TE4109 Lecture08 10 Fundamental Antenna Parameters 1

8/10/2019 TE4109 Lecture08 10 Fundamental Antenna Parameters 1

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TE4109 Antennas 1

Fundamental Parameters of Antennas

Introduction

Radiation Pattern

Radiation Power Density

Radiation Intensity

Beamwidth

Directivity

Antenna Efficiency

GainBeam Efficiency

Bandwidth

TE4109 Antennas 2

Radiation Pattern (1)

Definition: Representation of the radiation properties of the antennaas a function of angular position

Radiation pattern is usually determined in the far-field region

The spatial (angular) distribution of the radiated power isindependent of distance

Measurement is done at a constant radius from the source

Dependence of radiation pattern

, and

In general, the pattern is described in terms of the normalizedpattern with respect to the maximum value

Amplitude Field Pattern: the trace of the spatial (angular) variationof electric (magnetic) field intensity at a constant radius from theantenna

| ( , ) |E


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TE4109 Antennas 3


Power Pattern: The trace of the angular variation of thereceived/radiated power at a constant radius from the antenna

22| ( , ) | | ( , ) |

EH

=

Normalized Field Pattern:

{ }maxmax

2

10 10 2max max

| ( , ) |~ , max | ( , ) |

| ( , ) | | ( , ) |~ 20log 10log

EE E

E

E E

E E

=

=

Maximum in ,

TE4109 Antennas 4


Normalized Power Pattern:

2 2

2 2max max

2

10 2max

| ( , ) | | ( , ) |

| ( , ) |10log

E H

E H

E

E

=

Note that normalized power pattern and normalized field pattern areidentical when computed and plotted in dB


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TE4109 Antennas 5


0

Spherical CoordinateSystem

A point in space is specified

by 3 components : r, ,and

0 2

Constantine A. Balanis, Antenna Theory, Analysis and Design, 3rd Ed., 2005

TE4109 Antennas 6


The pattern can be a 3-D plot or (both and vary), or a 2-D plot

A 2-D plot is a plane with = constant, or = constant. The planemust contain the patterns maximum

http://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/current_lectures/L04_Param.pdf


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TE4109 Antennas 7


12-Element Yagi-Uda Antenna

4nec2 (Software for Antenna Simulation), available at http://home.ict.nl/~arivoors/

TE4109 Antennas 8


4nec2 (Software for Antenna Simulation), available at http://home.ict.nl/~arivoors/


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TE4109 Antennas 9

Antenna Types

Omnidirectional Antenna Pattern- Nondirectional in azimuth- Directional in elevation

Isotropic Radiator :A hypothetical lossless antenna having equalradiation in all direction

Directional Antenna :An antenna having the property of radiating orreceiving electromagnetic waves more effectively in some directionsthan in others

Omnidirectional Antenna :An antenna having non-directionalpattern in a given plane and a directional pattern in any orthogonalplane


TE4109 Antennas 10

Principal Patterns

For a linearly polarizedantenna, performanceis described in terms of

its principalE- andH-

plane patterns

E-Plane : The plane containing the electric-field vector and thedirection of maximum radiation

H-Plane : The plane containing the magnetic-field vector and thedirection of maximum radiation



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TE4109 Antennas 11

Radiation Pattern Lobes (1)

Radiation Lobe is a portionof the radiation patternbounded by regions ofrelatively weak radiationintensity

Major Lobe is the radiationlobe containing the directionof maximum radiation

More than one major lobesare possible

Minor Lobe is any lobeexcept a major lobe

Side Lobe is a radiation lobein any direction other than

the intended lobeBack Lobe is a radiationlobe which is approximatelyopposite to the main beam


TE4109 Antennas 12

Radiation Pattern Lobes (2)

Minor lobes usually represent radiation in undesired directions Level of minor lobes must be minimized Side Lobe Ratio (often expressed in dB) is a ratio of the power density

in the lobe in question to that of the major lobe

Half-Power Beamwidth (HPBW) :Angle between the two directionsin which radiation intensity is one-half value of the beamFirst-Null Beamwidth (FNBW) :Angle between the two directions inwhich radiation intensity is negligible (null occurs)



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TE4109 Antennas 13

Radian and Steradian (1)

The measure of a plane angle is aradian

For a full circle, 2

2rad 2

C r

r

r

=

= =

Arc Lengthrad

r=

One Radian : The plane angle withits vertex at the center of a circle of

radius rthat is subtended by an arc

whose length is rConstantine A. Balanis, Antenna Theory, Analysis and Design, 3rd Ed., 2005

TE4109 Antennas 14

Radian and Steradian (2)The measure of a solid angle is asteradian (sr)

2

2

, sr

[ sin( ) ] [ ]

dsd

r

r d rd

r

=

=

2

2

4 r

r

=

4 =

For a sphere of radius r

One Steradian : The solid angle withits vertex at the center of a sphere

of radius rthat is subtended by a

spherical surface area equal to thatof a square with each side of length

r( one steradian covers the area

of r2)

2

Area at, sr

r

r =

2ds r d =

sin( )d d d =



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TE4109 Antennas 15

Example 2.1

For a sphere of radius , find the solid angle (in square radians

or steradians) of a spherical cap on the surface of the sphere over

the north-pole region defined by spherical angles of 0 30 ,

0

Ar

1 2 1 2

360 . Do this

(a) exactly.

(b) using , where and are two

perpendicular angular separations of the spherical cap

passing through the north pole.

A

Example: see notes

TE4109 Antennas 16

Radiation Intensity (1)

Radiation Intensity Uin a given direction : The power radiated froman antenna per unit solid angle in that given direction

4, W/sr , Wrad rad

dPU P Ud

d = =

From now on, we will denote the radiated power simply by P

Magnitude of Poynting vector in the far zone and the radiationintensity

2| | ,W/m , WdP

W W Wds Ud ds

= = =

2( , ) ( , , )U r W r =

Power density depends on the distance from the source as 1/r2 (Farfield magnitude depends on ras 1/r)

Radiation intensity Udepends only on the direction (,) but not

on the distance r


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TE4109 Antennas 17

Radiation Intensity (2)

In the far-field zone, the radial field components are negligible, theremaining components are transverse and in phase

| | | |E H=

Far-field Poynting vector has only a radial component, and it is real

221 1 | | | |

2 2r

EW a W W H

= = =

2 22 2 2( , ) | | | ( , , ) | | ( , , ) |

2 2

r rU E E r E r

= = +

Power pattern is actually U(,) and the normalized power patternis 2

2max max

( , ) | |( , )

U EU

U E

= =

TE4109 Antennas 18

ExamplesRadiation intensity and pattern of an isotropic radiator

2

2

2

Radiated Power

( , , ) , W/m4

( , ) .

4( , ) 1

r r

P

PW r a a W

r

PU r W const

U

=

= =

= = =

=

Radiation intensity and pattern of an infinitesimal dipole

In the far-field region, the electric field is give by

2 2 22 2

2

2

( )sin( ) ( , ) sin( )

4

( )| | sin ( )

2 32

( , ) sin ( )

j rI l e

E j Er

r I lU E

U

= =

= =

=


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TE4109 Antennas 19

Example 2.2

20 2

0

The radial component of the radiated power density of an antenna

is given by

sin( ) (W/m )

where is the peak value of the power density, is the usual

sp

r r rW a W a Ar

A

= =

herical coordinate, and is the radial unit vector. Determine

the total radiated power.

ra

Example: see notes

TE4109 Antennas 20

Example 2.3

0

0

The radiation intensity of an antenna is given by

( , ) sin( ) (W/sr)

where is the peak value of the radiation intensity, and is the

usual spherical coordinate.

U A

A

=

Determine the total radiated power.

Example: see notes


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TE4109 Antennas 21

Beamwidth

Resolution capability of an antenna to distinguish between two sources isequal to half of FNBW

Linear Scale2 2( , ) cos ( )cos (3 )U =Constantine A. Balanis, Antenna Theory, Analysis and Design, 3rd Ed., 2005

TE4109 Antennas 22

Example 2.4

2 2

The normalized radiation intensity of an antenna is represented by

( ) cos ( ) cos (3 ), (0 90 , 0 360 ).

Find the

(a) half-power beamwidth HPBW (in radians and degrees) (b) first-null

U =

beamwidth FNBW (in radians and degrees)

Example: see notes


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TE4109 Antennas 23

Directivity (1)

Directivity : Ratio of the radiation intensity in a given direction andthe radiation intensity averaged over all directions

Note that the average radiation intensity is equal to the total power

radiated by the antenna divided by 4

If the direction is not specified, the direction of maximum radiationintensity is implied

[ ]10(dB) 10 log (dimensionless)D D=

( , ) ( , )( , ) 4

( / 4 )

U UD

P P

= =

max

max 0 4

U

D D P= =

Directivity is dimensionless. The maximum directivity is always 1

TE4109 Antennas 24

Directivity (2)

For antennas with orthogonal polarization components, the totaldirectivity is the sum of the partial directivities for any twoorthogonal polarizations

( , ) ( , ) ( , )D D D = +

4 ( , ) 4 ( , )( , )

4 ( , ) 4 ( , )( , )

U UD

P P P

U UD

P P P

= =+

= =+

WhereDandDare partial directivities, which are given by

, power radiated in all directions

contained in , field components, respectively

P

=


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TE4109 Antennas 25

Directivity (3)

Directivity of an isotropic source:

0

0

max

( , ) .4

4

( , )( , ) 4 1

1

PU const U

P U

UD

P

D

= = =

=

= =

=

TE4109 Antennas 26

Directivity (4)

Relationship between directivityD and radiation intensity U

max

2

max4

0 0

2

0 0

max 0 2

0 0

( , ) ( , )

( , ) sin( )

( , )( , ) 4

( , )( , ) 4

( , ) sin( )

14

( , ) sin( )

U U U

P Ud U U d d

UDP

UD

U d d

D D

U d d

=

= =

=

=

= =


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TE4109 Antennas 27

Example 2.5

20 2

0

As an illustration, find the maximum directivity of the antenna

whose radiated power density is given by

sin( ) (W/m )

where is the peak value of the pow

r r rW a W a Ar

A

= =

er density, is the usual

spherical coordinate, and is the radial unit vector. Write an

expression for the directivity as a function of the directional

angles and .

ra

Example: see notes

TE4109 Antennas 28

Example 2.6

Find the maximum directivity of an infinitesimal dipole. Write

an expression for the directivity as a function of the directional

angles and .

Example: see notes


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TE4109 Antennas 29

Beam Solid Angle (1)

Beam Solid AngleA : Solid angle through which all the power ofthe antenna would flow if its radiation intensity Uwere constantand equal to the maximum radiation intensity Umax for all angleswithin A

max AU P =

Proof

max max4

2

4

4max 0 0

( , )sin( )

A

A

A

P Ud U d U

UdUd U d d

U

= = =

= = =

2

0 0

( , )sin( )A U d d

=

TE4109 Antennas 30

Beam Solid Angle (2)

We know that

max 0 2

0 0

14

( , )sin( )

D D

U d d

= =

max 0

4

A

D D

= =


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TE4109 Antennas 31

Directional Patterns (1)

For an antenna with one narrow major lobeand very negligible minor lobes (highlydirective antenna), the beam solid angle canbe approximated from (Kraus)

1 2A r r

1 half-power beamwidth in one plane (rad)r =

2 half-power beamwidth in a plane

at a right angle ot the other (rad)

r =

max 0

1 2

4

r r

D D

= =


TE4109 Antennas 32

Directional Patterns (2)If the beamwidths are known in degrees,then

max 0 21 2

1 2

4 41,253

180

d d

d d

D D

=

1 half-power beamwidth in oneplane (degrees)

d =

2 half-power beamwidth in a plane

at a right angle ot the other (degrees)

d =

Formula of Tai and Pereira

max 0 2 21 2

32ln(2)

r r

D D

=+



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TE4109 Antennas 33

Example 2.7

0

0

The radiation intensity of the major lobe

of many antennas can be adequately

represented by

( , ) cos( )

where is the maximum radiation

intensity. The radiation intensity exist

U B

B

=

s

only in the upper hemisphere (0 /2,

0 2 ), and it is shown in Figure 2.15.

Find the

(a) beam solid angle: exact and

approximate

(b) maximum directivity; exact using

(2-23) and approximate using (2-26). Example: see notes


TE4109 Antennas 34

Omnidirectional Patterns (1)

Some antennas (such as dipoles, loops) exhibit omnidirectionalpatterns

Omnidirectional patterns can be approximated by

( , ) sin ( ) 0 , 0 2nU =

where n represents both integer and noninteger values



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TE4109 Antennas 35

Omnidirectional Patterns (2)


TE4109 Antennas 36

Example 2.8

Design an antenna with omnidirectional amplitude pattern with a

half-power beamwidth of 90 . Express its radiation intensity by

( , ) sin ( ). Determine the value of and attempt to identify

elements

nU n =

that exhibit such pattern. Determine the directivity of theantenna using (2-16a), (2-33a), and (2-33b).

Example: see notes


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TE4109 Antennas 37

Antenna Efficiency (1)

Losses at the input terminals and within the structure of theantenna

Reflection at antenna inputterminal

I2R losses

Conduction loss

Dielectric loss

inP

P


TE4109 Antennas 38


In general, the overall efficiency can be written as

0

cd

r c d

e

e e e e =

2reflection efficiency (1 )

conduction efficiency

dielectric efficiency

voltage reflection coefficient at antenna

input terminal

r

c

d

r

i

e

e

e

V

V

= =

=

=

= =

Usually, ec and edare very difficult to compute. Even bymeasurements they cannot be separated.

2

0 (1 )cde e= radiation efficiency, which is used to

relate gain and directivity

cde =

0

in

Pe

P=


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TE4109 Antennas 39


0 characteristic impedance of lineZ =

antenna input impedanceAZ =

1

1

VSWR

VSWR

=

+

1

1VSWR

+ =

0 1

0Z

AZ

A A AZ R jX= +

fPin

P

rP P

0

0

A

A

Z Z

Z Z

=

+

2

2

10

| |

1 | |

Return Loss (dB)=10 log ( / )

in f r

r

in

f

in

r in

P P P

P

P

P

P

P P

= +

=

=

TE4109 Antennas 40


0 Short CircuitAZ =

0 0

0 0

/ 1 0 11

/ 1 0 1

1 | | 1 1

1 | | 1 1

A A

A A

Z Z Z Z

Z Z Z Z

VSWR

= = = =

+ + +

+ += = =

0Z

AZ

A A AZ R jX= +

fPinP

rP P

http://physics.usask.ca/~hirose/ep225/animation/standing1/images/anim-stwave-11.gif


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TE4109 Antennas 41


0/ 1/ 4AZ Z =

0 0

0 0

/ 1 1/ 4 1 0.6/ 1 1/ 4 1

1 | | 1 0.6 1.64

1 | | 1 0.6 0.4

A A

A A

Z Z Z ZZ Z Z Z

VSWR

= = = = + + +

+ += = = =

max

max

max

0Z

AZ

A A AZ R jX= +

fPinP

rP P

http://physics.usask.ca/~hirose/ep225/emref5.gif

TE4109 Antennas 42

Antenna Gain (1)

Gain : Ratio of the radiation intensity U in a given direction and theradiation intensity that would be obtained if the power fed to theantenna were radiated isotropically

( , ) ( , )( , ) 4 (dimensionless)

/(4 )in in

U UG

P P

= =

( , )( , )

/(4 )

UD

P

=

In most cases, we deal with relative gain

Relative Gain : the ratio of the power gain in a given direction to thepower gain of a reference antenna in its reference direction

Power input for both antennas must be the same

Reference antenna is usually a dipole, horn, or any other antennawhose gain can be calculated or it is known

In most cases, the reference antenna is a lossless isotropic source


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TE4109 Antennas 43

Antenna Gain (2)

When the direction is not stated, the power gain is the maximumgain (in the direction of maximum radiation)

From IEEE Standards, gain does not include losses arising fromimpedance mismatches (reflection losses) and polarizationmismatches (losses)

, 1

( , ) ( , )

cd in cd

cd

P e P e

G e D

=

=

In a similar manner,

max 0 max 0( , ) ( , )m m cd m m cd cd G G G e D e D e D = = = = =

[ ]max 10 max(dB) 10log (dimensionless)cdG e D=

assuming no

impedance mismatch

(reflection losses = 0)

TE4109 Antennas 44

Antenna Gain (3)

For antennas with orthogonal polarization components, the totalgain is the sum of the partial gains for any two orthogonalpolarizations

( , ) ( , ) ( , )G G G = +

4 ( , )( , )

4 ( , )( , )

in

in

UG

P

UG

P

=

=

Where Gand Gare partial gains, which are given by

total input (accepted) power to (by) the antennainP =


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TE4109 Antennas 45

Antenna Gain (4)

For many practical antennas, an approximate formula for the gain,corresponding to (2-27) or (2-27a) for the directivity, is

max 0

1 2

30,000

d d

G G

=

max 0 2

1 21 2

4 41,253

180d dd d

D D

=

In practice, whenever the term gain is used, it usually refers tothe maximum gain.

Compared with

TE4109 Antennas 46

Example 2.10

A lossless resonant half-wavelength dipole antenna, with input

impedance of 73 ohms, is connected to a transmission line whose

characteristic impedance is 50 ohms. Assuming that the pattern

of the anten3

0

na is given approximately by

( , ) sin ( )find the maximum absolute gain of this antenna.

U B =


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TE4109 Antennas 47

Beam Efficiency (1)

For antenna with its major lobe

directed along thez-axis, thebeam efficiency (BE) is definedby

1power transmitted within cone angle

power transmitted by the antenna ( )BE

P

=

where 1 is the half-angle of the cone within which the percentage of totalPower is to be found

1


TE4109 Antennas 48

Beam Efficiency (2)

If 1 is chosen as the angle where the first null or minimum occurs,then

Beam efficiency indicates the amount of power in the major lobecompared to the total power

12

0 02

0 0

( , ) sin( )

( , ) sin( )

U d dBE

U d d

=


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TE4109 Antennas 49

Frequency Bandwidth (FBW)

Frequency Bandwidth (FBW) : Range of frequencies, within whichthe antenna characteristics (input impedance, pattern) conform tocertain specifications

Antenna characteristics: Input impedance, radiation pattern,beamwidth, polarization, side-lobe level, gain, beam direction andwidth, radiation efficiency, and etc.

Broadband Antenna: FBW is the ratio of the upper to the lowerfrequencies, where the antenna performance is acceptable

max

min

FBW f

f=

Narrowband Antenna : FBW is a percentage of the frequency

difference over the center frequency

FBW as large as 40:1 have been designed

Frequency Independent Antenna

max min

0

FBW 100%f f

f

=

0 max min

0 max min

( ) / 2, or f f f

f f f

=

=

TE4109 Antennas 50

Homework Assignment (1)

Time Allowed: 1 Week2.3

2.6

2.11

(a) and (c)

2.12

2.18

(a)

2.19

2.27

(a) and (b)


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TE4109 Antennas 51


Hints for 2.11 (a)

sin( ) sin( )

0 , 0

U

=

TE4109 Antennas 52


Hints for 2.11 (b)

3sin( )sin ( )

0 , 0

U

=


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TE4109 Antennas 53


Hints for 2.27

2sin( ) cos ( )

0 , and 0 / 2, 3 / 2 2

U

=

TE4109 Lecture08 10 Fundamental Antenna Parameters 1

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