Micro Strip Patch Antenna

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

26

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.

27

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

32

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

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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.

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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.

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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

41

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

43

Return loss showing 3 Bands with return loss less than 10dB.

Figure 5. 1 1 S-parameter plot showing resonant frequencies


Figure 5.12: smith chart

44

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.

45

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 7 S-parameter for iteration 2

47


Figure 5. 1 8 Smith chart for

iteration 2

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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


FIgure 5. 2 1 Radiation pattern for iteration 3

The resonant frequencies obtained are: 20 GHz and 25.1 GHz.

50



Figure 5. 2 3 S-parameter display for iteration 3


51

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


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


54

Figure 5. 2 9 S-parameter for modified iteration 3


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

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Fig 5.31: Patch antenna

Fig 5.32: VSWR =1.7

56

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

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Fig 5.36: S- parameter= -11Db

Fig: 5.37: Radiation Pattern

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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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REFERENCES

[1]J. R. James, P. S. Hall, and C. Wood, “Microstrip antenna theory and design” IEE Electromagnetic Wave, Series 12 London, U. K. Peter Peregrinus, 1981.

[2]K. C. Gupta, “Recent advance in microstrip antenna,” Microwave Journal, No. 27, pp. 50–67, 1984.

[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.

[4]A. B. Nandgaonkar and S. B. Deosarkar, “Broadband stacked patch antenna for bluetooth applications,” Journal of Microwaves, Optoelectronics and Electromagnetic Application, Vol. 8, No. 1, pp. 1–5, 2009.

[5]I. K. Moussa and D. A. E. Mohamed and I. badran, “Analysis of stacked rectangular microstrip antenna,” 24th National Radio Science Conference, March 13-15, pp. 1– 10, 2007.

[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.

[7] R. Yamaguchi, ―Effect of Dimension of Conducting Box on Radiation Pattern of a Monopole Antenna for Portable Telephone,‖ IEEE Antennas and Propagation Society International Symposium Digest, pp. 669-672, 1992.

[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.

[10]K. L. Wong, Planar Antennas for Wireless Communications, Wiley-Interscience, John Wiley & Sons, 2003.

.

[11]K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, Chinchester, New York, 1990.

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[12] K. Sato, ―Characteristics of a Planar Inverted-F Antenna on a Rectangular Conducting Body,”Electronics and Communications in Japan, vol. 72, no. 10, pp. 43-51, 1989.

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Micro Strip Patch Antenna

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