what is an antenna? - university of delawaremirotzni/eleg413/antennas.pdf · what is an antenna?...

What is an Antenna?

Time varying charges cause radiation but NOT everything that radiates is an antenna!

+ -Now this is an antennaNot an antenna

What is an Antenna?

An antenna is a device that efficiently transitions between transmission line (or guided) waves to/from space waves.

N

What properties does a good antenna have?

1. It efficiently transfers energy from guided modes to free-space modes over the bandwidth of interest.

2. It sends energy out or collects energy in desirable locations.

3. It has a desirable footprint (i.e. size, weight and shape) for the application.

Antenna Types: Wire Antennas

Wire antennas are used as extensions of ordinary circuits & are most often found in “Lower” frequency applications. They can operate with two terminals in a Balancedconfiguration like the dipole or with an Unbalancedconfiguration using a Ground Plane for the other half of the structure.

Antenna Types: Aperture Antennas

Aperture antennas radiate from an opening or from a surface rather than a line and are found at Higherfrequencies where wavelengths are Shorter. Aperture antennas often have handfuls of Sq. Wavelengths of area & are very seldom fractions of a wavelength.

Antenna Types: Reflector AntennasAn antenna reflector is a device that reflects electromagnetic waves.It is often a part of an antenna assembly.

The most common reflector types are:1. A passive element slightly longer than and located behind a radiating dipole element that absorbs and re-radiates the signal in a directional way as in a Yagi antenna array.2. Corner reflector which reflects the incoming signal back to the direction it came from 3. Parabolic reflector which focuses a beam signal into one point, or directs a radiating signal into a beam

Fundamental Antenna Parameters

1. Radiation PatternAn antenna radiation pattern is defined as “a graphicalrepresentation of the radiation properties of the antennaas a function of space coordinates. In most cases, theradiation pattern is determined in the far-field region.Radiation properties include radiation intensity, fieldstrength, phase or polarization.

Coordinate System

Field Regions

DR1

R2

Reactive near-field region

λ3

1 62.0 DR =

Radiating near-field (Fresnel) region

λ

2

2 2 DR =

Far-field (Fraunhofer) region

Properties of Antenna Radiation in the Far Field

1. In the far-field the propagation direction of the radiation is almost entirely in the radial direction.



2. The electric field has the following form:

),(~~ φθfr

eEEjkr

o

−

=




3. It propagates like a plane wave. So what does that mean?

),(~~ φθfr

eEEjkr

o

−

=




3. It propagates like a plane wave. So what does that mean?a. E and H are polarized orthogonal to each other and

orthogonal to the direction of propagation.b. E and H are in phasec. H is smaller than E by the impedance

),(~~ φθfr

eEEjkr

o

−

=



2. It propagates like a plane wave. So what does that mean?a. E and H are polarized orthogonal to each other and

orthogonal to the direction of propagation.b. E and H are in phasec. H is smaller than E by the impedance

),(~~ φθfr

eEEjkr

o

−

=

φ

θ

φθη

φθ

afr

eEH

afr

eEE

jkro

jkr

o

ˆ),(~

ˆ),(~

−

−

=

=OR

θ

φ

φθη

φθ

afr

eEH

afr

eEE

jkro

jkr

o

ˆ),(~

ˆ),(~

−

−

−=

=OR a combination

Types of Radiation Patterns

Power Pattern – normalized power vs. spherical coordinate positionin the far field

Field Pattern – normalized |E| or |H| vs. spherical coordinate positionin the far field

),(ˆ),(ˆ~ φθφθ φφφθθθ fr

eEafr

eEaEjkrjkr −−

+=

),( φθθf

222*

21~

21~~Re

21),,( ϕθηη

ϕθ EEEHErPrad +==×=

),( φθφf

2),( φθθf2

),( φθφf

IdealizedPoint Radiator Vertical Dipole Radar Dish

Isotropic Omnidirectional Directional

Types of Radiation Patterns

Principal Patterns

1. E and H planesAntenna performance is often

described in terms of its principal E and H plane patterns.

• E-plane – the plane containing the electric field vector and the direction of maximum radiation.

• H-plane – the plane containing the magnetic field vector and the direction of maximum radiation.

Full Null BeamwidthBetween1st NULLS

Radiation Pattern Lobes

Main lobe

Side lobes

Back lobes

Radiation Pattern Lobes

Radiation Intensity

Aside on Solid Angles

ρ ρ=lengtharcrad0.1=θ

r

sr0.1=Ω

2rareasurface =

radianscecircumfrantotal π2=224 rrSareasurfacetotal o Ω=== π

srrSo

2=Ω

φθθ ddrds )sin(2=infinitesimal areaof surface of sphere

φθθ ddrdsd )sin(2 ==Ω

Radiation Intensity

∫∫ ⋅=S

avetot

rad dsPP ~

φθθφθ

φθφθππ

ddrrPP

rrPrP

avetot

rad

aveave

)sin(),,(

ˆ),,(),,(~

22

0 0∫ ∫=

=

Radiation Intensity

∫∫ ⋅=S

avetot

rad dsPP ~

φθθφθππ

ddrrPP avetot

rad )sin(),,( 22

0 0∫ ∫=

define ),,(),( 2 rPrU ave φθφθ =This assumes we are in the far field and the power varies as 1/r^2

ππ

φθ

φθφθθφθ

ππ

πππ π

44

),(

),()sin(),(

2

0 0

2

0 0

2

0 0

totrad

ave

totrad

PdU

U

dUddUP

=Ω

=

Ω==

∫ ∫

∫ ∫∫ ∫

The average radiation intensity for a given antennarepresents the radiation intensity of a point source (orisotropic antenna) that produces the same amount ofradiate power as the actual antenna.

Radiation Intensity

max

222

222*

),(),(

2),(

21~

21~~Re

21),,(

UUU

EErU

EEEHErPrad

ϕθϕθ

ηϕθ

ηηϕθ

ϕθ

ϕθ

=

+=

+==×=

Radiation IntensityExamples

0.1),(),(

4),,(),(

4),,(

max

2

2

==

===

=

UUU

constPrPrU

rPrP

totrad

rad

totrad

rad

ϕθϕθ

πϕθϕθ

πϕθ

1. Isotropic radiator

2. Hertzian Dipole

)(sin),(),(

)(sin42

)sin(42

121),(

0),,(

)sin(4

),,(

2

max

22

0

2

02222

0

θϕθϕθ

θπ

βηθπ

βηηη

ϕθ

ϕθ

θπ

βηϕθ

β

φθ

φ

β

θ

==

∆=

∆⋅=+=

=

∆=

−

−

UUU

IlreIlrEErU

rEreIljrE

rj

rj

Directive Gain

),(log10][),(

)(14

),(4

4

),(),(),(

10

maxmax

ϕθϕθ

π

ϕθπ

π

ϕθϕθϕθ

DdBD

ydirectivitP

UDD

PU

PU

UUD

totrad

o

totrad

totradave

=

≥==

===

Directive in dB

DirectivityExamples

0.1

0.1),(4),(

4),(

=

==

==

o

totrad

totrad

o

DP

UD

PUU

ϕθπϕθ

πϕθ

1. Isotropic radiator

2. Hertzian Dipole

23

)(sin23),(4),(

38

42)sin()(sin

42),(

)(sin422

1),(

0),,(),sin(4

),,(

2

2

02

0 0

22

0

4

22

0222

=

==

∆=⋅

∆=Ω=

∆=+=

=∆

=

∫ ∫∫∫

−

o

totrad

totrad

rj

D

PUD

IlddlIdUP

IlEErU

rEr

eljrE

θϕθπϕθ

ππ

βηθφθθπ

βηϕθ

θπ

βηη

ϕθ

ϕθθπ

βηϕθ

ππ

π

φθ

φ

β

θ

Antenna Gain

inputPUG ),(4),( ϕθπϕθ =

POWER DENSITY IN A CERTAIN DIRECTIONDIVIDED BY THE TOTAL POWER RADIATED

POWER DENSITY IN A CERTAIN DIRECTIONDIVIDED BY THE TOTAL INPUT POWERTO THE ANTENNA TERMINALS (FEED POINTS)

IF ANTENNA HAS OHMIC LOSS…THEN, GAIN < DIRECTIVITY

DIRECTIVITY

GAIN

Antenna Gain

Sources of Antenna System Loss1. 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 mismatchesAccording to IEEE standards the antenna gain does not include losses due toimpedance or polarization mismatches. Therefore the antenna gain only accounts for dielectric and conductive losses found in the antenna itself. HoweverBalanis and others have included impedance mismatch as part of the antenna gain.

The antenna gain relates to the directivity through a coefficient called theradiation efficiency (et)

),(),(),( ϕθϕθϕθ DeeeeDeG dcrpt ⋅=⋅=

conduction losses dielectric losses

1≤teimpedance mismatch

Polarization losses

Overall Antenna Efficiency

The overall antenna efficiency is a coefficient that accounts for all the differentlosses present in an antenna system.

lossesdielectricconductorelossesdielectrice

lossesconductionemismatchimpedanceefficiencyreflectione

mismatchesonpolarizatieeeeeeeee

cd

d

c

r

p

cdrp

e

dcrp

t

&

)(

====

=

⋅==

Reflection Efficiency

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

)()(

1 2

Ω=

Ω=

+

−=Γ

Γ−=

impedanceoutputgeneratorZimpedanceinputantennaZ

ZZZZ

e

output

input

generatorinput

generatorinput

r

Radiation Resistance

The radiation resistance is one of the few parameters that is relativelystraight forward to calculate.

24

2

),(22

oo

totalrad

radI

dU

IPR

∫∫ Ω== π

ϕθ

Example: Hertzian Dipole

22

2

22

0 0

22

4

32

38

43

842

2

38

42)sin()(sin

42),(

2

∆=

∆=

∆

=

∆=⋅

∆=Ω= ∫ ∫∫∫

λπηπ

πβη

ππ

βη

ππ

βηθφθθπ

βηϕθππ

π

llI

Il

R

IlddIldUP

o

o

rad

oototrad

Radiation Resistance

Example: Hertzian Dipole (continued)

47.09.7509.7501

9.7100

13

2377

377101

32

38

43

842

2

2

22

2

2

≈+−

−≈

Ω==

Ω==∆

∆=

∆=

∆

=

r

rad

o

o

rad

e

R

andllet

llI

Il

R

π

ηλ

λπηπ

πβη

ππ

βη

Antenna Radiation Efficiency

radcd

rad

ohmicrad

rad

total

radcd RR

RPP

PPPe

+=

+==

Conduction and dielectric losses of an antenna are very difficult to separate andare usually lumped together to form the ecd efficiency. Let Rcd represent the actuallosses due to conduction and dielectric heating. Then the efficiency is given as

For wire antennas (without insulation) there is no dielectric losses only conductorlosses from the metal antenna. For those cases we can approximate Rcd by:

σωµ

π 22o

cd blR =

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

Antenna Radiation Efficiency

For wire antennas (without insulation) there is no dielectric losses only conductorlosses from the metal antenna. For those cases we can approximate Rcd by:

σωµ

π 22o

cd blR =

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

Example Problem:A half-wavelength dipole antenna, with an input impedance of 73Ω is to beconnected to a generator and transmission line with an output impedance of50Ω. 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)(sin),( 3 θφθ oBU ≈

Example Problem:A half-wavelength dipole antenna, with an input impedance of 73Ω is to beconnected to a generator and transmission line with an output impedance of50Ω. 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 antennaSOLUTIONFirst determine the directivity of the antenna.

)(sin),( 3 θφθ oBU ≈

totradP

UD ),(4),( ϕθπϕθ =

697.1316

)(sin316

43

)(sin4),(

max0

32

0

3

===

=

=

π

θππ

θπϕθ

DD

B

BD o

Example Problem: Continued

SOLUTIONNext step is to determine the efficiencies

965.0)507350731()1(

22 =

+−

−=Γ−=

=

r

cdrt

e

eee

radcd

radcd RR

Re+

=

964.09991.0965.0

9991.00628.073

73

0628.0107.52

10410102)001.0(2

015.022 7

79

=⋅==

=+

=

Ω=⋅⋅⋅⋅

==−

cdrt

cd

ocd

eee

e

blR ππ

πσωµ

π

Example Problem: Continued

SOLUTIONNext step is to determine the gain

dBdBG

GG

G

DeeG cdr

14.2)636.1(log10)(

636.1316964.0

)(sin316964.0),(

),(),(

100

max0

3

==

===

=

=

π

θπ

ϕθ

ϕθϕθ

Antenna Type Gain (dBi) Gain over Isotropic

Power Levels

HalfWavelength 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

LargeReflecting Dish

50 100,000x

Small Reflecting Dish

40 10,000x

Effective Aperture

plane waveincident

AphysicalPload

incphysicalload WAP?=Question:

Effective Aperture

plane waveincident

AphysicalPload


Answer: Usually NOTinc

loadeffinceffload W

PAWAP =⇒=

Effective Aperture

plane waveincident

AphysicalPload


Answer: Usually NOTinc

loadeffinceffload W

PAWAP =⇒=

oeff DAπλ4

2

=

Directivity and Maximum Effective Aperture (no losses)

Effective Aperture

plane waveincident

AphysicalPload

inc

loadeffinceffload W

PAWAP =⇒=

Directivity and Maximum Effective Aperture (with losses)

2*2

2 ˆˆ4

)1( awocdem DeA ρρπλ

⋅Γ−=

conductor and dielectric losses reflection losses

(impedance mismatch)polarization mismatch

Friis Transmission Equation (no loss)

Antenna #2

Antenna #1

R

Goal is to determine the power received by Antenna #2.

(θt,φt)(θr,φr)


Antenna #2

Antenna #1

R

The transmitted power density supplied by Antenna #1at a distance R and direction (θr,φr) is given by:

24),(

RDP

W ttgttt π

ϕθ=

(θt,φt)(θr,φr)


Antenna #2

Antenna #1

R


24),(

RDP

W ttgttt π

ϕθ=

(θt,φt)(θr,φr)

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

rttgtt

rtr AR

DPAWP 24

),(π

ϕθ==

W/m^2

Watts


Antenna #2

Antenna #1

R


24),(

RDP

W ttgttt π

ϕθ=

(θt,φt)(θr,φr)


πλϕθ

πϕθ

πϕθ

4),(

4),(

4),( 2

22rrgrttgtt

rttgtt

rtr

DR

DPA

RDP

AWP ===

W/m^2

Watts

oeff DAπλ4

2

=


Antenna #2

Antenna #1

R


24),(

RDP

W ttgttt π

ϕθ=

(θt,φt)(θr,φr)


),(),(4

4),(

4),(

4),(

2

2

22

rrgrttgtt

r

rrgrttgttr

ttgttrtr

DDRP

P

DR

DPA

RDP

AWP

ϕθϕθπλ

πλϕθ

πϕθ

πϕθ

=

===


Antenna #2

Antenna #1

R

(θt,φt)(θr,φr)

),(),(4

2

rrgrttgtt

r DDRP

P ϕθϕθπλ

=

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

rotot

r DDRP

P2

4

=

πλ

Friis Transmission Equation ( loss)

Antenna #2

Antenna #1

R

(θt,φt)(θr,φr)

2*2

22 ˆˆ),(),(4

)1)(1( awrrgrttgttrcdrcdtt

r DDR

eePP ρρφθφθ

πλ

⋅

Γ−Γ−=

conductor and dielectric lossestransmitting antenna

conductor and dielectric lossesreceiving antenna

reflection losses in transmitter(impedance mismatch)

reflection losses in receiving(impedance mismatch)

polarization mismatch

free space loss factor

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.

Friis Transmission Equation: Example #1A 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 65.142 609.344 14

375.06.02

=⋅⋅

⋅⋅=

π

0.4100.210

375.06800

83

10/6max

10/3max

==

==

===

r

t

DD

me

efcλ

rotot

r DDRP

P2

4

=

πλ


rotot

r DDRP

P2

4

=

πλ


rotot

r DDRP

P2

4

=

πλ

0.4100.210

375.06800

83

10/6max

10/3max

==

==

===

r

t

DD

me

efcλ


rotot

r DDRP

P2

4

=

πλ

nWwattsPr 65.142 609.344 14

375.06.02

=⋅⋅

⋅⋅=

π

0.4100.210

375.06800

83

10/6max

10/3max

==

==

===

r

t

DD

me

efcλ


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 (~ 1.6 GHz). 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.

Friis Transmission Equation: Example #2A 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 (~ 1.6 GHz). 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.

rotot

r DDRP

P2

4

=

πλ


rotot

r DDRP

P2

4

=

πλ

0.2511064.110

1875.06800

83

10/24max

10/14.2max

==

==

===

r

t

DD

me

efcλ


rotot

r DDRP

P2

4

=

πλ

0.2511064.110

1875.06800

83

10/24max

10/14.2max

==

==

===

r

t

DD

me

efcλ

pWwattsPr 15.025164.1 781,0004

1875.00.12

=⋅⋅

⋅

⋅=π


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.

Friis Transmission Equation: Example #3A 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.

WwattsPt 821000000,10

36,000,0004025.0

101002

12

=

⋅⋅

⋅

⋅=

−

π0.100010000,1010

025.06800

83

10/30max

10/40max

==

==

===

t

r

DD

me

efcλ

rotot

r DDRP

P2

4

=

πλ

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 samepower density as the actual target.

222 4lim

4lim m

WWR

RWW

inc

s

R

inc

Rs

=⇒

=

∞→∞→πσ

πσ σ (radar cross section) m2

R (distance from target) mWs (scattered power density) W/m2

Winc (incident power density) W/m2

Radar Cross Section (RCS)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 samepower density as the actual target.

222 4lim

4lim m

WWR

RWW

inc

s

R

inc

Rs

=⇒

=

∞→∞→πσ

πσ

22

2

222

2

2 4lim4lim mE

ERm

E

ER

inc

scat

Rinc

scat

R

=

/

/=

∞→∞→π

κ

κπσ

),,,( rrtt ϕθϕθσσ =rtrt ϕϕθθ ≠≠ , Transmitter and receiver not in

the same location (bistatic RCS)

rtrt ϕϕθθ == , Transmitter and receiver in the same location (usually the same antenna) called mono-static RCS

Radar Cross Section (RCS)

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

(insect) to 106 m2 (ship). Due to thelarge dynamic range a logarithmic power scale is most often used.

=

==

1log10log10 22

2 1010m

ref

mdBmdBsm

σσσ

σσ

100 m2 20 dBsm

10 m2 10 dBsm

1 m2 0 dBsm

0.1 m2 -10 dBsm

0.01 m2 -20 dBsm

Radar Range Equation (no losses)

Power density incident on the target is a functionof the transmitting antenna and the distance between the target and transmitter:

24),(

t

ttgttinc R

DPW

πϕθ

=



24),(

t

ttgttinc R

DPW

πϕθ

=

The amount of power density scattered by the target in the direction of the receiver of the receiver is then given by:

),,,( rrtt ϕθϕθσσ =Note that in general:

),(),,,(),( ttincrrttrrs WW ϕθϕθϕθσϕθ ⋅=



24),(

t

ttgttinc R

DPW

πϕθ

=




The amount of power density that reaches the detector is given by:

22 44 r

inc

r

sr R

WR

WWπ

σπ

⋅==



24),(

t

ttgttinc R

DPW

πϕθ

=





( )22 44 rt

gtt

r

incr RR

DPR

WWπ

σπ

σ ⋅⋅=

⋅=



24),(

t

ttgttinc R

DPW

πϕθ

=





( )22 44 rt

gtt

r

incr RR

DPR

WWπ

σπ

σ ⋅⋅=

⋅=

The amount of power delivered by the receiver is then given by:

πλ

πσ

4)4(

2

2 grrt

gttrrr D

RRDP

AWP ==

oeff DAπλ4

2

=

Radar Range Equation (no losses)Power density incident on the target is a functionof the transmitting antenna and the distance between the target and transmitter:

24),(

t

ttgttinc R

DPW

πϕθ

=





( )22 44 rt

gtt

r

incr RR

DPR

WWπ

σπ

σ ⋅⋅=

⋅=

The amount of power delivered by the receiver is then given by:

πλ

πσ

4)4(

2

2 grrt

gttrrr D

RRDP

AWP ==

oeff DAπλ4

2

=

ππλσ

4)4( 2

2grgt

rtt

r DDRRP

P=



oeff DAπλ4

2

=

ππλσ

4)4( 2

2grgt

rtt

r DDRRP

P=

Radar Range Equation (losses)

2*2

22 ˆˆ44

)1)(1( awrt

grgttrcdrcdt

t

r

RRDD

eePP ρρ

πλ

πσ ⋅

Γ−Γ−=

what is an antenna? - university of delawaremirotzni/eleg413/antennas.pdf · what is an antenna?...

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