ECE422: Radio and Microwave Wireless Systems Radio and Microwave Wireless Systems Antenna Radiation...
Transcript of ECE422: Radio and Microwave Wireless Systems Radio and Microwave Wireless Systems Antenna Radiation...
ECE422: Radio and Microwave WirelessSystems
Antenna Radiation Patterns
University of Toronto
Prof. Sean Victor Hum
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Antenna Radiation Pattern
“A mathematical functionor graphical representationof the radiation propertiesas a function of spacecoordinates”
Field strength,directivity, radiationintensity, power density,phase, etc.
Normally plotted in thefar-field of the antennaPlotted at a fixed distance(radius) r from antenna
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Field vs. Power Patterns
Field Pattern Power Pattern
HPBW = half power beamwidth
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Radiation Pattern Lobes and Beamwidths
3D pattern
2D cut (e.g. yz-plane)
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Radiation Pattern Types
Isotropic – equal radiationin all directions
Not physically realizablebut a useful theoreticalreference
Omnidirectional –possessing anon-directional pattern ina given plane
Useful for broadcastscenarios
Directional – having apreferred direction oftransmission/reception
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Principal Planes and Patterns
E-plane – plane containingthe electric-field vector anddirection of maximumradiationH-plane – plane containingthe magnetic-field vectorand direction of maximumradiation
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Radiation Pattern of a Dipole
3D pattern E-plane cut H-plane cut
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Field Regions
Near-field region (r < R1) –non-radiating [reactive]antenna fields dominateRadiating near-field region(R1 < r < R2) – radiatingfields dominate butangular distributiondepends on rFar-field (r > R2) – angularfield distribution does notdepend on r
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Example: Paraboloidal Reflector
Field measurements in thedifferent regions produceseemingly differentradiation patternsOnly in the far-field are thepatterns invariant ofobservation distance!
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Pattern Quantification: Solid Angle
Radians are a measure ofplane angle: 1 rad subtendsan arc of length r
C = 2πr
rads =Cr
=2πr
r= 2π
Steradians are a measure ofsolid angle: 1 sr subtends aspherical area of area r2
A = 4πr2
srs =Ar2 =
4πr2
r2 = 4π
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Pattern Quantification: Solid Angle
Radiation patterns aredescribed using aggregateparameters that quantifypowerKnowing the fieldsproduced by an antenna,power density (Poyntingvector) can be computedPower is computed bytaking the surface integralof power density
Pav =12
Re[E ×H∗]
Wrad =
S
Pav · n ds′
P0 = r P0 = rWrad
4πr2
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Pattern Quantification: Surface Integrals
Radiation integrals oftenuse spheres as the closedsurfaceRadius of sphere chosen tobe in the far fieldda = r2 sinθdθdφ [m2]
dΩ =dar2 = sinθdθdφ [sr]
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Radiation Intensity
Definition: power radiated per unit solid angle
U = r2Pav,r [W/sr]
Wrad =
Ω
UdΩ =
∫ 2π
0
∫ π
0U sinθdθdφ
In the far field,
U(θ, φ) =r2
2η|E(r, θ, φ)|2 ≈
r2
2η
[|Eθ(r, θ, φ)|2 + |Eφ(r, θ, φ)|2
]
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Directivity (D)
Definition: the ratio of the radiation intensity in a givendirection to the radiation intensity averaged over alldirections
D depends on θ, φGenerally maximum directivity is of most interest
D =UU0
=4πUWrad
Dmax ≡ D0 =Umax
U0=
4πUmax
Wrad
Can also be expressed in decibels with respect to isotropicantenna (dBi): 10 log10(D)
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Generalized Form of Directivity
Define a pattern function such that
U = B0F(θ, φ)
Then,
Prad = B0
∫ 2π
0
∫ π
0F(θ, φ) sinθdθdφ
D(θ, φ) = 4πF(θ, φ)∫ 2π
0
∫ π0 F(θ, φ) sinθdθdφ
D0 =4π[∫ 2π
0
∫ π0 F(θ, φ) sinθdθdφ
]/F(θ, φ)|max
≡4πΩA
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Beam Solid Angle
ΩA =1
F(θ, φ)|max
∫ 2π
0
∫ π
0F(θ, φ) sinθdθdφ
Solid angle through whichall the radiated powerwould flow if its radiationintensity were constant(= Umax) for all angleswithin ΩA
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Directivity Approximations
High-gain antennas oftenhave most power focusedin a tight beam withnegligible sidelobes; then:
ΩA ≈ θ1rθ2r
D0 =4πΩA≈
4πθ1rθ2r
≈41, 253θ1dθ2d
where θ1 and θ2 are thehalf-power beamwidthsintwo orthogonal planes(rads/degs)
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