Antenna lecture course CHapter 2_(2)[1].pdf

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1. AsossaUniversity
Electrical and Computer Engineering Department
Post-Graduate Program
Advanced Antenna Systems
By: H/Maryam G.
Jan 18, 2023
14/22/2023

2. CHAPTER II
Antenna Parameters and Design Considerations
➢RadiationPattern
➢RadiationPowerDensityandRadiationIntensity
➢Beamwidth,DirectivityandGain
➢AntennaEfficiency
➢FRIISTransmissionEquation
➢RFRadiationHazardsandSolutions
24/22/2023

3. Antenna Radiation and Reception
➢Duetoabsenceoftransmissionlineconductors,thefieldlinesjointogetherandan
electromagneticwaveisgeneratedwithsphericalwavefrontwhosesourceisthesignal
generatorconnectedattheinputend.
34/22/2023

4. Field Regions
➢The field patterns generated by a radiating antenna vary with distance and
are associated with (i) radiating energy and (ii) reactive energy.
➢The space surrounding an antenna is subdivided into three regions:
1.Reactivenear-field
2.Radiatingnear-field(Fresnel)and
3.RadiatingFar-field(Fraunhofer).
➢Theboundariesoftheseregionsarenotdefinedpreciselybutareonly
approximations.
➢Althoughnoabruptchangesinthefieldconfigurationsarenotedasthe
boundariesarecrossed,therearedistinctdifferencesamongthem.
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5. ➢Theboundariesseparatingtheseregionsarenotunique,althoughvariouscriteria
havebeenestablishedandarecommonlyusedtoidentifytheregions.
54/22/2023
▪Reactive near field??????≤??????
�
▪Radiating near field??????
&#3627409359;<??????≤??????
&#3627409360;
▪Radiating Far-field ??????>??????
&#3627409360;
where Dis the length of the largest element
in the antenna.

6. Reactivenear-fieldregion
➢Isportionofthenear-fieldregionimmediatelysurroundingtheantennawherein
thereactivefieldpredominates.
➢Formostantennas,theouterboundaryofthisregioniscommonlytakentoexist
atadistance:
whereλisthewavelength(meter)andDisthelargestdimensionoftheantenna(meter).
Radiatingnear-field(Fresnel)region
➢Isregionofthefieldofanantennabetweenthereactivenear-fieldregionandthe
far-fieldregionwhereinradiationfieldspredominateandwhereintheangular
fielddistributionisdependentuponthedistancefromtheantenna.
➢Iftheantennahasamaximumdimensionthatisnotlargecomparedtothe
wavelength,thisregionmaynotexist.
64/22/2023

7. ➢Foranantennafocusedatinfinity,theradiatingnear-fieldregionissometimes
referredtoastheFresnelregion.Theboundaryforthisregion:
➢Inthisregionthefieldpatternis,ingeneral,afunctionoftheradialdistanceand
theradialfieldcomponentmaybesubstantial.
Far-field(Fraunhofer)region
➢Istheregionofthefieldofanantennawheretheangularfielddistribution
isessentiallyindependentofthedistancefromtheantenna.Itiscommonly
takentoexistatdistances.
➢Inthisregion,thefieldcomponentsareessentiallytransverseandtheangular
distributionisindependentoftheradialdistancewherethemeasurementsaremade.
➢Typicalchangesofantennaamplitudepatternshapefromreactivenearfieldtoward
thefarfield.
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8. 84/22/2023

9. ➢Theamplitudepatternofanantenna,astheobservationdistanceis
variedfromthereactivenearfieldtothefarfield,changesinshape
becauseofvariationsofthefields,bothmagnitudeandphase.
➢Atypicalprogressionoftheshapeofanantenna,withthelargest
dimensionD,isshowninfig,Itisapparentthatinthereactivenearfield
regionthepatternismorespreadoutandnearlyuniform,withslight
variations.
➢Astheobservationismovedtotheradiatingnear-fieldregion(Fresnel),
thepatternbeginstosmoothandformlobes.
➢Inthefar-fieldregion(Fraunhofer),thepatterniswellformed,usually
consistingoffewminorlobesandone,ormore,majorlobes.
94/22/2023

10. RadiationPatternLobes
➢Oncetheelectromagnetic(EM)energyleavestheantenna,theradiation
patterntellsushowtheenergypropagatesawayfromtheantenna.
➢Radiationpatternisdefinedasamathematicalfunctionoragraphical
representationoftheradiationpropertiesoftheantennaasafunctionofspace
coordinates.
➢Variouspartsofaradiationpatternarereferredtoaslobes.
➢Aradiationlobeisaportionoftheradiationpatternboundedbyregionsof
relativelyweakradiationintensity.
➢Itismaybeclassifiedintomajor(main)andminorlobes.Theminorlobefurther
classifiedassideandbacklobes.
➢Amajorlobealsocalledmainbeamisdefinedastheradiationlobecontaining
thedirectionofmaximumradiation.Infig.belowthemajorlobeispointinginthe
(&#3627409213;=&#3627409358;)direction.
➢Insomeantennas,suchassplit-beamantennas,theremayexistmorethanone
majorlobe.
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11. RadiationPatternLobes
➢Aminorlobeisanylobeexceptamajorlobe.Infigures(a)and(b)allthelobes
withtheexceptionofthemajorcanbeclassifiedasminorlobes.
➢Asidelobeisaradiationlobeinanydirectionotherthantheintendedlobe.
Usuallyasidelobeisadjacenttothemainlobeandoccupiesthehemispherein
thedirectionofthemainbeam.
➢Abacklobeisaradiationlobewhoseaxismakesanangleofapproximately
&#3627409359;??????&#3627409358;
??????
withrespecttothebeamofanantenna.Usuallyitreferstoaminorlobe
thatoccupiesthehemisphereinadirectionoppositetothatofthemajorlobe.
▪Fig:(a)demonstratesasymmetricalthreedimensionalpolarpattern
withanumberofradiationlobes.Someareofgreaterradiation
intensitythanothers,butallareclassifiedaslobes.
▪Fig:(b)illustratesalineartwo-dimensionalpatternwherethesame
patterncharacteristicsareindicated.
114/22/2023

12. 124/22/2023
Fig.: (a) Radiation lobes and
beam widths of an antenna
3-D polar pattern

13. Fig: (b) Linear 2-D plot of power pattern and its associated lobes and beam widths.
134/22/2023

14. RadiationPatternLobes
144/22/2023
Figure: Normalized three-dimensional
amplitude field pattern( in linear scale)

15. RadiationPattern:
➢Inmostcases,theradiationpatternisdeterminedinthefar-field
(Fraunhofer)regionandisrepresentedasafunctionofthedirectional
coordinates.
➢Radiationpropertiesincludepowerdensity,radiationintensity,field
strength,directivity,phaseorpolarization.
➢Aconvenientsetofcoordinatesisshowninfig.below.Atraceofthe
receivedelectric(magnetic)fieldataconstantradiusiscalledthe
amplitudefieldpattern.
➢Theradiationpropertyofmostconcernisthetwo-orthreedimensional
spatialdistributionofradiatedenergyasafunctionoftheobserver’s
positionalongapathorsurfaceofconstantradius.
➢Ontheotherhand,agraphofthespatialvariationofthepowerdensity
alongaconstantradiusiscalledanamplitudepowerpattern.
154/22/2023

16. 164/22/2023
Fig: Coordinate system for antenna analysis:

17. RadiationPattern:
➢Anyfieldpatterncanberepresentedinthreedimensionalsphericalcoordinatesas
infig.aboveorbyplanecutsthroughthemainlobeaxis.
➢Oftenthefieldandpowerpatternsarenormalizedwithrespecttotheirmaximum
value,resultinginnormalizedfieldandpowerpatterns.
➢Also,thepowerpatternisusuallyplottedonalogarithmicscaleormorecommonly
indecibels(dB).
➢Thenormalizedorrelativepatternswhicharedimensionlessquantitieswith
maximumvalueofunityareobtainedbydividingthepatterncomponentbyits
maximumvalue.
➢Atdistancesthatarelargecomparedtothesizeoftheantennaandthe
wavelength,theshapeofthefieldpatternisindependentofdistance.
➢Thepatternsofinterestareofthisfar-fieldcondition,sinceinpracticereceptionof
radiateantennaisinthefar-fieldregion.
➢Thenormalizedpowerpatterncanbeobtainedbydividingthecomponentof
powerperunitareacalledPoyntingvectortoitsmaximumvalue.
174/22/2023

18. 184/22/2023
➢Weplaceanantennaatthecenter.The
electricfieldcomponentsare and
.
➢Theradiatedpowerwillbeinthe
directionofthePoyntingvectorP=EXH.
Powerpatternis .Thenormalized
powerpatternis.
Normalized field
pattern
Normalized power
pattern

19. Figure: Two-dimensional normalized (a) field pattern (in linear scale) (b) power pattern
(in linear scale), and (c) power pattern (in dB)
194/22/2023

20. RadiationPattern:
➢Amplitudefieldpattern:Atraceofthereceivedelectric/magneticfieldat
aconstantradius.
➢Amplitudepowerpattern:Agraphofthespatialvariationofthepower
densityalongaconstantradius.
A.Fieldpattern(inlinearscale):typicallyrepresentsaplotofthe
magnitudeoftheelectricormagneticfieldasafunctionoftheangular
space.
B.Powerpattern(inlinearscale):typicallyrepresentsaplotofthesquare
ofthemagnitudeoftheelectricormagneticfieldasafunctionofthe
angularspace.
C.Powerpattern(indB):representsthemagnitudeoftheelectricor
magneticfield,indecibels,asafunctionoftheangularspace.
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21. 214/22/20232
|E|-pattern 2
|E|-pattern in dB scale |E|-pattern

22. Isotropic, Directional, and Omni-directional Patterns
224/22/2023
➢IsotropicAntenna:Ahypotheticallosslessantennapatternhavingequal
radiationinalldirections.
▪Ideal,notphysicallyrealizable.
▪Oftentakenasareferenceforexpressingthedirectivepropertiesofactualantennas.
➢DirectionalAntenna:isonehavingthepropertyofradiatingorreceiving
electromagneticwavesmoreeffectivelyinsomedirectionsthaninothers.
▪Examplesofantennaswithdirectionalradiationpatternsarehornantenna,dipole
antenna,etc.
➢Itisseenthatthepatterninfig.belowisnon-directionalintheazimuthplane
anddirectionalintheelevationplane.
➢ThistypeofapatternisdesignatedasOmni-directionalAntenna,anditis
definedasonehavinganessentiallynon-directionalpatterninagivenplaneand
adirectionalpatterninanyorthogonalplane.
▪AnOmni-directionalpatternisspecialtypeofadirectionalpattern.

23. 234/22/2023
Nondirectional Pattern
Directional Pattern
Orthogonal Plane

24. 244/22/2023
Fig: Sample of 2-D polar pattern.

25. RadianandSteradian
254/22/2023
➢Themeasureofaplaneangleisaradian.
Oneradianisdefinedastheplaneangle
withitsvertexatthecenterofacircleof
radiusrthatissubtendedbyanarcwhose
lengthisr.
➢Themeasureofasolidangleisasteradian.
Onesteradianisdefinedasthesolidangle
withitsvertexatthecenterofasphereof
radiusrthatissubtendedbyaspherical
surfaceareaequaltothatofasquarewith
eachsideoflengthr.
➢Agraphicalillustrationisshowninfig
below.

26. RadianandSteradian
➢Sincethecircumferenceofacircleofradius&#3627408479;is&#3627408438;=2??????&#3627408479;,thereare
2??????rad(2??????&#3627408479;/&#3627408479;)inafullcircle.Andsincetheareaofasphereofradius&#3627408479;
is&#3627408436;=4??????&#3627408479;
2
,thereare4??????sr(4??????&#3627408479;
2
/&#3627408479;
2
)inaclosedsphere.
➢Theinfinitesimalarea&#3627408465;&#3627408436;onthesurfaceofasphereofradiusr,shownin
figabove,isgivenby:
➢Therefore,theelementofsolidangle&#3627408465;??????ofaspherecanbewrittenas:
264/22/2023

27. RadiationPowerdensity
➢Electromagneticwavesareusedtotransportinformationthroughawireless
mediumoraguidingstructure,fromonepointtotheother.
➢Itisthennaturaltoassumethatpowerandenergyareassociatedwith
electromagneticfields.
➢Thequantityusedtodescribethepowerassociatedwithanelectromagnetic
waveistheinstantaneousPoyntingvectordefinedas:
S = E X H*
where:S=Instantaneouspowervector(W/m
2
)
E=instantaneouselectric-fieldintensity(V/m)
H=instantaneousmagnetic-fieldintensity(A/m)
➢SincethePoyntingvectorisapowerdensity,thetotalpowercrossingaclosed
surfacecanbeobtainedbyintegratingthenormalcomponentofthePoynting
vectorovertheentiresurface.
274/22/2023

28. ➢For time-harmonic EM fields:
➢Poynting vector:
➢Time average Poynting vector (average power density or radiation density):
▪TheΤ
1
2factorappearsbecausetheEandHfieldsrepresentpeakvalues,andit
shouldbeomittedforRMSvalues:
➢So that an Average power radiated power becomes:
284/22/2023

29. Example: The average power density is given by:
The total radiated power becomes:
294/22/2023

30. RadiationIntensity
➢Radiationintensityinagivendirectionisdefinedas“thepowerradiated
fromanantennaperunitsolidangle.”
➢Theradiationintensityisafar-fieldparameter,anditcanbeobtainedby
simplymultiplyingtheradiationdensitybythesquareofthedistance.
➢Inmathematicalformitisexpressedas:
where:U=radiationintensity(W/unitsolidangle)
W
rad=radiationdensity(W/m
2
)
304/22/2023

31. Beamwidth
➢Itisdefinedastheangularseparationbetweentwoidenticalpointson
oppositesideofthepatternmaximum.Inanantennapattern,therearea
numberofbeamwidths.
➢OneofthemostwidelyusedbeamwidthsistheHalf-PowerBeamwidth
(HPBW),whichisdefinedbyIEEEas:“Inaplanecontainingthedirectionof
themaximumofabeam,theanglebetweenthetwodirectionsinwhichthe
radiationintensityisone-halfvalueofthebeam.”
➢Anotherimportantbeamwidthistheangularseparationbetweenthefirst
nullsofthepattern,anditisreferredtoastheFirst-NullBeamwidth
(FNBW).
➢BoththeHPBWandFNBWaredemonstratedforthepatterninFigure
However,inpractice,thetermbeamwidth,withnootheridentification,
usuallyreferstoHPBW.
314/22/2023

32. ➢Thebeamwidthofanantennaisaveryimportantfigureofmeritandoften
isusedasatrade-offbetweenitandthesidelobelevel;Asthebeamwidth
decreases,thesidelobeincreasesandviceversa.
➢Themostcommonresolutioncriterionstatesthattheresolutioncapability
ofanantennatodistinguishbetweentwosourcesisequaltohalfthefirst-
nullbeamwidth(FNBW/2),whichisusuallyusedtoapproximatethehalf
powerbeamwidth(HPBW).
➢Thatis,twosourcesseparatedbyangulardistancesequalorgreaterthan
FNBW/2≈HPBWofanantennawithauniformdistribution.
➢Iftheseparationissmaller,thentheantennawilltendtosmooththe
angularseparationdistance.
➢Example:Referexample2.4inyourtextbook(ANTENNATHEORY,4
th
editionby:
ConstantineA.Balanis).
324/22/2023

33. Directivity
➢Directivityisameasureoftheantenna‘sabilitytofocustheenergyinoneor
morespecificdirections.
➢Directivityofanantennadefinedastheratiooftheradiationintensityina
givendirectionfromtheantennatotheradiationintensityaveragedover
alldirections.
➢Theaverageradiationintensityisequaltothetotalpowerradiatedbythe
antennadividedby4π.
➢Ifthedirectionisnotspecified,thedirectionofmaximumradiationintensity
isimplied.
➢Statedmoresimply,thedirectivityofanonisotropicsourceisequaltothe
ratioofitsradiationintensityinagivendirectionoverthatofanisotropic
source.
334/22/2023

34. ➢Inmathematicalform,itcanbewrittenas:
➢Ifdirectionisnotmentioned,itimpliesthedirectionofmaximum
radiationintensity,maximumdirectivityisexpressedas:
where:
344/22/2023

35. Gain
➢Definedastheratiooftheintensity,inagivendirection,totheradiation
intensitythatwouldbeobtainedifthepoweracceptedbytheantennawere
radiatedisotopically.
➢Thegainoftheantennaiscloselyrelatedtothedirectivity,itisameasure
thattakesintoaccounttheefficiencyoftheantennaaswellasitsdirectional
capabilities.
➢Theradiationintensitycorrespondingtotheisotopicallyradiatedpoweris
equaltothepoweraccepted(input)bytheantennadividedby4π.In
equationformthiscanbeexpressedas:
354/22/2023

36. Bandwidth
➢Thebandwidthofanantennaisdefinedastherangeoffrequencieswithinwhich
theperformanceoftheantenna,withrespecttosomecharacteristic,conformsto
aspecifiedstandard.
➢Thebandwidthcanbeconsideredtobetherangeoffrequencies,oneithersideof
acentrefrequency(usuallytheresonancefrequencyforadipole),wherethe
antennacharacteristicsarewithinanacceptablevalueofthoseatthecentre
frequency.
▪Forbroadbandantennas,thebandwidthisusuallyexpressedastheratioofthe
upper-to-lowerfrequenciesofacceptableoperation.
▪Example:a10:1bandwidthindicates:upperfrequencyis10timesgreaterthanthelower.
➢Fornarrowbandantennas,thebandwidthisexpressedasapercentageofthe
frequencydifference(upperminuslower)overthecentrefrequencyofthe
bandwidth.
▪Example:a5%bandwidthindicatesthatthefrequencydifferenceofacceptableoperationis
5%ofthecentrefrequencyofthebandwidth.
364/22/2023

37. Polarization
➢Polarizationisdefinedasthe
propertyofanEMwavedescribing
thetime-varyingdirectionand
relativemagnitudeoftheE-field
vector.
➢Inotherwords,Polarizationof
radiatedwavedescribesthe
oscillationdirectionandrelative
magnitudeoftheelectricfield.
➢Specifically,thefiguretracedasa
functionoftimebytheextremity
ofthevectoratafixedlocationin
space,andthesenseinwhichitis
traced,asobservedalonggiven
direction.
374/22/2023
Fig: Polarization of EM waves

38. 384/22/2023
(a) Linear polarization (b) Circular polarization and (c) Elliptical polarization
•Blue line : Electric field of a radiated/received wave
•Red and green line : Consisting of (one) two orthogonal, in-phase components
•Purple line : Polarized along a plane
(a) (b) (c)

39. ➢Polarizationmaybeclassifiedaslinear,circular,orelliptical.
➢Ifthevectorthatdescribestheelectricfieldatapointinspaceasafunction
oftimeisalwaysdirectedalongaline,thefieldissaidtobelinearly
polarized.
➢Ingeneral,however,thefigurethattheelectricfieldtracesisanellipse,and
thefieldissaidtobeellipticallypolarized.
➢Linearandcircularpolarizationsarespecialcasesofelliptical,andtheycan
beobtainedwhentheellipsebecomesastraightlineoracircle,respectively.
➢Thefigureoftheelectricfieldistracedinaclockwise(CW)or
counterclockwise(CCW)sense.Clockwiserotationoftheelectric-fieldvector
isalsodesignatedasright-handpolarizationandcounterclockwiseasleft-
handpolarization.
394/22/2023

40. Input Impedance
➢Inputimpedanceisdefinedastheimpedancepresentedbyanantennaat
itsinputterminalsortheratioofthevoltagetocurrentatapairofinput
terminalsortheratiooftheappropriatecomponentsoftheelectricto
magneticfieldsatapoint.
Fig: Transmitting antenna and its equivalent circuits.
404/22/2023
Loss
resistance
Radiation
resistanceg g g
Z R jX=+
= Generator impedance (ohms)
= Resistance of generator impedance (ohms)
= Reactance of generator impedance (ohms)g
Z g
R g
X

41. ➢Theratioofthevoltagetocurrentattheseterminals(designatedasa-b),
withnoloadattached,definestheimpedanceoftheantennaas:
&#3627408513;
??????=??????
??????+????????????
??????
Where:&#3627408461;
??????=antennaimpedanceatterminalsa–b,(Ω)
??????
??????=antennaresistanceatterminalsa–b,(Ω)
&#3627408459;
??????=antennareactanceatterminalsa–b,(Ω)
➢Inputimpedanceatapairofterminalswhicharetheinputterminalsof
theantenna.InFig.abovetheseterminalsaredesignatedasa−b.
414/22/2023

42. ➢Tofindtheamountofpowerdeliveredto??????
??????forradiationandtheamount
dissipatedin??????
??????asheat.
424/22/2023( ) ( )
gg
g
t r L g A g
VV
I
Z R R R j X X
==
+ + + + 1
22
2
( ) ( )
g
g
r L g A g
V
I
R R R j X X
==
+ + + +
 2
2
22
1
22 ( ) ( )
g
r
r g r
r L g A g
V R
P I R
R R R j X X

==
+ + + +
 2
2
22
1
22 ( ) ( )
g
L
L g L
r L g A g
V R
P I R
R R R j X X

==
+ + + +

➢Power delivered to the antenna for radiation.
➢Power that dissipated as heat.
➢Maximum powerdelivered to the
antenna when conjugate matching.
➢Conjugate matching;r L g
R R R+= Ag
XX=−

43. 434/22/202322
22
2 4( ) 8 ( )
gg
rr
r
r L r L
VV RR
P
R R R R
   
==
   
++
    2
2
8 ( )
g
L
L
rL
V R
P
RR

=

+
 2 2 2
2
1
8 ( ) 8 8
g g g g
g
r L r L g
V V VR
P
R R R R R
   
= = =
   
++
    22
22
8 ( ) 8 ( )
gg g rL
g r L
r L r L
VV R RR
P P P
R R R R
    +
= + = =
   
++
   
➢Powerthatdissipatedasheatintheinternalresistanceofthegenerator=powerfor
radiation+powerthatdissipatedasheatintheantenna.
➢Iftheantennaislosslessandmatchedtothetransmissionlinehalfofthetotalpowersuppliedbythe
generatorisradiatedbytheantennaduringconjugatematching,andtheotherhalfisdissipatedasheatin
thegenerator.1 ( 0)
r
cd L
rL
R
eR
RR

= = =

+


44. 444/22/2023
➢Conjugate matching ( to remove imaginary components)r L T A T
R R R X X+ = = −
▪Power delivered to the load ??????
??????:
▪Power that scattered of (re-radiated):
▪Power that dissipated as heat through ??????
??????: 2 2 2
2
1
8 ( ) 8 8
T T T T
T
r L r L T
V V VR
P
R R R R R
   
= = =
   
++
    22
22
2 4( ) 8 ( )
TT rr
r
r L r L
VV RR
P
R R R R
   
==
   
++
    2
2
8 ( )
T L
L
rL
V R
P
RR

=

+

Which is collected or capturedPower

45. AntennaRadiationEfficiency
➢Theantennaefficiencythattakesintoaccountthereflection,conduction,
anddielectriclosses.
➢Theconductionanddielectriclossesofanantennaareverydifficultto
computeandinmostcasestheyaremeasured.
➢Evenwithmeasurements,theyaredifficulttoseparateandtheyareusually
lumpedtogethertoformthee
cdefficiency.
➢Theresistance??????
??????isusedtorepresenttheconduction-dielectriclosses.
➢Theconduction-dielectricefficiencye
cdisdefinedastheratioofthepower
deliveredtotheradiationresistance??????
??????tothepowerdeliveredto??????
??????and
??????
??????.Itisgivenby:
454/22/2023

46. Antenna Efficiency
➢Thepowerefficiencyofanantennaorantennaefficiencyistheratioofpowerradiatedto
totalpowerinputtotheantenna.Thus,iftheradiationresistance??????
??????andtheloss
resistance??????
??????isknown,theantennaefficiencycanexpressedas:
▪Here, I is the current flowing through the antenna terminals. Multiplying &#3627409212;
&#3627408514;by 100,
one may obtain the percentage antenna efficiency.
➢Thetotalantennaefficiencye
0isusedtotakeintoaccountlossesattheinput
terminalsandwithinthestructureoftheantenna.Suchlossesmaybedueto:
➢Reflections because of the mismatchbetween the transmission line and the antenna.
➢I
2
R losses (conduction anddielectric).
464/22/2023

47. Fig: Reference terminals and antenna losses.
474/22/2023
➢Ingeneral,theoverall
efficiencycanbewritten
as:
e
0=e
re
ce
d

48. FRIISTransmissionEquation
➢TheFRIISTransmissionEquationrelatesthepowerreceivedtothepower
transmittedbetweentwoantennasseparatedbyadistance:
.……………(far-fieldregion)
where:Disthelargestdimensionofeitherantenna.
48Prepared by: H/MARYAM G.08/05/2013 E.C

49. ➢FRIISTransmissionEquationisexpressedby:
where: , is the gain of antenna (dimensionless)
, is power density (Τ&#3627408458;&#3627408462;&#3627408481;&#3627408481;&#3627408474;
2
)
,is total received power (Watt)
49Prepared by: H/MARYAM G.08/05/2013 E.C

50. Example
1.Thenormalizedradiationintensityofanantennaisrepresentedby:
&#3627408482;??????=&#3627408464;??????&#3627408480;
2
??????&#3627408464;??????&#3627408480;
2
3??????;(0 ≤ ??????≤ 90
0
,0≤??????≤360
0
)
a.FindHPBW(indegreesandradians)
b.FindFNBW(indegreesandradians)
2.Iftheimpedanceofahornantennais(&#3627408461;
&#3627408436;=20+??????30)Ωandthecharacteristics
impedanceof50Ω,thenevaluatevoltagereflectioncoefficientattheinput
terminaloftheantennaandcalculatetheoverallvoltagestandingwaveratio?
3.AGSM1800celltowerantennaistransmitting20Wofpowerinthefrequency
rangeof1840to1845MHz.Thegainoftheantennais17dB.Findthepower
densityatadistanceof(a)50mand(b)300minthedirectionofmaximum
radiation.
4.Thetransmittingandreceivingantennasareseparatedbyadistanceof200??????and
havedirectivegainsof25and18dB,respectively.If5mWofpoweristobe
received,calculatetheminimumtransmittedpower.
50Prepared by: H/MARYAM G.08/05/2013 E.C

51. Solution:
1.Ans: a) HPBW ≈0.5 rad; ≈28.65
0
b) FNBW ≈1.047 rad; ≈60
0
2.Ans: Γ= −0.206+??????0.517=0.56∠112
0
; VSWR = 3.55
3.Power density:
4.Minimum transmitted power:
Given that ??????
??????&#3627408465;&#3627408437;=25&#3627408465;&#3627408437;=10&#3627408473;????????????
10??????
??????;??????
??????=10
2.5
=316.23
Similarly, ??????
??????&#3627408465;&#3627408437;=18&#3627408465;&#3627408437;=10&#3627408473;????????????
10??????
??????;??????
??????=10
1.8
=63.1
Using the FRIIS equation, we have: ??????
??????=??????
????????????
??????
??????
4????????????
2
??????
??????;??????
??????=??????
??????
4????????????
??????
2
1
??????
????????????
??????
=&#3627409359;.????????????&#3627409361;&#3627408458;
51Prepared by: H/MARYAM G.08/05/2013 E.C

52. RF Hazards
524/22/2023

53. RF Hazards
534/22/2023

54. RF Hazards
544/22/2023

55. RF Hazards
554/22/2023

56. RF Hazards
564/22/2023

57. RF Hazards
574/22/2023

58. RF Hazards
584/22/2023

59. RF Hazards
594/22/2023

60. RF Hazards
604/22/2023

61. RF Hazards
614/22/2023

62. RF Hazards
624/22/2023

63. Potential Solutions
634/22/2023

64. Any Questions?
END !
644/22/2023