Gain is 4dBi at 2.4 GHz
58
Fig 5.36: S- parameter= -11Db
Fig: 5.37: Radiation Pattern
59
Case2: Distance between stacks, d =0.05λ
Fig 5.38: VSWR=1.3
Fig 539: Gain versus frequency plot. Gain=5Dbi.
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Fig 5.40: S- parameter=-13 dB
Fig 5.41: Radiation pattern.We see that there is no back lobes,hence lesser loss and thus higher gain
61
Result:
We observe that ;
Bandwidth without stacking:13MHz
Bandwidth with stacking:50MHz
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FUTURE SCOPE
The antenna can be used extensively in the communication sector. Its applications are
Wi-Max, 3G and 4G mobile communication applications. Due to high frequencies
obtained the percentage bandwidth and the bit rate increases and thus can be used for
Direct To Home service (DTH).Also, currently the antenna is being used in military
by the troops for short distance communication. It can be used in Electronic Counter
Measure (ECM) and Electronic Counter Counter Measure (ECCM).It can also be
used in Wireless Local Loop (WLL) in telephony sector. Satellite communication can
also be improved by using the multiple frequencies. However attenuation increases at
high frequencies but with better system designing these disadvantages can be
overcome. This antenna is suitable for applications in ICMS, DECT, UMTS,
Bluetooth and WLAN systems. Because of linear phase and good impedance match,
with some further optimization and manufacturing aspect, this antenna can serve in
UWB and wireless USB applications.
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[3]S. A. Long and M. D. Walton, “A dual-frequency circulardisc antenna,” IEEE Transactions on Antenna and Propagation USA, AP-27, pp. 270–273, 1979.
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[6]W. Chen, K. F. Lee, and R. O. Lee, “Input impedance of coaxially fed rectangular microstrip antenna on electrically thick substrate,” Microwave optical Technology Letters, Vol. 6, No. 6, pp. 387–390, 1993.
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[8] McLean, J. S., ―A Re-Examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas,IEEE Transactions on Antennas and Propagation, vol. 44, pp. 672-676, May 1996.
[9] H. Morishita, Y. Kim, and K. Fujimoto, ―Design Concept of Antennas for Small Mobile Terminals and the Future Perspective,‖ IEEE Antennas and Propagation Magazine, vol. 44, no. 5, pp. 30-43, October 2002.
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