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Chapter 2Chapter 2Fundamental Properties Fundamental Properties
of Antennasof Antennas
ECE 5318/6352Antenna Engineering
Dr. Stuart Long
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IEEE StandardsIEEE Standards
Definition of Terms for Antennas
IEEE Standard 145-1983
IEEE Transactions on Antennas and Propagation Vol. AP-31, No. 6, Part II, Nov. 1983
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Radiation PatternRadiation Pattern(or Antenna Pattern)(or Antenna Pattern)
“The spatial distribution of a quantity which characterizes the electromagnetic field
generated by an antenna.”
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Distribution can be aDistribution can be a
Mathematical function
Graphical representation
Collection of experimental data points
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Quantity plotted can be aQuantity plotted can be a
Power flux density W [W/m²]
Radiation intensity U [W/sr]
Field strength E [V/m]
Directivity D
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Graph can beGraph can be
Polar or rectangular
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Graph can beGraph can be
Amplitude field |E| or power |E|²
patterns
(in linear scale) (in dB)
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Graph can beGraph can be
2-dimensional or 3-D
most usually several 2-D “cuts”
in principleplanes
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Radiation pattern can beRadiation pattern can be
IsotropicEqual radiation in all directions (not physically realizable, but valuable for comparison purposes)
DirectionalRadiates (or receives) more effectively in some directions than in others
Omni-directionalnondirectional in azimuth, directional in elevation
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Principle patternsPrinciple patterns
E-plane Plane defined by E-field and direction of maximum radiation
H-plane Plane defined by H-field and direction of maximum radiation
(usually coincide with principle planes of the coordinate system)
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Coordinate SystemCoordinate System
Fig. 2.1 Coordinate system for antenna analysis.
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Radiation pattern lobesRadiation pattern lobes
Major lobe (main beam) in direction of maximum radiation (may be more than one)
Minor lobe -
any lobe but a major one
Side lobe -
lobe adjacent to major one
Back lobe –
minor lobe in direction exactly
opposite to major one
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Side lobe level or ratio (SLR)Side lobe level or ratio (SLR)
(side lobe magnitude / major lobe magnitude)
-
20 dB typical
< -50 dB very difficultPlot routine included on CD for rectangular and polar graphs
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Polar PatternPolar Pattern
Fig. 2.3(a) Radiation lobes and
beamwidths of an antenna pattern
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Linear PatternLinear Pattern
Fig. 2.3(b) Linear plot of power pattern and
its associated lobes and beamwidths
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Field RegionsField Regions
Reactive near fieldReactive near fieldenergy stored not radiated
λ= wavelengthD= largest dimension of the antenna
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62.0 DR
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Field RegionsField Regions
Radiating near field (Fresnel)Radiating near field (Fresnel)radiating fields predominatepattern still depend on Rradial component may still be appreciable
λ= wavelengthD= largest dimension of the antenna
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262.0 DRD
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Field RegionsField Regions
Far field (Far field (FraunhoferFraunhofer))
field distribution independent of Rfield components are essentially transverse
2
2 DR
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RadianRadian
Fig. 2.10(a) Geometrical arrangements for defining a radian
r2
radians in full circlearc length of circle
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SteradianSteradian
one steradian subtends an area of
4π
steradians in entire sphere
ddrdA sin2
Fig. 2.10(b) Geometrical arrangements for defining a steradian.
ddrdAd sin2
2rA
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Radiation power densityRadiation power density
HEW
Instantaneous Poynting vector
Time average Poynting vector
[ W/m ²
]
Total instantaneousPower
Average radiated Power
[ W/m ²
]
s
sWP d [ W ]
HEW
Re21
avg
s
avgrad dP s
W[ W ]
[2-8]
[2-9]
[2-4]
[2-3]
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Radiation intensityRadiation intensity“Power radiated per unit solid angle”
avgWrU 2
far zone fields without 1/r
factor
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),,(2
),(
rrU E
222
),,(),,(2
rErEr
[W/unit solid angle]
[2-12a]
2 2o o1 ( , ) ( , )2
E E
Note: This final equation does not have an r in it. The “zero”
superscript means that the 1/r term is removed.
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Directive GainDirective Gain
Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions
radog
PU
UUD 4
Directivity GainDirectivity Gain
((DDgg) --
directivity in a given direction
[2-16]
0 4radPU
(This is the radiation intensity if the antenna radiated its power equally in all directions.)
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1 , sin4 S
U U d d
Note:
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Directivity Directivity
rad
max
o
maxo
PU
UUD 4
Do (isotropic) = 1.0
og DD 0
DirectivityDirectivity
----
DDoo
value of directive gain in direction of maximum radiation intensity
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BeamwidthBeamwidth
Half power beamwidthHalf power beamwidthAngle between adjacent points where field strength is 0.707 times the maximum, or the power is 0.5 times the maximum (-3dB
below maximum)
First null beamwidthFirst null beamwidthAngle between nulls in pattern
Fig. 2.11(b) 2-D power patterns (in linear scale) of U()=cos²()cos³()
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Approximate directivity for Approximate directivity for omnidirectional patternsomnidirectional patterns
McDonaldMcDonald
2HPBW0027.0HPBW
101
oD
π
π
PozarPozar
(HPBW in degrees)
Results shown with exact values in Fig. 2.18
HPBW1818.01914.172 oD
nU sin
Better if no minor lobes [2-33b]
[2-32]
[2-33a]
For example
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Approximate directivity for directional patternsApproximate directivity for directional patterns
KrausKraus
1 2 1 2
4 41, 253o
r r d d
D
π/2
π
Tai & PereiraTai & Pereira
Antennas with only one narrow main lobe and very negligible minor lobes
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22
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815,7218.22
ddrr
oD
nU cos
[2-30b]
[2-31]
[2-27]
For example
(
) HPBW in two perpendicular planes in radians or in degrees)1 2,r r
1 2,d d
Note: According to Elliott, a better number to use in the Kraus formula is 32,400 (Eq. 2-271 in Balanis). In fact, the 41,253 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one).
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Approximate directivity for Approximate directivity for directional patternsdirectional patterns
Can calculate directivity directly (sect.2.5), can evaluate directivity numerically (sect. 2.6)
(when integral for
Prad
cannot be done analytically,analytical formulas cannot be used )
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GainGainLike directivity but also takes into account efficiency of antenna
(includes reflection, conductor, and dielectric losses)
oin
oin
ZZZZ
;1 2
eo
: overall eff.
er
: reflection eff.
ec
: conduction eff.
ed : dielectric eff.
Efficiency
source) isotropic(lossless,PU
PUeDeG
in
max
rad
maxooooabs
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dcro eeee dccd eee
[2-49c]
radcd
in
PeP
rado
inc
PeP
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GainGain
By IEEE definition “gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses)”
source) isotropic(lossless,PUDeG
in
maxocdo
4 [2-49a]
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BandwidthBandwidth
“frequency range over which some characteristic conforms to a standard”
Pattern bandwidth
Beamwidth, side lobe level, gain, polarization, beam direction
polarization bandwidth example: circular polarization with axial
ratio < 3 dB
Impedance bandwidth
usually based on reflection coefficient
under 2 to 1 VSWR typical
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BandwidthBandwidth
Broadband antennas usually use ratio (e.g. 10:1)
Narrow band antennasusually use percentage (e.g. 5%)
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PolarizationPolarization
Linear
Circular
Elliptical
Right or left handed
rotation in time
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PolarizationPolarization
Polarization loss factor
p
is angle between wave and antenna polarization
2 2ˆ ˆ cosw a pPLF [2-71]
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Input impedanceInput impedance“Ratio of voltage to current at terminals of antenna”
ZA
= RA
+ jXA
RA
= Rr
+ RL
Rr
= radiation resistanceRL
= loss resistance
ZA
= antenna impedance at terminals a-b
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Input impedanceInput impedance
Antenna radiation efficiencyAntenna radiation efficiency
2
2 2
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1 1( )2 2
g rr
cdr L
g r g L
I RPower Radiated by Antenna Pe
Power Delivered to Antenna P P I R I R
[2-90]
Lr
rcd
RRRe
Note: this works well for those antennas that are modeled as a series RLC circuit –
like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values.
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Friis Transmission EquationFriis Transmission Equation
Fig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis
transmission equation
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Friis Transmission EquationFriis Transmission Equation
et = efficiency of transmitting antenna
er = efficiency of receiving antennaDt = directive gain of transmitting antennaDr = directive gain of receiving antenna = wavelengthR = distance between antennas
assuming impedance andpolarization matches
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4),(),(
RDDee
PP rrrttt
rtt
r
[2-117]
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Radar Range EquationRadar Range Equation
Fig. 2.32 Geometrical arrangement of transmitter, target, and receiver for radar range equation
2
2144),(),(
RRDDee
PP rrrttt
t
rcdrcdt
[2-123]
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Radar Cross SectionRadar Cross Section
RCS
Usually given symbol
Far field characteristic
Units in [m²]
4 r
inc
UW
incident power density on body from transmit directionincW
scattered power intensity in receive directionrU
Physical interpretation: The radar cross section is the area of an equivalent ideal “black body”
absorber that absorbs all incident power that then radiates it equally in all directions.
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Radar Cross Section (Radar Cross Section (RCS)
Function of
Polarization of the wave
Angle of incidence
Angle of observation
Geometry of target
Electrical properties of target
Frequency
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Radar Cross Section (Radar Cross Section (RCS)