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Fundamental Antenna Parameters

1. Radiation Pattern

An antenna radiation pattern is defined as a graphical

representation of the radiation properties of the antenna

as a function of space coordinates. In most cases, the

radiation pattern is determined in the far-field region.

Radiation properties include radiation intensity, field

strength, phase or polarization.

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Coordinate System

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Idealized

Point Radiator Vertical Dipole Radar Dish

IsotropicOmnidirectional Directional

Types of Radiation Patterns

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Full Null Beamwidth

Between

1st NULLS

Radiation Pattern Lobes

Main lobe

Side lobes

Back lobes

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Radiation Pattern Lobes

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Field Regions

D

R1

R2

Reactive near-field region

3

1 62.0DR

Radiating near-field

(Fresnel) region

2

2 2D

R

Far-field (Fraunhofer)

region

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Radiation Intensity

Aside on Solid Angles

lengtharcrad0.1

r

sr0.1

2rareasurface

radianscecircumfrantotal 2224 rrSareasurfacetotal o

srr

So2

ddrds )sin(2

infinitesimal area

of surface of sphere

ddr

dsd )sin(

2

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Radiation Intensity

4

dUPsr

Wd

dPU

tot

rad

tot

rad

dsPPmW

ds

dPP rad

tot

rad

tot

radrad 2

radPrU2

),,( rPrad decays as 1/r2 in the far fieldsince

),( U will be independent of r

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Radiation Intensity

m ax

222

222*

),(),(

2),(

2

1~

2

1~~

2

1

),,(

U

UU

EEr

U

EEEHErPrad

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Radiation Intensity

Examples

0.1),(

),(

4),,(),(

4),,(

ma x

2

2

U

UU

constP

rPrU

rPrP

tot

radrad

tot

radrad

1. Isotropic radiator

2. Hertzian Dipole

)(sin),(

),(

)(sin42

)sin(42

1

2

1),(

0),,(

)sin(4

),,(

2

m ax

2

2

0

2

02222

0

U

UU

Il

r

eIlrEErU

rE

r

eIljrE

rj

rj

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Directive Gain

)(14

),(4

4

),(),(),(

m axm ax ydirectivit

P

UDD

P

U

P

U

U

UD

totrad

o

tot

rad

tot

radave

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Directivity

Examples

0.1

0.1),(

4),(

4),(

o

tot

rad

tot

rado

D

P

UD

PUU

1. Isotropic radiator

2. Hertzian Dipole

2

3

)(sin2

3),(4),(

3

8

42)sin()(sin

42),(

)(sin422

1),(

0),,(),sin(4

),,(

2

2

0

2

0 0

2

2

0

4

2

2

0222

o

tot

rad

tot

rad

rj

D

P

UD

Ildd

lIdUP

IlEErU

rEr

eljrE

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Antenna Gain

inputP

UG

),(4),(

POWER DENSITY IN A CERTAIN DIRECTION

DIVIDED BY THE TOTAL POWER RADIATED

POWER DENSITY IN A CERTAIN DIRECTION

DIVIDED BY THE TOTAL INPUT POWER

TO THE ANTENNA TERMINALS (FEED POINTS)

IF ANTENNA HAS OHMIC LOSS

THEN, GAIN < DIRECTIVITY

DIRECTIVITY

GAIN

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Antenna Gain

Sources of Antenna System Loss

1. losses due to impedance mismatches

2. losses due to the transmission line

3. conductive and dielectric losses in the antenna

4. losses due to polarization mismatches

According to IEEE standards the antenna gain does not include losses due to

impedance or polarization mismatches. Therefore the antenna gain only

accounts for dielectric and conductive losses found in the antenna itself. However

Balanis and others have included impedance mismatch as part of the antenna gain.

The antenna gain relates to the directivity through a coefficient called the

radiation efficiency (et)

),(),(),( DeeeDeG dcrt

conduction losses dielectric losses

1te

impedance mismatch

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Overall Antenna Efficiency

The overall antenna efficiency is a coefficient that accounts for all the different

losses present in an antenna system.

lossesdielectricconductore

lossesdielectrice

lossesconductione

mismatchimpedanceefficiencyreflectione

mismatchesonpolarizatie

eeeeeeee

cd

d

c

r

p

cdrp

e

dcrp

t

&

)(

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Reflection Efficiency

The reflection efficiency through a reflection coefficient (G) at the input (or feed)to the antenna.

)(

)(

12

G

G

impedanceoutputgeneratorR

impedanceinputantennaR

RR

RR

e

output

input

generatorinput

generatorinput

r

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Radiation Resistance

The radiation resistance is one of the few parameters that is relatively

straight forward to calculate.

2

4

2

),(22

oo

total

rad

radI

dU

I

P

R

Example: Hertzian Dipole

22

2

22

0 0

2

2

4

3

2

3

8

4

3

8

422

3

8

42

)sin()(sin

42

),(

2

ll

I

Il

R

Ildd

IldUP

o

o

rad

ootot

rad

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Radiation Resistance

Example: Hertzian Dipole (continued)

0063.09.750

9.7501

079.0

10000

1

3

2377

377100

1

3

2

3

8

4

3

8

422

2

22

2

2

r

rad

o

o

rad

e

R

andl

let

ll

I

Il

R

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Antenna Radiation Efficiency

radcd

radcd

RR

Re

Conduction and dielectric losses of an antenna are very difficult to separate and

are usually lumped together to form the ecd efficiency. Let Rcd represent the actual

losses due to conduction and dielectric heating. Then the efficiency is given as

For wire antennas (without insulation) there is no dielectric losses only conductor

losses from the metal antenna. For those cases we can approximate Rcd by:

22

ocd

b

lR

where b is the radius of the wire, is the angular frequency, is the conductivityof the metal and l is the antenna length

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Example Problem:

A half-wavelength dipole antenna, with an input impedance of 73 is to beconnected to a generator and transmission line with an output impedance of

50. Assume the antenna is made of copper wire 2.0 mm in diameter and theoperating frequency is 10.0 GHz. Assume the radiation pattern of the antenna is

Find the overall gain of this antenna

SOLUTION

First determine the directivity of the antenna.

)(sin),(3

o

BU

tot

rad

P

UD

),(4),(

697.1

3

16

)(sin3

16

4

3

)(sin4),(

m ax0

3

2

0

3

DD

B

BD o

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Example Problem: Continued

SOLUTION

Next step is to determine the gain

dBdBG

GG

G

DeeG cdr

14.2)636.1(log10)(

636.13

16964.0

)(sin3

16

964.0),(

),(),(

100

max0

3

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Antenna Type Gain (dBi) Gain over

Isotropic

Power Levels

Half

Wavelength

Dipole

1.76 1.5x

Cell Phone

Antenna

(PIFA)

3.0 2.0x 0.6 Watts

Standard Gain

Horn

15 31x

Cell phone

tower

antenna

6 4x

Large

ReflectingDish

50 100,000x

Small

Reflecting

Dish

40 10,000x

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Effective Aperture

plane wave

incidentAphysicalPload

incphysicalload WAP?

Question:

Answer: Usually NOT

inc

loadeffinceffload

W

PAWAP

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Directivity and Maximum Effective Aperture

(no losses)

Antenna #2

transmit receiver

R

Direction of wave propagation

Antenna #1

Atm, DtArm, Dr

oem DA

4

2

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Directivity and Maximum Effective Aperture

(include losses)

Antenna #2

transmit receiver

R

Direction of wave propagation

Antenna #1

Atm, DtArm, Dr

2*

22

4)1( awocdem DeA

G

conductor and

dielectric lossesreflection losses

(impedance mismatch)polarization mismatch

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Friis Transmission Equation (no loss)

Antenna #2

Antenna #1

R

The transmitted power density supplied by Antenna #1

at a distance R and direction (r,r)is given by:

24

),(

R

DPW

ttgtt

t

(t,t)

(r,r)

The power collected (received) by Antenna #2 is given by:

),(),(4

4

),(

4

),(

4

),(

2

2

22

rrgrttgt

t

r

rrgrttgtt

r

ttgtt

rtr

DDRP

P

D

R

DPA

R

DPAWP

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Friis Transmission Equation (no loss)

Antenna #2

Antenna #1

R

(t,t)

(r,r)

),(),(4

2

rrgrttgt

t

r DDRP

P

If both antennas are pointing in the direction of their maximum radiation pattern:

roto

t

r DDRP

P2

4

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Friis Transmission Equation ( loss)

Antenna #2

Antenna #1

R

(t,t)

(r,r)

2*

2

22),(),(

4

)1)(1( awrrgrttgttrcdrcdtt

r DD

R

ee

P

P

GG

conductor and

dielectric losses

transmitting antenna

conductor and

dielectric losses

receiving antenna

reflection losses in transmitter

(impedance mismatch)

reflection losses in receiving

(impedance mismatch)

polarization mismatch

free space loss factor

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Friis Transmission Equation: Example #1

A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of

800.0 MHz. The cell tower is 1 mile away and has an antenna with a directivity of 6 dBi.Assuming that the power at the input terminals of the transmitting antenna is 0.6 W, and

the antennas are aligned for maximum radiation between them and the polarizations are

matched, find the power delivered to the receiver. Assume the two antennas are well

matched with a negligible amount of loss.

nWwattsPr 65.142609.34414

375.06.0

2

2*maxmax

2

22

4)1)(1( awrttrcdrcdtt

r

DDReeP

P

GG

= 0 = 0= 1= 1= 1

0.410

0.210

375.06800

83

10/6m ax

10/3m ax

r

t

D

D

me

efc

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Friis Transmission Equation: Example #2

A half wavelength dipole antenna (max gain = 2.14 dBi) is used to communicate from an

old satellite phone to a low orbiting Iridium communication satellite in the L band (~ 1.6GHz). Assume the communication satellite has antenna that has a maximum directivity of

24 dBi and is orbiting at a distance of 781 km above the earth. Assuming that the power at

the input terminals of the transmitting antenna is 1.0 W, and the antennas are aligned for

maximum radiation between them and the polarizations are matched, find the power

delivered to the receiver. Assume the two antennas are well matched with a negligible

amount of loss.

pWwattsPr 15.025164.1781,0004

1875.00.1

2

2*maxmax

2

22

4)1)(1(

awrttrcdrcdt

t

r DDR

eeP

P

GG

= 0 = 0= 1= 1= 1

0.25110

64.110

1875.06800

83

10/24m ax

10/14.2m ax

r

t

D

D

me

e

f

c

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Friis Transmission Equation: Example #2

A roof-top dish antenna (max gain = 40.0 dBi) is used to communicate from an old satellite

phone to a low orbiting Iridium communication satellite in the Ku band (~ 12 GHz).Assume the communication satellite has antenna that has a maximum directivity of 30 dBi

and is orbiting at a distance of 36,000 km above the earth. How much transmitter power is

required to receive 100 pW of power at your home. Assume the antennas are aligned for

maximum radiation between them and the polarizations are matched, find the power

delivered to the receiver. Assume the two antennas are well matched with a negligible

amount of loss.

Wwatts

Pt 82

1000000,1036,000,0004

025.0

101002

12

2*maxmax

2

22

4)1)(1(

awrttrcdrcdt

t

r DDR

eeP

P

GG

= 0 = 0= 1= 1= 1

0.100010

000,1010

025.06800

83

10/30m ax

10/40m ax

t

r

D

D

me

e

f

c

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Radar Range Equation

Definition: Radar cross section or echo area of a target is defined as the area when interceptingthe same amount of power which, when scattered isotropically, produces at the receiver the same

power density as the actual target.

22

24lim

4lim m

W

WR

R

WW

inc

s

R

inc

Rs

(radar cross section) m2

R (distance from target) m

Ws (scattered power density) W/m2

Winc (incident power density) W/m2

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Radar Range Equation (no losses)

Power density incident on the target is a function

of the transmitting antenna and the distance

between the target and transmitter:

24

),(

t

ttgtt

incR

DPW

The amount of power density scattered by the

target at the location of the receiver is then given

by:

22)4(

),(

4 rt

ttgtt

r

incsRR

DP

RWW

The amount of power delivered by the receiver is

then given by:

4),(

)4(

),( 2

2 rrgr

rt

ttgtt

rsr DRR

DPAWP

4

),(),(

)4( 2

2rrgrttgt

rtt

rDD

RRP

P ),,,( rrtt

Note that in general:

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Radar Range Equation (losses)

2*

2

22

44

),(),()1)(1( aw

rt

rrgrttgt

trcdrcdt

t

r

RR

DDee

P

P

GG

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Radar Cross Section (RCS)

Definition: Radar cross section or

echo area of a target is defined as

the area when intercepting

the same amount of power which,

when scattered isotropically,

produces at the receiver the same

power density as the actual target.

22

24lim

4lim m

W

WRR

WWinc

s

R

inc

Rs

2

2

2

22

2

2

2 4lim4lim mE

ERm

E

ER

inc

scat

Rinc

scat

R

),,,( rrtt rtrt ,

Transmitter and receiver not in

the same location (bistatic RCS)

rtrt ,Transmitter and receiver in the

same location (usually the same

antenna) called mono-static RCS

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Radar Cross Section (RCS)

RCS Customary Notation:Typical RCS values can span 10-5m2

(insect) to 106 m2 (ship). Due to the

large dynamic range a logarithmic

power scale is most often used.

1log10log10

22

2 1010m

ref

m

dBmdBsm

100 m2 20 dBsm10 m2 10 dBsm1 m2 0 dBsm0.1 m2 -10 dBsm0.01 m2 -20 dBsm