ECE-D Antenna 4

8/14/2019 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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ECE-D Antenna 4