Antennas and Wave Propagation

JNTUK III B.Tech- I Sem Unit- 1

1. B.TECH (III YEAR –I SEM)
Prepared by:
Mr. P.Venkata Ratnam.,M.Tech., (Ph.D)
Associate Professor
Department of Electronics and Communication Engineering
RAJAMAHENDRI INSTITUTE OF ENGINEERING & TECHNOLOGY
(Affiliated to JNTUK, Kakinada, Approved by AICTE -Accredited by NAAC )
Bhoopalapatnam, Rajamahendravaram, E.G.Dt, Andhra Pradesh

2. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

3. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

4. AnantennaisdefinedbyWebster‘sDictionaryas―
ausuallymetallicdevice(asarodorwire)for
radiatingorreceivingradiowaves.
TheIEEEStandardDefinitionsofTermsfor
Antennasdefinestheantennaoraerialas―ameans
forradiatingorreceivingradiowaves.
Inotherwordstheantennaisthetransitional
structurebetweenfree-spaceandaguidingdevice.
Theguidingdeviceortransmissionlinemaytakethe
formofacoaxiallineorahollowpipe(waveguide).

5. Anantennamaybeapieceofconductingmaterial
intheformofawire,rodoranyothershapewith
excitation
An antenna is a source or radiator of EM waves
An antenna is a sensor of EM waves
An antenna is a transducer
An antenna is an impedance matching device
An antenna is a coupler between a generator and
space or vice-versa

7. Types of Antennas :
1.Wire antennas:
Dipole, Monopole, Loop antenna, Helix antennas
Usually these are used in Personal applications,
Automobiles, Buildings, Ships, Aircrafts and
Spacecrafts.

8. 2. Aperture antennas:
Horn antennas, Waveguide opening
Usually used in aircrafts and space crafts,
because these antennas can be flush-mounted.

9. 3. Reflector antennas:
Parabolic reflectors, Corner reflectors .
Thesearehighgainantennasusuallyusedin
radioastronomy,microwavecommunication
andsatellitetracking.

10. 4.Lens antennas:
Convex-plane, co vex-convex , convex-concave
and concave-plane lenses
These antennas are usually used for very high
frequency applications.

11. 5.Microstrip antennas :
Rectangular, Circular etc. shaped metallic
patch above a ground plane
Used in Aircraft, Spacecraft, Satellites, Missiles,
Cars, Mobile phones etc.

12. 6. Array antennas :
Yagi-Uda antenna, Microstrip Patch array,
Aperture array, Slotted waveguide array
Used for very high gain applications with added
advantage, such as controllable radiation
pattern.

13. Whenelectricchargesundergoaccelerationor
deceleration,electromagneticradiationwillbe
produced.
Henceitisthemotionofcharges,thatcurrentisthe
sourceofradiation.
Hereitmaybehighlightedthat,notallcurrent
distributionswillproduceastrongenoughradiation
forcommunication.
Antennasradiateorcouplesordirectselectromagnetic
energyinthedesiredorassigneddirection.
Anantennamaybeisotropicornondirectional
(Omni-directional)andunisotropicorDirectional.

14. To give a mathematical flavor to it, as we know :
Asshownintheseequations,tocreateradiation(electric
field),theremustbeatime-varyingcurrentdI/dtoran
acceleration(ordeceleration)aofachargeq.
If the charge is not moving, a current is not created and
there is no radiation.

15. If a charge is moving with an uniform velocity
There is no radiation if the wire is straight, and
infinite in extent
There is radiation if the wire is curved, bent,
discontinuous, terminated, or truncated
If the charge is oscillating in a time-motion, it radiates
even if the wire is straight.
These situations are shown in Fig. below

16. So, it is the current distribution on the antennas
that produce the radiation.
Usually these current distributions are excited
by transmission lines and waveguides

17. Radiation from a Single Wire :
Conductingwiresarecharacterizedbythe
motionofelectricchargesandthecreationof
currentflow.
Assumethatanelectricvolumechargedensity,
qv(coulombs/m3),isdistributeduniformlyin
acircularwireofcross-sectionalareaAand
volumeV.

18. Current density in a volume with volume charge
density qV(C/m
3
)
J
z= qV. V
z(A/m
2
)
Surface current density in a section with a surface
charge density qS(C/m
2
)
Js = qS.Vz(A/m)
Current in a thin wire with a linear charge density qI
(C/m):
Iz= ql.VzA
Toaccelerate/deceleratecharges,oneneedssourcesof
electromotiveforceand/ordiscontinuitiesofthe
mediuminwhichthechargesmove.
Suchdiscontinuitiescanbebendsoropenendsof
wires,changeintheelectricalpropertiesoftheregion,
etc.

19. In summary:
Itisafundamentalsinglewireantenna.Fromtheprinciple
ofradiationtheremustbesometimevaryingcurrent.
For a single wire antenna:
1.If a charge is not moving, current is not created and there is
no radiation.
2. If charge is moving with a uniform velocity:
a. There is no radiation if the wire is straight, and infinite
in extent.
b. There is radiation if the wire is Curved, Discontinuous,
Terminated, Bent or Truncated.
3. If charge is oscillating in a time-motion, it radiates even if
the wire is straight.

20. Radiation from a Two Wire :
Let us consider a voltage source connected to a
two-conductor transmission line which is
connected to an antenna.
This is shown in Figure, Applying a voltage
across the two conductor transmission line
creates an electric field between the conductors.

21. Radiation from a Dipole :
The radiation of energy when done through
such a bent wire, the end of such transmission
line is termed asdipoleor dipole antenna.
Now let us attempt to explain the mechanism
by which the electric lines of force are detached
from the antenna to form the free-space waves.

22. Current distribution on a thin wire antenna :
Let us consider a lossless two wire transmission
line in which the movement of charges creates a
current having value Iwith each wire.
This current at the end of the transmission line is
reflected back, when the transmission line has
parallel end points resulting in formation of
standing waves in combination with incident
wave.

23. When the transmission line is flared out at 90
0
forming geometry of dipole antenna.
Thecurrentdistributionremainsunalteredand
theradiatedfieldsnotgettingcancelledresulting
innetradiationfromthedipole.
Ifthelengthofthedipolel<λ/2,thephaseof
currentofthestandingwaveineachtransmission
lineremainssame.

24. If diameter of each line is small d<< λ/2,
Thecurrentdistributionalongthelineswillbe
sinusoidalwithnullatendbutoverall
distributiondependsonthelengthofthedipole
The current distribution for dipole of length
l << λ

25. When l > λ, the current goes phase reversal
between adjoining half-cycles.
Hence, current is not having same phase along
all parts of transmission line.
This will result into interference and cancelling
effects in the total radiation pattern.

26. Thecurrentdistributionswehaveseenrepresent
themaximumcurrentexcitationforanytime.
Thecurrentvariesasafunctionoftimeaswell.

28. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

29. Antenna Parameters :
Todescribetheperformanceofanantenna,
definitionsofvariousparametersarenecessary.
Someoftheparametersareinterrelatedandnot
allofthemneedbespecifiedforcomplete
descriptionoftheantennaperformance.
RadiationPatterns.PatternsinPrincipalPlanes,
MainLobeandSideLobes,Beamwidths,
Polarization,BeamArea,RadiationIntensity,Beam
Efficiency,Directivity,Gain,Resolution,Antenna
Apertures,ApertureEfficiency,EffectiveHeight

31. Anantennaradiationpatternorantennapatternis
definedas―amathematicalfunctionoragraphical
representationoftheradiationpropertiesofthe
antennaasafunctionofspacecoordinates.
Radiationpropertiesincludepowerfluxdensity,
radiationintensity,fieldstrength,directivity,phaseor
polarization.
Theradiationpropertyofmostconcernisthetwo-
orthreedimensionalspatialdistributionof
radiatedenergyasafunctionoftheobserver‘s
positionalongapathorsurfaceofconstantradius.

32. Atraceofthereceivedelectric(magnetic)fieldat
aconstantradiusiscalledfieldpattern.
Ontheotherhand,agraphofthespatial
variationofthepowerdensityalongaconstant
radiusiscalledpowerpattern.
Oftenthefieldandpowerpatternsare
normalizedwithrespecttotheirmaximumvalue,
yieldingnormalizedfieldandpowerpatterns.

33. For an antenna, the
a).Fieldpattern(inlinearscale)typically
representsaplotofthemagnitudeofthe
electricormagneticfieldasafunctionofthe
angularspace.
b).Powerpattern(inlinearscale)typically
representsaplotofthesquareofthe
magnitudeoftheelectricormagneticfieldasa
functionoftheangularspace.
c).Powerpattern(indB)representsthe
magnitudeoftheelectricormagneticfield,in
decibels,asafunctionoftheangularspace.

35. Coordinate system for antenna analysis

36. Dividing a field component by its maximum value,
we obtain a normalized or relative field pattern which is
a dimensionless number with maximum value of unity
Eθ(θ,ɸ) →The θ-component of the electric field as a
function of angles θ and ɸ(v/m)
Eɸ(θ,ɸ) → The ɸ-component of electric field as a
function of angle θ and ɸ(v/m)
δθ(θ,ɸ) or δɸ(θ,ɸ) → The phase angles of both the
field components (deg. Or rad.)

37. Below Figures are principal plane field and
power patterns in polar coordinates.

38. Theangularbeamwidthatthehalf-powerlevel
orhalf-powerbeamwidth(HPBW)(or−3-dB
beamwidth)andthebeamwidthbetweenfirst
nulls(FNBW)
Anisotropicradiatorisdefinedas―a
hypotheticallosslessantennahavingequal
radiationinalldirections.
Adirectionalantennaisone―havingthe
propertyofradiatingorreceiving
electromagneticwavesmoreeffectivelyin
somedirectionsthaninothers.

39. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

40. For a linearly polarized antenna, performance is
often described in terms of its principal E-and
H-planepatterns
TheE-planeisdefinedas―theplanecontaining
theelectricfieldvectorandthedirectionof
maximumradiation
TheH-planeas―theplanecontainingthe
magnetic-fieldvectorandthedirectionof
maximumradiation.

41. For this example, the x-z plane (elevationplane;
θ) is the principal E-plane
The x-y plane (azimuthalplane; ɸ) is the
principal H-plane.

43. Radian and Steradian:
Themeasureofaplaneangleisaradian.One
radianisdefinedastheplaneanglewithits
vertexatthecenterofacircleofradiusrthatis
subtendedbyanarcwhoselengthisr.
ThemeasureofasolidangleisasteradianOne
steradianisdefinedasthesolidanglewithits
vertexatthecenterofasphereofradiusrthatis
subtendedbyasphericalsurfaceareaequalto
thatofasquarewitheachsideoflengthr.

44. Since the area of a sphere of radius ris A = 4πr
2
,
there are 4π sr(4πr
2
/r
2
) in a closed sphere.

45. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

46. Main Lobe and Side Lobes :
Variouspartsofaradiationpatternarereferred
toaslobes,whichmaybesubclassifiedintomajor
ormain,minor,side,andbacklobes.
Aradiationlobeisaportionoftheradiationpattern
boundedbyregionsofrelativelyweak
radiationintensity.

47. Amajorlobe(alsocalledmainbeam)isdefinedasthe
radiationlobecontainingthedirectionofmaximum
radiation.
Aminorlobeisanylobeexceptamajorlobe.allthe
lobeswiththeexceptionofthemajorcanbe
classifiedasminorlobes.
A side lobe is a radiation lobe in any
direction other than the intended lobe.
A back lobe is a radiation lobe whose axis
makes an angle of approximately 180◦
with respect to the beam of an antenna.

48. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

49. Beam Width :
Intheradiationpatternofanantenna,themain
lobeisthemainbeamoftheantennawhere
maximumandconstantenergyradiatedbythe
antenna.
Beam widthis the aperture angle from where
most of the power is radiated.
The two main considerations of this beam width
are
Half Power Beam Width(HPBW)
First Null Beam Width(FNBW).

50. Half-Power Beam Width :
According to the standard definition, “The angular
separation, in which the magnitude of the radiation
pattern decreases by 50% (or -3dB) from the peak of
the main beam, is theHalf Power Beam Width.”
In other words, Beam width is the area where most
of the power is radiated, which is the peak power.
Half power beam widthis the angle in which
relative power is more than 50% of the peak power,
in the effective radiated field of the antenna.

51. First Null Beam Width :
Accordingtothestandarddefinition,“The
angularspanbetweenthefirstpatternnulls
adjacenttothemainlobe,iscalledastheFirst
NullBeamWidth.”
Simply,FNBWistheangular
separation,quotedaway
fromthemainbeam,which
isdrawnbetweenthenull
pointsofradiationpattern,
onitsmajorlobe

53. Introduction
Radiation Mechanism(Single wire, 2 wire, Dipoles )
Current Distribution on a thin wire antenna.
Antenna Parameters
Radiation Patterns
Patterns in Principal Planes
Main Lobe and Side Lobes
Beam widths
Polarization

54. Antenna Polarization :
Polarizationofanantennainagivendirectionis
definedasvectororientationofElectricfield
componentoftheWaveradiatedbytheantenna.
Inpractice,polarizationoftheradiatedenergy
varieswiththedirectionfromthecenterofthe
antenna,sothatdifferentpartsofthepatternmay
havedifferentpolarizations.
Polarizationthenisthecurvetracedbytheend
pointofthearrow(vector)representingthe
instantaneouselectricfield.
The field must be observed along the direction of
propagation.

55. Polarization may be classified as
Linear Polarization
Circular Polarization
Elliptical Polarization
Thelinearpolarizationoftheantennahelpsin
maintainingthewaveinaparticulardirection,
avoidingalltheotherdirections.(bothVertical
andHorizontalpolarizations)
Thoughthislinearpolarizationisused,the
electricfieldvectorstaysinthesameplane.
Hence,weusethislinearpolarizationto
improvethedirectivityoftheantenna.

56. When a wave is circularly polarized, the electric
field vector appears to be rotated with all its
components loosing orientation.
The mode of rotation may also be different at times.
However, by usingcircular polarization, the effect of
multi-path gets reduced and hence it is used in
satellite communications such asGPS.
Another form of polarization is known as Elliptical
polarization. It occurs when there is a mix of linear
and circular polarization.
This can be visualized as before by the tip of the
electric field vector tracing out an elliptically shaped
corkscrew.

58. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

59. Beam Area :
Beamareaisthesolidanglethroughwhichall
thepowerradiatedbytheantennaP(θ,Ø)
maintaineditsmaximumvalueoverΩ
Aand
waszeroelsewhere.
Theradiatedbeamoftheantennacomesout
fromanangleattheantenna,knownassolid
angle,wherethepowerradiationintensityis
maximum.
Thissolidbeamangleistermedasthebeam
area.ItisrepresentedbyΩ
A.

60. TheradiationintensityP(θ,Ø)shouldbe
maintainedconstantandmaximumthroughout
thesolidbeamangleΩ
A,itsvaluebeingzero
elsewhere.

61. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

62. Radiation Intensity :
Thepowerradiatedfromanantennaperunit
solidangleiscalledtheradiationintensityU
Radiationemittedfromanantennawhichis
moreintenseinaparticulardirection,indicates
themaximumintensityofthatantenna.
Theemissionofradiationtoamaximum
possibleextentisnothingbuttheradiation
intensity.

63. Theradiationintensityisafar-fieldparameter,
anditcanbeobtainedbysimplymultiplyingthe
radiationdensitybythesquareofthedistance.
In mathematical form it is expressed as
U (θ, ɸ) = r
2
P
rad(θ, ɸ)
Where
U (θ, ɸ)= radiation intensity (W/unit solid angle)
P
rad(θ, ɸ) = radiation density (W/m
2
)

64. Thus the total power radiated is given by

65. ThustheradiationintensityU(θ,ɸ)is
expressedinwattspersteradiananditis
definedastimeaveragepowerperunitsolid
angle.
The average value of radiation intensity of an
isotropic source is given by

66. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

67. Beam Efficiency :
Thebeamefficiencystatestheratioofthe
beamareaofthemainbeamtothetotalbeam
arearadiated
ThebeamareaΩAconsistsofthemainbeam
areaΩMplustheminor-lobeareaΩm.
Thus,
ΩA= ΩM+ Ω m

68. The ratio of the main beam area to the (total)
beam area is called the (main) beam efficiency
εMThus,

69. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

70. Directivity :
Directivityofanantennaorarrayisameasure
oftheantenna’sabilitytofocustheenergyin
oneormorespecificdirections.
Youcandetermineanantenna’sdirectivityby
lookingatitsradiationpattern.
Inanarraypropagatingagivenamountof
energy,moreradiationtakesplaceincertain
directionsthaninothers
Itisdefinedastheratioofmaximumradiation
intensityoftestantennatotheradiation
intensityofanisotropicantenna.

71. Directivity is defined as the ratio of maximum
radiation intensity to the average radiation
intensity.
Directivity (D) in terms of total power radiated
is

72. The directivity of an antenna is equal to the ratio
of the maximum power density P(θ,ɸ)
max
(watts/m
2
) to its average value over a sphere
as observed in the far field of an antenna.
Thus,

73. Therefore, the directivity
Thus,thedirectivityistheratiooftheareaofa
sphere(4πsr)tothebeamareaΩAoftheantenna.
Thesmallerthebeamarea,thelargerthe
directivityD.

74. If the half-power beamwidths of an antenna are
known, its directivity

75. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

76. Gain :
Gainofanantenna(inagivendirection)isdefined
as“theratiooftheintensity,inagivendirection,to
theradiationintensitythatwouldbeobtainedifthe
poweracceptedbytheantennawereradiated
isotropically.
In equation form this can be expressed as
Whenthedirectionisnotstated,thepowergainis
usuallytakeninthedirectionofmaximum
radiation.

77. ThegainGofanantennaisanactualor
realizedquantitywhichislessthanthe
directivityDduetoohmiclossesintheantenna
Intransmitting,theselossesinvolvepowerfed
totheantennawhichisnotradiatedbutheats
theantennastructure.
Theratioofthegaintothedirectivityisthe
antennaefficiencyfactor.Thus,η
G=ηD
Whereηistheantennaefficiencyfactor(0<k<1)

78. Resolution :
Theresolutionofanantennaisdefinedashalf
ofthebeamwidthbetweenfirstnulls
Buthalfthebeamwidthbetweenfirstnullsis
approximatelyequaltotheHPBWofan
antenna.
Practically,HPBWisslightlylessthan
FNBW/2

79. Theantennabeamareaisgivenbytheproduct
oftwohalfpowerbeamwidthintwoprinciple
planes.
IfthereareNno.ofpointsourcesofradiation
distributeduniformly,thenantennaresolve
thoseandisgivenby

80. But by the definition, the directivity of antenna
is defined as,
Hence D = N →So, ideally no. of point sources
resolved by an antenna is equal to directivity of
an antenna.
Theresolutionofantennaisalsocalled
RayleighResolution

81. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

82. Antenna Apertures :
ApertureofanAntennaistheareathroughwhichthe
powerisradiatedorreceive.ConceptofAperturesis
mostsimplyintroducedbyconsideringaReceiving
Antenna.
LetthePoyntingvector,orpowerdensity,oftheplane
wavebeSwattspersquaremeterandthearea,or
physicalapertureofthehorn,beApsquaremeters.

83. If the horn extracts all the power from the wave
over its entire physical aperture, then the total
power P absorbed from the wave is
P= S.Ap=(E
2
/Z). Ap Watts
Where S is pointing impedance of medium
Z is intrinsic impedance of medium
E is rms value of electric field

84. Effectiveapertureisdefinedastheratioof
powerreceivedintheloadtotheaverage
powerdensityproducedatthepoint
Powerreceivedbytheantennamaybedenoted
byPR.
Anantennashouldhavemaximumusefularea
toextractenergyandthusthemax.effective
apertureisobtainedwhenpowerreceivedis
maximum,denotedbyAem.

85. LetuscalculateeffectiveaperturefortheHerzian
dipole,whentheHertziandipoleisusedasthe
receivingantenna
It extracts power from the incident waves and
delivers it to the load, producing voltage in it.
The voltage induced in the antenna is given by
Voc = |E| dL
Where
|E| is the magnitude of Electric Field
Intensity produced at the receiving point
dL is the length of the Hertzian dipole

86. Then the current flowing the load is given by
I = Voc / Z + ZL
For the maximum power transfer condition,
load is selected as the complex conjugate of the
antenna impedance (ZL = Z*)
SubstitutingthevaluesofimpedanceZandZL,
thecurrentflowingcanbewrittenas

87. Therefore
The maximum effective aperture is given by

88. Now

89. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

90. Aperture Efficiency :
Accordingtothestandarddefinition,“Aperture
efficiencyofanantenna,istheratiooftheeffective
radiatingarea(oreffectivearea)tothephysicalarea
oftheaperture.
Anantennahasanaperturethroughwhichthe
powerisradiated.
Thisradiationshouldbeeffectivewithminimum
losses.
Thephysicalareaoftheapertureshouldalsobe
takenintoconsideration,astheeffectivenessofthe
radiationdependsupontheareaoftheaperture,
physicallyontheantenna.

91. The mathematical expression for aperture
efficiency is as follows

92. Beam Area
Radiation Intensity
Beam Efficiency
Directivity
Gain and Resolution
Antenna Apertures
Aperture Efficiency
Effective Height
illustrated Problems

93. Effective Height :
TheEffectivelengthistheratioofthe
magnitudeofvoltageattheopenterminalsof
thereceivingantennatothemagnitudeofthe
fieldstrengthoftheincidentwavefront,inthe
samedirectionofantennapolarization.
Whenanincidentwavearrivesattheantenna’s
inputterminals,thiswavehassomefield
strength,whosemagnitudedependsuponthe
antenna’spolarization.
Thispolarizationshouldmatchwiththe
magnitudeofthevoltageatreceiverterminals.

94. The mathematical expression for effective
length is
Leff= Voc/ E i
Where
Leffis the effective length.
Voc is open-circuit voltage.
Eiis the field strength of the incident wave.

96. Summary of Important Parameters and Associated Formulas

99. Thank you