ece-d antenna 4
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Antenna
Terminologies & Measurements
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Radiation pattern
A trace or a Graphical representation of power, gain, intensity, fieldstrength in a particular space co-ordinates
By keeping two co-ordinates constant, and varying the third, thepatterns can be drawn.
For example:
r and are kept constant, for various , the power at a far-fielddistance can be
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Polar plot
Most convenient plot is Polar plot for radiation graphs.
will be called as Elevation angle (o to 180)
as Azimuthal angle (0 to 360)
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Isotropic and Directional
Isotropic: a lossless antenna having equal radiation in all direction, like circularradiation pattern
Isotropic antenna is an ideal, unrealizable antenna. Practical antennas areDirectional
Directional: The maximum power or gain will be in particular direction of or
Omni-directional: Its special type in Directional.
In azimuthal or Elevation angles the antenna is isotropic and directional in either.
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Radiation pattern - Lobes A quantitative portions of radiation pattern are
Lobes Major radiated energy bounded by Major-
Lobe, and others are Minor Lobes.
Minor lobes are still classified into Side lobesand Back lobes
Between two lobe, the zero radiation points arecalled Null points
Major lobe
Major lobes
Back lobe
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Null ponits
Each Radiation pattern will have many numberof lobes, so many number of Null points willbe there.
With symmetry, they are refered as 1st , 2nd ,..Null ponits
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Beam Level
Maximum power is taken by Major lob, and maximum
power direction also within Major lob, obviously. Our aim also, to get maximum power within Major lobe
To define the side lobes: How smaller the side lobes areor which level they are with respect to major lobe,called Side lobe level or Side lobe ratio
As much as bigger theratio, that much directional
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Half Power Beam width
In Major lobe itself, over how much angle at leasthalf of the power is radiated?, called Half powerBeam width (HPBW).
For example, it maximum power radiated is 12dB,place the 9dB point (ie 12dB-3dB), make a arc.
The angle difference or range the arc occupiesover the major lobe is HPBW.
Max
3dB point
HPWB
Simply as minimum HPBW,
that much directive.
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First Null Beam width
On both side of symmetry, the anglebetween first null points is called FNBW.
FNBW will be always bigger than HPBW.
This is useful measure to define the Major
Lobe
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Compare!
For same Yagi-Uda antenna, different radiation pattern got, which is high directive??!
http://images.google.co.in/imgres?imgurl=http://www.pignatti.it/images/Wireless/Yagi2.jpg&imgrefurl=http://www.pignatti.it/Y-2400-02.html&usg=__1-FoIGuo35mrdp3gOihq4lE1VFU=&h=300&w=300&sz=24&hl=en&start=24&um=1&tbnid=AJIJRMc5DxnA9M:&tbnh=116&tbnw=116&prev=/images?q=radiation+pattern+yagi&ndsp=18&hl=en&sa=N&start=18&um=1&newwindow=1 -
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For a /2 antenna
Consider the Magnitude is unity, now find the HPBW
sin
cos2
cos
2E
r
eIj
jkro
Where, over - radiation is constant
2
1
sin
cos2
cos
)2/1(
2
=
1sin
cos2
cos
=
sin1
cos2
cos
=
oo 60or60 =
!!Am I correct? oHPBW 120=
oFNBW 180=
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i.e.
HPBW
FNBW
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Take a problem
A normalized radiation power intensity is
described for an antenna as:
22 sinsin=U
nd the Half power beam width for Azimuthal and Elevation an
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Radian and Steradian
One Radian: the angle for which the vertex isequal to radius (2-D)
For example: A circle of radius R will havecircumference of C=2R, so we can say 2 radfor full circle
One steradian: A solid angle for which the R2
circumference area created by radius R (3-D). So a solid sphere will have 4 sr for full.
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Radiation Power Density If the Electric and Magnetic Field created by an antenna are E
and H, then the average power can be calculated using
poynting vector
Then the power radiated:
( ) [ ]= HEzyxWavg Re2
1,,
[ ] sdHEP srad
= .Re21
rrad
rad a
r
PW
4
2
=
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Radiation Intensity
Power radiated from an antenna per solid angle
Mostly its considered in Far-Field condition
Here U=radiation intensity (W/unit solid angle ) Wrad = radiation density (W/m
2)
From this total power can be obtained,
Where, d is called Unit solid angle = sin.d.d
radWrU2=
ddUUdPrad ..sin
0
2
0
==
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Problem-A
Find the total power radiated for U=A0sin
ddUUdPrad ..sin
0
2
0
==
ddPrad ..sin2
0
2
0
=
02A=
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Directivity
Also called directive gain, specifies the measure ofdirectionality of an antenna.
Defined as the ratio of the radiation intensity in a givendirection from the antenna to the radiation intensity
averaged over all direction
==
40 radP
U
U
UD
===
4
max
0
maxmax0
radP
U
U
UDD
Umax is the maximum radiation
intensity, found maximum powerdirection
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Problem-B
Calculate the directivity and maximumdirectivity for the Problem-A
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Problem-C If the average power calculated over is
defined as
ravg ar
AW
sin2
20
=
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The Maximum directivity can be approximated as
A is called Beam Solid angle(Sr)
To convert to degrees, divide Aby (180/)
Its further approximated to
HPBWHPBWAD
440 ==
( )
HPBWHPBWHPBWHPBWD
253,41/18042
0 ==
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Problem-D
Calculate the maximum directivity for theradiation intensity, U=A0cos
The radiation exits in upper half alone
(0/2, 02)
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Gain
Measure of efficiency and directivity can explicitly seen in Antennagain.
The Absolute gain is defined as, in the text book, the ratio in theradiation intensity, in the given direction, to the accepted powerof isotropic radiation intensity.
In other words,
Here input power can be related to radiated power by,
ecd is radiation efficiency, a dimensionless quantity.
( )
inP
U
Total
,.4
powerinput
intensityRadiation.4Gain ==
incdrad PeP .=
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Relation between Gain and directivity
While replacing the Input power in-terms of radiated power,
From this relation, we can say the Maximum gain as
Approximated to;(for complicated radiation patterns)
( )
=
radcdP
Ue
,
.4Gain ( ) ( ) ,., DeG cd=
( ) ( ) ,., 00 DeG cd=
HPBWHPBW
G
000,300 =
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Radiation efficiency
Describes the how much of input power is utilized forradiation, since the practical antennas are lossy and notmatched properly they will have efficiency of less thanone.
The total radiation efficiency is
er= reflection efficiency=(1-2)
ec = conduction efficiency ed = dielectric efficiency
For simplicity, the er.ec=ecd, which highly depending in the
area, shape and material of antenna. For lossless antenna,
ecd=1
dcr eeee =0
( )
0
0
ZZ
ZZ
in
in
+
=
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Problem-A
A lossless resonant half-wave dipole antenna, withinput impedance of 73, is to be connected to atransmission line whose characteristics impedanceis 50. If the radiation intensity of that antenna is
U=B0sin3, find the Maximum gain of the antenna.
Soultion
Find D0, and calculate the reflection efficiency using impedance
Since Lossless, ecd=1
Finally calculate in-terms of dB
Answers: D0=1.697, e0=0.965, G0=1.636=2.14dB
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Input Impedance
The radiation of Electric and Magnetic field components aredefined by ratio of voltage to current at the input ofantenna, called Input Impedance, which can be represent as
For a good antenna, the resistance part should be greater than
reactance. The resistance is further classified by Radiationresistance and Loss resistance, as
AAA jXRZ +=
Amount of energy left
Amount of energy stored
LrA RRR +=
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Equivalent circuit
Generator
RL
Rr
XA
Rg, Xg ( )
+
=2
2
8Lr
rTr
RR
RVP
VT
( )
+=
2
2
8Lr
LTL
RR
RVP
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Then, the total power from resistance;
Pr+PL=Induced power by antenna, PC
Here the radiation efficiency can be defined as
( ) ( )
++
+= 2
2
2
2
88Lr
LT
Lr
rT
C RR
RV
RR
RV
P
( )
+=
Lr
T
RR
V 1
8
2
C
rcd
P
Pe ==
powerTotal
powerRadiated
( )Lr
r
RR
R
+=
Clears that When Rr>>RL, the antenna efficiency and gain will be very high
However, the RL is depending on conductance of antenna, defined as
22
oL
P
lR =
land P are length and perimeter of the antenna, respectively, P=2b, where b is radius of wire
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Problem-B
A resonant /2 half-wave dipole antenna is made of
copper(=5.7107S/m) wire. Determine theradiation efficiency of antenna if antenna operates
atf=100MHz and radius of wire is b=310-4.
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