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INTRODUCTION
CHAPTER 1
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INTRODUCTION
Reflector antennas, in one form or another, have been in use
since the discovery of electromagnetic wave propagation in 1888 by
Hertz. Although reflector antennas take many geometrical
configurations, some of the most popular shapes are the plane,
corner, and curved reflectors. t has been shown by geometrical
optics that if a beam of parallel rays is incident upon a reflector
whose geometrical shape is a parabola, the radiation will converge
at a spot which is known as the focal point. n the same manner, if a
point source is placed at the focal point, the rays reflected by aparabolic reflector will emerge as a parallel beam. !ince the
transmitter "receiver# is placed at the focal point of the parabola,
the configuration is usually known as front fed. $he illumination of a
parabolic reflector antenna depends on the properties of the feed
used. $he widespread use of reflectors has simulated interest in the
development of feeds to improve the aperture efficiency and to
provide greater discrimination against noise radiation from ground.n order to obtain a high efficiency it is necessary that the radiation
pattern as uniform as possible and produces little spillover energy.
%esides it is desirable that the radiation pattern of the feed is
symmetrical and the feed should possess a well defined phase
center. &hen fed effectively from the focus paraboloid reflectors
produce high gain pencil beam with low side lobes and good cross
polarization discrimination characteristics. $he symmetrical focusfed paraboloid is the most widely used reflector for medium and
high gain pencil beam applications such as in Radio Astronomy and
it is considered to be a good compromise between performance and
cost. $his pro'ect describes the analysis of the focus fed parabolic
reflector and its Radiation properities in ()*)RA+ )$H- A*
A/)R$0R) A//R-A$-* )$H-.
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1. DIPOLEFEED
1. DIPOLERADIATIONPATTERN
2. DIPOLEMULTIICATI0NPATTERN
3. DIPOLEBEAMEFFICIENCY
2. SQUARECORNER FEED
3. HORNFEED
1. RADIATIONPATTERN BYVARYAINGSEVERALLENGTHS
2. SQUARECORNER BEAMEFFICIENCY
1. RADIATIONPATTERNS BYVARAYINGHORNDIMENSIONS
2. HORNPHASEVARIATION
FED TO A PARABOLIC REFLECTOR 1. f/D RATIO 2.APERTURE EFFICIENCY 3. GAIN
SELECTION OF FEED
3
1.1 PROCESSING STEPS
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1. DIPOLEFEED
1. DIPOLERADIATIONPATTERN
2. DIPOLEMULTIICATI0NPATTERN
3. DIPOLEBEAMEFFICIENCY
2. SQUARECORNER FEED
3. HORNFEED
1. RADIATIONPATTERN BYVARYAINGSEVERAL
LENGTHS
2. SQUARECORNER BEAMEFFICIENCY
1. RADIATIONPATTERNS BYVARAYINGHORN
DIMENSIONS
2. HORNPHASEVARIATION
FED TO A PARABOLIC REFLECTOR 1. f/D RATIO 2.APERTURE EFFICIENCY 3. GAIN 4. GENERAL CHARACTERISTICS
AFTER REFLECTION THE RADIATION PATTERNS OFEACH FEED ARE CALCULATED USING
1.GENERAL METHOD2.APERTURE APPROXIMATION METHOD
SELECTION OF FEED
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BASIC ANTENNA
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CHAPTER 2
BASIC ANTENNA
An antenna is a transducer designed to transmit or receive
electro magnetic waves. n other words, antennas convert
electromagnetic waves into electrical currents and vice versa.
Antennas are used in systems such as radio and television
broadcasting, point6to6point radio communication, wireless +A*,
radar, and space e7ploration. Antennas usually work in air or outer
space, but can also be operated under water or even through soil
and rock at certain freuencies for short distances.
/hysically, an antenna is an arrangement of conductorsthat
generate a radiating electromagnetic fieldin response to an applied
alternating voltage and the associated alternating electric current,
or can be placed in an electromagnetic field so that the field will
inducean alternating current in the antenna and a voltage between
its terminals. !ome antenna devices "parabolic antenna, HornAntenna# 'ust adapt the free space to another type of antenna
F! 2.1 "#$% #&'(&
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2.1 ANTENNA PARAMETERS
1. )ffective length
2. Resonant freuency
3. (ain
4. irectivity
5. Radiation pattern
9. +obe levels
:. mpedance
8. )fficiency
;. %and width
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R($+&' f,(-(&%
$he >resonant freuency> and >electrical resonance> is related
to the electrical length of the antenna. $he electrical length is
usually the physical length of the wire divided by its velocity factor
"the ratio of the speed of wave propagation in the wire to c
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radiated at the same distance by an hypothetical isotropic antenna.
&e write >hypothetical> because a perfect isotropic antenna cannot
e7ist in reality.!ometimes, the half6wave dipole is taken as a
reference instead of the isotropic radiator. $he gain is then given ind%d "decibels over dipole#=
(ain @"ma7imum radiation intensity in a given direction #
"ma7imum radiation intensity from isotropic antenna direction #
#B,"
#B,"ma7
E
EG
isotriopic
=
D,(%')'
Antenna directivity is usually measured in d%i, or decibels
above isotropic. $his number is obtained by measuring the gain in
the strongest lobe, and comparing it to the total gain "as if all power
was radiated uniformly in all directions#=
#"log1< 1polarization> of an antenna is the orientation of the
electric field ")6plane# of the radio wave with respect to the )arth?s
surface and is determined by the physical structure of the antenna
and by its orientation. t has nothing in common with antenna
directionality terms= >horizontal>, >vertical> and >circular>. $hus, a
simple straight wire antenna will have one polarization when
mounted vertically, and a different polarization when mounted
horizontally. >)lectromagnetic wave polarization filters> are
structures which can be employed to act directly on the
electromagnetic wave to filter out wave energy of an undesired
polarization and to pass wave energy of a desired polarization.
A&'(& #(,',(
As a receiver, antenna aperture can be visualised as the area
of a circle constructed broadside to incoming radiation where all
radiation passing within the circle is delivered by the antennato a
matched load. "*ote that transmittingand receiving are reciprocal,
so the aperture is the same for both.# $hus incoming power density
"watts per suare metre# 7 aperture "suare metres#@ available
powerfrom antenna "watts#. Antenna gainis directly proportional to
aperture. An isotropicantenna has an aperture of
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M4
2
where N is the wavelength. An antenna with a gain of ( has an
aperture Ae@M4
2
G
(enerally, antenna gain is increased by directing radiation in a
single direction, while necessarily reducing it in all other directions
since power cannot be created by the antenna. $hus a larger
aperture produces a higher gain and narrower beamwidth.+arge
dish antennas, many wavelengths across, have an aperture nearlyeual to their physical area.
A&'(& (ff(%')( #,(#
n telecommunication, antenna effective area or effective
aperture is the functionally euivalent area from which an antenna
directed toward the source of the received signalgathers or absorbs
the energy of an incident electromagnetic wave.*ote 1= Antenna
effective area is usually e7pressed in suare meters.*ote 2= n the
case of parabolic and horn6parabolic antennas, the antenna
effective area is about
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M4
2GAeff =
where ( is the antenna gain "not in decibels# and N is the
wavelength. $his formula can be derived as a conseuence of
electromagnetic reciprocitywhich relates the transmit properties of
an antenna to the receiving properties. t may not hold if the
antenna is made with certain non6reciprocal materials. +ike the
antenna gain, the effective area varies with direction. f no direction
is specified, the ma7imum value is assumed
R(#'+&$* '+ *$%# #,(#
!imply increasing the size of antenna does not guarantee an
increase in effective areaO however, other factors being eual,
antennas with higher ma7imum effective area are generally
larger.n the case of wire antennas, there is no simple relationship
between physical area and effective area. n the case of aperture
antennas "for e7ample, horns and parabolic reflectors# considered in
their direction of ma7imum radiation, the aperture efficiencyis the
ratio of effective area to physical area=
physapeff AeA =
where eapis the aperture efficiency, Aphysis the physical size of
the aperture, and Aeffis the effective aperture. the definition section
above, derived from the Cederal !tandard, implies that the aperture
efficiency is
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uniform illumination of the aperture, phase variations of the
aperture field "typically due to surface errors in a reflector and high
flare angle in horns#, and scattering from obstructions. $he incident
wavefront may also not be completely phase coherent due tovariations in the propagating mediumO this results in an increase in
the effective area of an antenna not resulting in a commensurate
increase in signal, an effect known as ?aperture loss?.
R##'+& ,($$'#&%(
t is defined as that system resistance, when substituted in
series with an antenna, will consume the same power as actually
radiated.
A&'(& "(# 5'*
t is a measure of the directivity of an antenna,which
represents an angular width measured on the radiation pattern
between two points.
1:
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REFLECTORS
CHAPTER 3
REFLECTORS
A spherical wave front "one in which the energy spreads out in
all directions# spreads out as it travels away from the antenna and
produces a pattern that is not very directional. A wave front that
e7ists in only one plane does not spread because all of the wave
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front moves forward in the same direction. Cor an antenna to be
highly directive, it must change the normally spherical wave front
into a plane wave front. any highly directive microwave antennas
produce a plane wave front by using a reflector to focus theradiated energy.
Reflectors antennas in one form or other have been in use
since the discovery of electromagnetic wave propagation in 1888 by
H)R$P. Although reflector antennas take many geometrical
configurations, some of the most important shapes are planar,
corner and curved. t has been shown by geometrical optics that if a
beam of parallel rays are incident upon a reflector whose
geometrical shape is a parabola, the incident will converge at a spot
which is known as the focal point. n the same way if appoint source
is placed at the focal /ont the rays will emerge as a parallel beam.
!ince the transmitter is placed at the focal point of parabola the
configuration is known as front feed. Another arrangement that
avoids placing the feed at the focal point is known as a cassegrain
feed.cassegrian showed that incident parallel rays can be focused to
a point by utilizing two reflectors. $o accomplish this main reflector
must be a parabola, the secondary reflector must be a hyperbola
and the feed placed along the a7is of the parabola usually at or near
verte7.
$he day in, day out need of reflectors for use in radio
astronomy, micro wave communication and satellite tracking
resulted in spectacular progress in the development of sophisticated
design, analytical, fabrication techniues. n case of a parabolic
reflector the illumination over the aperture is entirely dependent on
the feed radiation characteristics. !ince the aperture efficiency,
gain, side lobe levels and beamwidth are the most important
parameters and are entirely dependent on the aperture illumination
characteristics, the feed pattern plays an important role in the
design and analysis of parabolic reflector.
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3.1 S',%',(
$he reflector dish can be solid, mesh or wire in construction
and it can be either fully circular or somewhat rectangular
depending on the radiation pattern of the feeding element. !olid
antennas have more ideal characteristics but are troublesome
because of weight and high wind load. esh and wire types weigh
less, are easier to construct and have nearly ideal characteristics if
the holes or gaps are kept under 11< of the wavelength.&ire6type
parabolic antenna "&i6Ci &+A* antenna at 2,4(hz#. -riented to
provide horizontal polarization= the reflector wires and the feed
element are both horizontal. $his antenna has a greater e7tent in
the vertical plane and hence, a narrower beamwidth in that plane.
$he feed element has a wider beam in the vertical direction than the
horizontal and hence matches the reflector by illuminating it
fully.ore e7otic types include the off6set parabolic antenna,
(regorian and Fassegrain types. n the off6set, the feed element is
still located at the focal point, which because of the angles utilized,
is usually located below the reflector so that the feed element and
support do not interfere with the the main beam. $his also allows for
easier maintenance of the feed, but is usually only found in smaller
antennas.$he /ARA%-+F R)C+)F$-R is most often used for high
directivity.
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Cig 3.1 simple parabolic antennas
Cig 3.2 Fylindrical paraboloid Cig 3.3 Forner reflctor
3.2 R(f(%'+, ,##'+&$
icrowaves travel in straight lines as do light rays. $hey can
also be focused and reflected 'ust as light rays can, as illustrated by
the antenna shown in figure. A microwave source is placed at focal
point C. $he field leaves this antenna as a spherical wave front. As
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each part of the wave front reaches the reflecting surface, it is
phase6shifted 18< degrees. )ach part is then sent outward at an
angle that results in all parts of the field traveling in parallel paths.
%ecause of the special shape of a parabolic surface, all paths from Cto the reflector and back to line Q are the same length. $herefore,
when the parts of the field are reflected from the parabolic surface,
they travel to line Q in the same amount of time.
.
Cig 3.4= /arabolic reflector radiations C6focus of paraboloid.
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PARABOLIC REFLECTOR
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CHAPTER 4
PARABOLIC REFLECTOR
A parabolic reflector, known as a parabolic dish or a parabolic
mirror, is a reflectivedevice, commonly formed in the shape of a
paraboloid of revolution. /arabolic reflectors can either collect or
distribute energysuch as light, sound, or radio waves.
$he parabolic reflector functions due to the geometricproperties of the paraboloid shape= if the angle of incidence to the
inner surface of the collector euals the angle of reflection, then any
incoming ray that is parallel to the a7is of the dish will be reflected
to a central point, or >focus>. %ecause many types of energy can be
reflected in this way, parabolic reflectors can be used to collect and
concentrate energy entering the reflector at a particular angle.
!imilarly, energy radiating from the >focus> to the dish can betransmitted outward in a beam that is parallel to the a7is of the
dish.
4.1 APPLICATIONS
Gohn Hadleyintroduced parabolic mirrors into practical
astronomyin 1:21 when he used one to build a reflecting telescope
with very little spherical aberration. %efore that, telescopes used
spherical mirrors. +ighthouses also commonly used parabolic
mirrors to collimate a point of light from a lantern into a beam,
before being replaced by more efficient fresnel lenses in the 1;th
century. $he most common modern applications of the parabolic
reflector are in satellite dishes, telescopes "including radio
telescopes#, parabolic microphones, and many lightingdevices such
as spotlights, car headlights, /AR Fansand +) housings.
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http://en.wikipedia.org/wiki/Mirrorhttp://en.wikipedia.org/wiki/Paraboloid_of_revolutionhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Lighthttp://en.wikipedia.org/wiki/Soundhttp://en.wikipedia.org/wiki/Radio_wavehttp://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/John_Hadleyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Reflecting_telescopehttp://en.wikipedia.org/wiki/Spherical_aberrationhttp://en.wikipedia.org/wiki/Sphericalhttp://en.wikipedia.org/wiki/Lighthousehttp://en.wikipedia.org/wiki/Fresnel_lenshttp://en.wikipedia.org/wiki/Satellite_dishhttp://en.wikipedia.org/wiki/Telescopehttp://en.wikipedia.org/wiki/Parabolic_microphonehttp://en.wikipedia.org/wiki/Electric_lighthttp://en.wikipedia.org/wiki/Spotlighthttp://en.wikipedia.org/wiki/Headlighthttp://en.wikipedia.org/wiki/Stage_lighting_instrument#PAR_lightshttp://en.wikipedia.org/wiki/Mirrorhttp://en.wikipedia.org/wiki/Paraboloid_of_revolutionhttp://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Lighthttp://en.wikipedia.org/wiki/Soundhttp://en.wikipedia.org/wiki/Radio_wavehttp://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/John_Hadleyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Reflecting_telescopehttp://en.wikipedia.org/wiki/Spherical_aberrationhttp://en.wikipedia.org/wiki/Sphericalhttp://en.wikipedia.org/wiki/Lighthousehttp://en.wikipedia.org/wiki/Fresnel_lenshttp://en.wikipedia.org/wiki/Satellite_dishhttp://en.wikipedia.org/wiki/Telescopehttp://en.wikipedia.org/wiki/Parabolic_microphonehttp://en.wikipedia.org/wiki/Electric_lighthttp://en.wikipedia.org/wiki/Spotlighthttp://en.wikipedia.org/wiki/Headlighthttp://en.wikipedia.org/wiki/Stage_lighting_instrument#PAR_lights -
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/arabolic reflectors suffer from an aberrationcalled coma.
$his is primarily of interest in telescopes because most other
applications do not reuire sharp resolution off the a7is of the
parabola.$he -lympic Clamehas been lit using a parabolic reflectorconcentrating sunlight. A parabolic reflector pointing upward can be
formed by rotating a reflective liuid, like mercury, around a vertical
a7is. $his makes the liuid mirror telescopepossible.
P#,#"+% #&'(&$
$he parabolic antenna is a high6gain reflector antenna used
for radio, television and data communications, and also for
radiolocation "RAAR#, on the 0HC and !HC parts of the
electromagnetic spectrum. $he relatively short wavelength of
electromagnetic "radio# energy at these freuencies allows
reasonably sized reflectors to e7hibit the very desirable highly
directional response for both receiving and transmitting.
/arabolic antennas at the Lery +arge Array Radio $elescope in*ew e7ico, 0!A.A typical parabolic antenna consists of a parabolic
reflector illuminated by a small feed antenna.$he reflector is a
metallic surface formed into a paraboloidof revolution and "usually#
truncated in a circular rim that forms the diameter of the antenna.
$his paraboloid possesses a distinct focal pointby virtue of having
the reflective property of parabolasin that a point light source at
this focus produces a parallel light beam aligned with the a7is of
revolution.
$he feed antenna is placed at the reflector focus. $his antenna is
typically a low6gain type such as a half6wave dipole or a small
waveguidehorn. n more comple7 designs, such as the Fassegrain
antenna, a sub6reflector is used to direct the energy into the
parabolic reflector from a feed antenna located away from the
primary focal point. $he feed antenna is connected to the
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http://en.wikipedia.org/wiki/Aberration_in_optical_systemshttp://en.wikipedia.org/wiki/Coma_(optics)http://en.wikipedia.org/wiki/Olympic_Flamehttp://en.wikipedia.org/wiki/Sunlighthttp://en.wikipedia.org/wiki/Liquid_mirror_telescopehttp://en.wikipedia.org/wiki/Radarhttp://en.wikipedia.org/wiki/Ultra_high_frequencyhttp://en.wikipedia.org/wiki/Microwavehttp://en.wikipedia.org/wiki/Parabolic_reflectorhttp://en.wikipedia.org/wiki/Parabolic_reflectorhttp://en.wikipedia.org/wiki/Feed_hornhttp://en.wikipedia.org/wiki/Paraboloidhttp://en.wikipedia.org/wiki/Focal_pointhttp://en.wikipedia.org/wiki/Parabola#Reflective_Property_of_Parabolashttp://en.wikipedia.org/wiki/Low-gain_antennahttp://en.wikipedia.org/wiki/Dipole_antennahttp://en.wikipedia.org/wiki/Waveguidehttp://en.wikipedia.org/wiki/Horn_(telecommunications)http://en.wikipedia.org/wiki/Cassegrain_antennahttp://en.wikipedia.org/wiki/Cassegrain_antennahttp://en.wikipedia.org/wiki/Aberration_in_optical_systemshttp://en.wikipedia.org/wiki/Coma_(optics)http://en.wikipedia.org/wiki/Olympic_Flamehttp://en.wikipedia.org/wiki/Sunlighthttp://en.wikipedia.org/wiki/Liquid_mirror_telescopehttp://en.wikipedia.org/wiki/Radarhttp://en.wikipedia.org/wiki/Ultra_high_frequencyhttp://en.wikipedia.org/wiki/Microwavehttp://en.wikipedia.org/wiki/Parabolic_reflectorhttp://en.wikipedia.org/wiki/Parabolic_reflectorhttp://en.wikipedia.org/wiki/Feed_hornhttp://en.wikipedia.org/wiki/Paraboloidhttp://en.wikipedia.org/wiki/Focal_pointhttp://en.wikipedia.org/wiki/Parabola#Reflective_Property_of_Parabolashttp://en.wikipedia.org/wiki/Low-gain_antennahttp://en.wikipedia.org/wiki/Dipole_antennahttp://en.wikipedia.org/wiki/Waveguidehttp://en.wikipedia.org/wiki/Horn_(telecommunications)http://en.wikipedia.org/wiki/Cassegrain_antennahttp://en.wikipedia.org/wiki/Cassegrain_antenna -
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associated radio6freuency "RC# transmittingor receiving euipment
by means of a coa7ial cabletransmission lineor hollow waveguide.
4.2 IDEAL CONDITIONS OF PARABOLIC REFLECTOR
1.&hen a bunch of parallel beams are reflected towards parabolic
reflector, then after reflecting these beams are colliminated at a
single point called C-F0!.
2.Any beam from the focus is reflected towards reflector, after
reflecting the beams travels parallel to the a7is of reflector.
3.parabolic reflector converts the spherical wave in to plane wave.
4.$he distance travelled by a any ray from focus to the parabola and
by reflection to the plane perpendicular to the parabola a7is is the
same for all rays no matter what angle they eminate from the
focus.
%ut in practical these are not possible.%ecause of losses occuringdue to spill over,tappering,illumination losses.ue to these losses
the apperture efficiency decreases and illuminated energy wasted.
4.3 CHARACTERISTICS OF PARABOLIC REFLECTOR
1. fd ratio "focal length to diameter ratio#
2. (ain
3. Radiation pattern
4. $otal Aperture efficiency
5. llumination and its losses
9. ($ ratio
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4.3.1 f/D ,#'+ 6f+%# (&!'* '+ #('(, ,#'+7
-ne of the important parameter to measure the performance
of the parabolic reflector. t determines how much power illuminated
towards it. All parabolic dishes have the same parabolic curvature, but
some are shallow dishes, while others are much deeper and more like
a bowl. $hey are 'ust different parts of a parabola which e7tends to
infinity. A convenient way to describe how much of the parabola is
used is the S ratio, the ratio of the focal length S to the diameter of
the dish. All dishes with the same f ratio reuire the same feed
geometry, in proportion to the diameter of the dish. $he values of S
ratios, typically from
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F! 4.1 V#,#'+&$ +f '*( '*('# )#( 5'* '*( f+%# (&!'* f+,
# f9( #('(,$ +f 0.2: 0.4: 1.;: #& 3
0 20 40 600
2
4
6
--->f(meters)
d=0.2 meters
0 20 40 600
5
10
15
--->f(meters)
d=0.4 meters
0 20 40 600
20
40
60
angle theta(in degrees)
-->f(meters)
d=1.5 meters
0 20 40 600
50
100
angle theta(in degrees)
--->f(meters)
d=3 meters
F! 4.2 V#,#'+&$ +f '*( '*('# )#( 5'* '*( #('(,$ f+, #
f9( f+%# (&!'*$ +f 0.1: 0.2;: 1.;: #& 3
0 20 40 600
0.05
0.1
0.15
0.2
--->d(meters)
f=0.1 meter
0 20 40 600
0.2
0.4
0.6
0.8
--->d(meters)
f=0.25 meters
0 20 40 600
10
20
30
--->angle theta(in degrees)
-->d(meters)
f=1.5 meters
0 20 40 600
50
100
150
--->angle theta(in degrees)
--->d(meters)
f=3 meters
$he general formula for finding f to ratio is given by an
antenna placed at the focal point of a parabolic reflector is said toilluminate the parabolic reflector. $he antenna has a beamwidth
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which is the how wide an angle the antenna would make if it were
radiating a beam of radio waves. $he beamwidth is a property of the
antenna itself and is the same regardless if the antenna is used for
receiving or transmitting. n designing a parabolic antenna, theantenna needs to properly illuminate its parabolic reflectorO that is,
the beamwidth of the antenna needs to match the f ratio of the
parabolic reflector. -therwise, the antenna of an over illuminated
parabolic reflector would receive a noise from behind the parabolic
reflector. +ikewise, an under illuminated parabolic reflector does not
use its total surface area to focus a signal on its antenna.
#2
cot"25.<
D
f=
&here f6focal length
6diameter
T 6 subtend angle
As U varies f become varies.
$he different relations between f, , V as shown in above plots
4.3.2 G#& +f # #,#"+% ,(f(%'+,
(ain @"ma7imum radiation intensity in a given direction #
"ma7imum radiation intensity from isotropic antenna direction #.
0sing the formula for the area of a circle, the area of the aperture of
a parabolic reflector is
#4
M"
2DA =
$his area is used in calculating the gain of a parabolic
reflector. $he gain ( of a parabolic reflector is proportional to the
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ratio of the area of the aperture to the suare of the wavelength l of
the incoming radio waves. W is the efficiency of the parabolic
reflector and has a practical value of 5
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4.3.4 T+'# (ff%(&%
$he percentage of signal power transmitted or received
compared to the theoritical power from the proportion of a sphere
covered by the antennas beam.
Cor an antenna with a circular aperture or reflector of a
diameter"# and geometric surface" #4
M"
2DA = ,then aperture
efficiency is where is the efficiency of the antenna.
$he efficiency of the antenna is the product of several factors
which take account of the illumination law,spillover loss,surface
impairments,resistive and mismatch losses etc.
............YYY fZsi nnnnn =
$he '+& (ff%(&%6&7 specifices the illumination
law of the reflector with respect to uniform illumination. 0niform
illumination leads to high level of secondary lobes.A compromise is
achieved by attenuating the illumination at the reflector
boundaries"aperture at the taper#.n the case of cassegrain antenna
the best compromise is obtained for an illumination attenuation at
the boundaries of 1< to 12 db which leads to an illumination
efficiency& of the order of ;1X.
$he $+)(, (ff%(&% &$ is defined as the ratio of the
energy radiated by the primary source which is intercepted by the
reflector to the total energy radiated by the primary source.$he
difference constitutes the spillover energy.$he larger the angle
under which the reflector is viewed from the source,the greater the
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spillover efficiency.However,for a given source radiation pattern,the
illumination level at the boundaries becomes less with large values
of view angle and the illumination efficiency collapses.A
compromise leads to spillover efficiency of the order of 8
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3. Cocal point error
4. echanical support
$he above parameters decrease efficiency.Hence we must decrease
this loss.n the definition section above, derived from the Cederal
!tandard, and implies that the aperture efficiency is
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F! 4.4 T*( )#,#'+& +f '*( #(,',( (ff%(&% 5'* '*(
'*('# #$ # f&%'+& +f '*( f(( #''(,& !)(& " 26&
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0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
---->f(meters)
---->aperture
efficiency
F! 4.> V#,#'+& & '*( #(,',( (ff%(&% 5'* '*( %*#&!(
& '*( f/ ,#'+ f+, '*( f(( #''(,& !)(& " 26&
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0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
--->diameter(meters)
---->aperture
efficiency
#7 I'+& #& '$ +$$($
!ome of the difficulties found in real antennas are easier to
understand when considering a transmitting antenna, but are also
present in receiving antennas, since antennas are reciprocal. -ne
difficulty is finding a point source, since any antenna, even a half6wave
dipole at 1< (Hz, is much bigger than a point. )ven if we were able to
find a point source, it would radiate eually in all directions, so the
energy that was not radiated toward the reflector would be wasted.
$he energy radiated from the focus toward the reflector illuminates
the reflector, 'ust as a light bulb would. !o we are looking for a point
source that illuminates only the reflector.
llumination
!pillover loss
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F! 4. &f+, f(( '+&
F! 4.10 D$* '+& 5'* )#,+$ '+& '#(,$
63": >": 10": 20"7
$he above figures represent the illumination and its spillover
losses. ifferent edge tapers produce different amounts ofillumination loss and spillover loss. A small edge taper result in
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larger spillover loss, while a large edge taper reduces the spillover
loss at e7pense of the increased illumination loss.
F! 4.11 $* 6PARABOLIC REFLECTOR7 '+& 5'*
)#,+$ f/D ,#'+$ 6f/D0.@;: 0.>;: 0.;: 0.4;7
"7S
(',
+f E
#&(
#&
H
P#&(
-n
paper,we can
only
depict
radiation in one plane. Cor simple antenna with linear polarization,
like a dipole, this is all we really care about. A dish however, is threedimensional, so we must feed it uniformly in all planes. $he usual
plane for linear polarization is the )6plane, while the plane
perpendicular to it called H6plane. 0nfortunately, most antennas not
only have different radiation patterns in the )6plane and H6planes, but
also have different phase centers in each plane, so both phase centers
cannot be at the focus.
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%7 F+%# L(&!'* E,,+,
$he critical focal length suggests that it is crucial to have the phase
center of the feed e7actly at the focus of the reflector. !ince the
phase center is rarely specified for a feed horn, we must determine it
empirically, by finding the ma7imum gain on a reflector with known
focal length. f we are using a feed horn with different phase centers
in the )6 and H6planes, we can also estimate the loss suffered in each
plane by referring to Cigure. +ateral errors in feed horn position are far
less seriousO small errors have little effect on gain, but do result in
shifting the beam slightly off bore sight.
7 M(%*#&%# $+,'
$here are two critical mechanical problems= mounting the feed horn
to the dish, and mounting the dish to the tripod. ost small dishes
have no backing structure, so the thin aluminum surface is easily
deformed. $he mounting structure for the feed horn is in the RC field,
so we must minimize the blockage it causes. &e do this by keepingthe support strut diameter small, by using insulating materials, and by
mounting the struts diagonally, so they aren?t in the plane of the
polarization. Ciberglass is a good materialO plant stakes or bicycle
flags are good sources.
4.3.; G/T 6GAIN TO TEMPERATURE RATIO7
&hen an antenna is receiving a signal from space, like a satellite or
)) signal there is a little background noise emanating from the sky
compared to the noise generated by the warm 3
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FEEDS FOR THE
PARABOLIC REFLECTOR
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CHAPTER ;
FEEDS FOR THE PARABOLIC REFLECTOR
;.1 FEED
Ceed is a source element in which all the energy is situated
at one point called feed element. (enerally the feed is placed at the
focus. ue to this we achieved high gain and sharp pencil beam
pattern. $he actual ?antenna? in a parabolic antenna, that is, the
device that interfaces the transmission line or waveguide containing
the radio6freuency energy to free space, is the feed element. $he
reflector surface is entirely passive. $his feed element should
usually be at the center of the reflector at the focal point of that
dish. $he focal point is the point where all reflected waves will be
concentrated. $he feed line connects the antenna to the receiver,
transmitter, or transceiver. $he line transfers radio6freuency "RC#
energy from a transmitter to an antenna, andor from an antenna to
a receiver, but, if operating properly, does not radiate or intercept
energy itself.
$he radiation from the feed element induces a current flow in
the conductive reflector surface which, in turn, re6radiates in the
desired direction, perpendicular to the directri7 plane of the
paraboloid. $he feed element can be any one of a multitude of
antenna types. &hichever type is used, it must e7hibit a directivity
that efficiently illuminates the reflector and must have the correct
polarization for the application 66 the polarization of the feed
determining the polarization of the entire antenna system. $he
simplest feed is a half6wave dipole which is commonly used at lower
freuencies, sometimes in con'unction with a closely coupled
parasitic reflector or >splash plate>. At higher freuencies a horn6
typebecomes more feasible and efficient. $o adapt the horn to a
43
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coa7ial antenna cable, a length of waveguide is used to effect the
transition.
F! ;.1 D#!,#$ +f # f+%# f(( #,#"+% ,(f(%'+, #&'(&
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D#!,# +f # f+%# f(( #,#"+% ,(f(%'+, +, $*
#&'(&with case f a feed is used as the source of transmission,
energy will be radiated from the antenna into space as well as
toward the reflector. )nergy which is not directed toward theparaboloid has a wide6beam characteristic which will destroy the
narrow pattern of the parabolic reflector. However, a
H)!/H)RFA+ !H)+ "not shown# may be used to direct most of
the radiation toward the parabolic surface and thus prevent the
destruction of the narrow pattern. irect radiation into space is
eliminated, the beam is made sharper, and more power is
concentrated in the beam. &ithout the shield, some of the radiated
field would leave the radiator directly. !ince this part of the field
that would leave the radiator would not be reflected, it would not
become a part of the main beam and could serve no useful purpose.
;.2 DIPOLE FEED
ipole antenna, developed by Heinrich Rudolph Hertz around
1889, is an antenna with a center6fed driven element for
transmitting or receiving radio freuency energy. A dipole antenna
is a straight electrical conductor measuring 12 wavelength from
end to end and connected at the center to a radio6freuency "RC#
feed line. $his antenna, also called a doublet, is one of the simplest
types of antenna, and constitutes the main RC radiating and
receiving element in various sophisticated types of antennas. $he
dipole is inherently a balanced antenna, because it is bilaterallysymmetrical.
deally, a dipole antenna is fed with a balanced, parallel6wire
RC transmission line. However, this type of line is not common. An
unbalanced feed line, such as coa7ial cable, can be used, but to
ensure optimum RC current distribution on the antenna element and
in the feed line, an RC transformer called a balun"contraction of the
words >balanced> and >unbalanced># should be inserted in the
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system at the point where the feed line 'oins the antenna. Cor best
performance, a dipole antenna should be more than 12 wavelength
above the ground, the surface of a body of water, or other
horizontal, conducting medium such as sheet metal roofing. $heelement should also be at least several wavelengths away from
electrically conducting obstructions such as supporting towers,
utility wires, guy wires, and other antennas.
ipole antennas can be oriented horizontally, vertically, or at
a slant. $he polarization of the electromagnetic field ")# radiated
by a dipole transmitting antenna corresponds to the orientation of
the element. &hen the antenna is used to receive RC signals, it is
most sensitive to ) fields whose polarization is parallel to the
orientation of the element. $he RC current in a dipole is ma7imum at
the center "the point where the feed line 'oins the element#, and is
minimum at the ends of the element. $he RC voltage is ma7imum at
the ends and is minimum at the center.$hese antennas are the
simplest practical antennas from a theoretical /oint of view.
F! ;.2 $( *#f 5#)( +( #&'(&
A short dipole is a physically feasible dipole formed by two
conductors with a total length very small compared with the
wavelength . $he two conducting wires are fed at the centre of the
dipole. &e assume the hypothesis that the current is ma7imal at the
centre "where the dipole is fed# and that it decreases linearly to be
zero at the ends of the wires. *ote that the direction of the current
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is the same in both the dipole branches 6 to the right in both or to
the left in both.
F! ;.3 R##'+& #''(,&$ +f $( +(
)mission is ma7imal in the plane perpendicular to the dipole and
zero in the direction of wires, that is, the current direction. $he
emission diagram is circular section torus shaped "left image# with
zero inner diameter. n the right image doublet is vertical in the
torus centre.
F! ;.4 UHF H#f 5#)( +(
;.3 DIPOLE CHARACTERISTICS
;.3.1 F,(-(&% )(,$$ (&!'*
ipoles that are much smaller than the wavelength of the
signal are called Hertzian, short, or infinitesimal dipoles. $hese have
a very low radiation resistance and a high reactance, making them
4:
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inefficient, but they are often the only available antennas at very
long wavelengths. ipoles whose length is half the wavelength of
the signal are called half6wave dipoles, and are more efficient. n
general radio engineering, the term dipole usually means a half6wave dipole "center6fed#.A half6wave dipole is cut to length
according to the formula DftE, where l is the length in feet and f is
the center freuency in Hz . $his is because the impedance of the
dipole is resistive pure at about this length. $he metric formula is
DmE, where l is the length in meters. $he length of the dipole
antenna is about ;5X of half a wavelength at the speed of light in
free space.
;.3.2 R##'+& #''(,& #& !#&
ipoles have a toroidal "doughnut6shaped# reception and
radiation pattern where the a7is of the toroid centers about the
dipole. $he theoretical ma7imum gain of a Hertzian dipole is 1< log
1.5 or 1.:9 d%i. $he ma7imum theoretical gain of a N26dipole is 1l/2
-> l /4
-->l
DIPOLE BEAM EFFICIENCY
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0.2
0.4
0.6
0.8
1
3
1
240
90
270
1 0
300
150
3
180
tend angle(radians
intensity
0.2
0.4
0.6
0.8
10
40
9
27030
0
33
180
tend angle(radians
ntens
0 0.5 1 1.5 2 2.5 3 3.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
theta
beame
fficiency
theta (vs)dipole beam efficiency
DIPOLE MULTIPLICATION PATTERNS
*@1 *@3"number of array
elements#
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0.2
0.4
0.6
0.8
3
10
9
27
0
33
180
i l i l i li i
subtend angle(ra ians
i
i
0 1 2 3 4 5 6 7-
- .
.6
.4
-0.2
0
.2
.
.
.
subtend angl
--*>l/4
->l/2
-->l
0.2
0.4
0.6
0.8
0
240
27
300
3
*@5 *@;"array
elements#
INTENSITY VARIATIONS BY CHANGING SPACING BETEEN
DIPOLES
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1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
.5
1
1. 5
2
2. 5
3
.
horn width(cm)
niu
e
o
plane
0 0 .5 1 1 .5 2 2.5 3 3.50
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
0. 8
0. 9
1
theta
beam
efficiency
theta (vs )squrecorner beam efficiency
HORN FEED RADIATION PATTERN f/D 6VS7 APERTURE
6IDTH ISE 7 EFFICIENCY
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2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4
.5
1
1. 5
2
2. 5
.
orn length(cm
iu
plne
f/D RATIO
0 0.5 10
2
4
6
angle theta
-->
f1
f vs theta if d=0.2
0 0.5 10
50
100
150
angle theta
-->
f2
f vs theta if d=4
0 0.5 10
500
1000
1500
angle theta
-->
f3
f vs theta if d=50
0 0.5 10
1000
2000
3000
angle theta
-->
f4
f vs theta if d=100
:;
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
f/d
apertureefficiency
f/d vs eap
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0 2 4 6 8 10 12 142
1
0
1
2
ngl
ieli
ne
i
i l li l
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16
i i
coor
inate
l
0 2 4 6 8 10 12 14 16
0. 2
.4
.6
0. 8
1
1. 2
.4
.6
1. 8
point on the x-axis
ii
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.5
1
.
2
.5
310
-
pertur
in
aper ure vs gain
PARABOLIC REFLECTOR SIMPLE
PARABOLA RADIATION PATTERN
PARABOLA CHARACTERISTICS APERTURE VS GAIN
6ESSENTRICITY7
FINAL
RESULTS6AFTER REFLECTING ON THE
PARABOLIC SURFACE7
DIPOLE RADIATION PATTERN ON THE DIRECTION OF
PARABOLA AXIS
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0 0.5 1 1.5 2 2.5 3 3.5
.
.02
0.03
0.04
0.05
0.06
0.07
. 8
.
.
theta1(subtend angle)
n
a
e
p
0 0.5 1 1.5 2 2.5 3 3.5
0
00
15 0
20 0
00
0
theta1(radians)
iel
in
ensiy
i l l i i
0 0.5 1 1 .5 2 2.5 3 3.5
.0 1
.0 2
0.03
0.04
0.05
0.06
0.07
.0 8
.0 9
.
theta1(subtend angle)
i
l
i
l
SQUARE CORNER
RADIATION PATTERN ON SQUARE CORNER
PATTERN ALONG THETA
THE DIRECTION OF PARABOLA AXIS
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2 3 4 5 6 7 8 9 10
00
20 0
40 0
50 0
00
00
00
theta1
il
i
i
i l l i i
1 2 3 4 5 6 7 8 9
00
300
400
500
0
0
0
phy1
ieli
nensi
i l l i i
0 0.5 1 1.5 2 2.5 3 3.5
00 0
2000
3000
00 0
00 0
phy1
il
i
i
i l l i i
0 0.5 1 1.5 2 2. .
00 0
00 0
3000
00 0
00 0
0
btend angl
ili
i
i l l i i
HORN PATTERN ALONG HORN PATTERN ALONG
THETA DIRECTION PHY DIRECTION
APERTUREAPPROXIMATION
METHOD DIPOLE FEED
ALONG THETA DIRECTION ALONG PHY
DIRECTION
SQUARE CORNER FEED
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2 3 4 5 6 7 8 9 1 00
0 0 0
0 0 0
0 0
8 0 0 0
1 0 0 0 0
2 0 0 0
0 0 0
0 0 0
0 0
s u b t e n d a n g l e
0 0.5 1 1.5 2 2.5 3 3.5
00 0
2000
3000
00 0
00 0
phy1
il
i
i
i l l i i
0 0.5 1 1.5 2 2.5 .
00 0
00 0
3000
00 0
00 0
00
btend angl
il
i
i
i l l i i
1 2 3 4 5 6 7 8 9
0 0 0
0 0 0
0 0
8 0 0 0
1 0 0 0 0
4 0 0 0
0 0 0
0 0 0
p h y 1
i
l
i
i
i e l a l o n g p y i re c i
ALONG THETA DIRECTION ALONG PHY DIR
HORN FEED
ALONG THETA DIRECTION ALONG PHY
DIRECTION
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0 0.5 1 1.5 2 2.5 3 3.5
10
15
subtend angle(radians)
ie
i
i
i i i
0 0 .5 1 1.5 2 2 .5 3 3.5- 0
5
-
-5
subtend ang l
ir
ii
ir i i l ir i
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
10
15
20
subtend angle(radians)
e
n
ens
y
0.8 0 .9 1 1 .1 1 .2 1 .3 1 .4 1 .5 1 .610
0
su b te n d a n g le
r l r
DIPOLE FEED INTENSITY6"7
DIRECTIVITY6DIPOLE7
HORN FEED INTENSITY 6B7
HORN DIRECTIVITY
APERTURE APPROXIMATION METHOD
DIPOLE FEED INTENSITY 6B7DIRECTIVITY
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0 0.5 1 1.5 2 2.5 3 3.5-
0
5
0
0
subtend ang l
i
ii
i i i l i i
0 0.5 1 1.5 2 2.5 3 3.55
25
30
5
subtend angle(radians)
i
ensiy
b
i i l i i
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
10
5
subtend angl
i
ii
i i i l i i
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
5
30
5
subtend angl
i
i
i i l i i
HORN FEED INTENSITY6B7 DIRECTIVITY
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ANALYSIS
Crom dipole feed radiation patterns , as length increases from
N4 to N the radiation intensity increases and the beam width
decreases. n the dipole multiplication patterns as the length increases
the radiation intensity increases the beam width become
decreases and the side lobes increases.Cor *@1,3,5,; cases
observed.
$he beam efficiency of dipole increases from < to 1 as
increases subtend angle for a given half wave dipole as
isotropic source.
Crom suarecorner feed radiation patterns , as length
increases from N2 to 2N the radiation intensity increases and
the beam width decreases.%ut the ma7imum intensity
decreases.
$he beam efficiency of suare corner increases from < to 1 as
increases subtend angle for a given half wave dipole as
isotropic source.
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Crom horn feed radiation patterns , as length increases from
1 to :.5 and width varies from
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CONCLUSIONS
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CONCLUSION
$he fundamental antenna concepts and a brief introduction
to the types of feeds have been discussed. Analysis of the parabolic
reflector characteristics like f, gain, radiation patterns has been
done and the corresponding results were plotted. $he primary
radiation patterns of each feed like dipole, suarecorner and hornwere calculated and then the far field pattern of each feed was
calculated by using general and aperture appro7imation methods.
ntensity and directivity of feeds were compared.
Crom results it can be concluded Horn feed has more intensity
and more directivity among three feeds. 0sing Aperture
appro7imation method we achieved more intensity and more
directivity than general method.
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BIBLIOGRAPHY
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