antennasgbtaylor/astr423/lectures/07_antennas.pdf2 g. taylor, astr 423 at unm outline •fourier...
TRANSCRIPT
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Astronomy 423 at UNMRadio Astronomy
AntennasGreg TaylorUniversity of New Mexico
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G. Taylor, Astr 423 at UNM
Outline
• Fourier Transforms • Interferometer block diagram• Antenna fundamentals• Types of antennas• Antenna performance parameters• Receivers• Dipole Antennas
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stationary time series
indefinitely long
but
statistical properties don’t vary with time
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time, minutes
assume that we are dealing with a fragment of an indefinitely long time series
timeseries,d
duration, Tlength, N
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one quantity that might be stationary is …
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“Power”
0
T
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0
T
Power
mean-squared amplitude of time series
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How is power related topower spectral density ?
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write Fourier Series asd=Gm
weremare the Fourier coefficients
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now use
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now use
coefficients of sines and cosines
coefficients of complex exponentials
Fourier Transformequals 2/T
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so, if we define the power spectral density of a stationary time series as
the integral of the p.s.d. is the power in the time series
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Example: Atmospheric CO2(after removing anthropogenic trend)
0 5 10 15 20 25 30 35 40 45 50-4
-2
0
2
4
time, years
CO2,
ppm
0 1 2 3 4 50
1
2
3
frequency, cycles per year
log1
0 ps
d of
CO
2
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0 0.5 1 1.5 2 2.5 3-3
-2
-1
0
1
2
3
4
time, years
CO2,
ppm
enlargement
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0 0.5 1 1.5 2 2.5 3-3
-2
-1
0
1
2
3
4
time, years
CO2,
ppm
enlargement
period of 1 year
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0 5 10 15 20 25 30 35 40 45 50-4
-2
0
2
4
time, years
CO
2, p
pm
0 1 2 3 4 50
1
2
3
frequency, cycles per year
log1
0 ps
d of
CO
2
power spectral density
frequency,cyclesperyear
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0 1 2 3 4 5 60
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
frequency, cycles per year
powe
r
cumulative power
power in time series
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Fourier Transforms 18
G. Taylor, Astr 423 at UNM
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Fourier Transforms 19
G. Taylor, Astr 423 at UNM
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G. Taylor, Astr 423 at UNM
Mixer
Software
Square law detector
Bandpass filter, IF amplifier
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G. Taylor, Astr 423 at UNM
E.g., pre-upgrade VLA observing
at 4.8 GHz (C band) Interferometer Block Diagram
Antenna
Front End
IF
Back End
Correlator
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G. Taylor, Astr 423 at UNM
• Antenna amplitude pattern causes amplitude to vary across the source.
• Antenna phase pattern causes phase to vary across the source.
• Polarization properties of the antenna modify the apparentpolarization of the source.
• Antenna pointing errors can cause time varying amplitude andphase errors.
• Variation in noise pickup from the ground can cause timevariable amplitude errors.
• Deformations of the antenna surface can cause amplitude andphase errors, especially at short wavelengths.
Importance of the Antenna Elements
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G. Taylor, Astr 423 at UNM
Wavelength > 1 m (approx) Wire AntennasDipole
Ae = Gl2/4p Yagi
Helixor arrays of these
Wavelength < 1 m (approx) Reflector antennas
Wavelength = 1 m (approx) Hybrid antennas (wire reflectors or feeds)
Feed
General Antenna Types
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G. Taylor, Astr 423 at UNM
Effective collecting area A(n,q,f) m2
On-axis response Ae = hAh = aperture efficiency
Normalized pattern(primary beam)A(n,q,f) = A(n,q,f)/Ae
Beam solid angle WA= ∫∫ A(n,q,f) dWall sky
Ae WA = l2
Basic Antenna Formulas
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G. Taylor, Astr 423 at UNM
f(u,v) = complex aperture field distributionu,v = aperture coordinates (wavelengths)
F(l,m) = complex far-field voltage patternl = sinqcosf , m = sinqsinf
F(l,m) = ∫∫aperturef(u,v)exp(2pi(ul+vm)dudvf(u,v) = ∫∫hemisphereF(l,m)exp(-2pi(ul+vm)dldm
For VLA: q3dB = 1.02/D, First null = 1.22/D, D = reflector diameter in wavelengths
Aperture-Beam Fourier Transform Relationship
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G. Taylor, Astr 423 at UNM
The Standard Parabolic Antenna Response
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G. Taylor, Astr 423 at UNM
Primary Antenna Key Features
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G. Taylor, Astr 423 at UNM
+ Beam does not rotate + Lower cost+ Better tracking accuracy + Better gravity performance- Higher cost - Beam rotates on the sky- Poorer gravity performance- Non-intersecting axis
Types of Antenna Mount
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G. Taylor, Astr 423 at UNM
Parallactic angle
Beam Rotation on the Sky
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G. Taylor, Astr 423 at UNM
Prime focus Cassegrain focus(GMRT) (AT)
Offset CassegrainNaysmith
(VLA) (OVRO)
Beam Waveguide Dual Offset(NRO)(ATA)
Reflector Types
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G. Taylor, Astr 423 at UNM
Prime focus Cassegrain focus(GMRT) (AT)
Offset CassegrainNaysmith
(VLA) (OVRO)
Beam Waveguide Dual Offset(NRO) (ATA)
Reflector Types
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G. Taylor, Astr 423 at UNM
Effelsberg 100-m telescope near Bonn, Germany
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G. Taylor, Astr 423 at UNM
DualOffset
Unblocked Aperture(GBT)
Reflector Types
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G. Taylor, Astr 423 at UNM
VLA and EVLA Feed System Design
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G. Taylor, Astr 423 at UNM
Example Feed Horn
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G. Taylor, Astr 423 at UNM
8 x 9Array for2-7 GHz
IvashinaEt al.
Focal Plane Arrays
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G. Taylor, Astr 423 at UNM
Aperture EfficiencyA0 = hA, h = hsf * hbl * hs * ht * hmisc
hsf = reflector surface efficiencyhbl = blockage efficiencyhs = feed spillover efficiencyht = feed illumination efficiencyhmisc= diffraction, phase, match, loss
hsf = exp(-(4ps/l)2)e.g., s = l/16 , hsf = 0.5
rms error s
Antenna Performance Parameters
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G. Taylor, Astr 423 at UNM
Primary Beam
l=sin(q), D = antenna diameter in contours:-3,-6,-10,-15,-20,-25,wavelengths -30,-35,-40 dBdB = 10log(power ratio) = 20log(voltage ratio)For VLA: q3dB = 1.02/D, First null = 1.22/D
pDl
Antenna Performance Parameters
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G. Taylor, Astr 423 at UNM
Pointing AccuracyDq = rms pointing error
Often Dq < q3dB /10 acceptableBecause A(q3dB /10) ~ 0.97BUT, at half power point in beamA(q3dB /2 ± q3dB /10)/A(q3dB /2) = ±0.3
For best VLA pointing use Reference Pointing. Dq = 3 arcsec = q3dB /17 @ 50 GHz
Dq
q3dB
Primary beam A(q)
Antenna Performance Parameters
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G. Taylor, Astr 423 at UNM
Subreflector mount
Quadrupod
El encoder
Reflector structure
Alidade structure
Rail flatness
Az encoder
Foundation
Antenna Pointing Design
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G. Taylor, Astr 423 at UNM
Surface: s = 25 µmPointing: Dq = 0.6 arcsec
Carbon fiber and invar reflector structure
Pointing metrology structureinside alidade
ALMA 12m Antenna
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G. Taylor, Astr 423 at UNM
Polarization
Antenna can modify the apparent polarization properties of the source:• Symmetry of the optics• Quality of feed polarization splitter• Circularity of feed radiation patterns• Reflections in the optics• Curvature of the reflectors
Antenna Performance Parameters
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G. Taylor, Astr 423 at UNM
Cross polarized Cross polarizedaperture distribution primary beam
VLA 4.8 GHzcross polarizedprimary beam
Off-Axis Cross Polarization
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G. Taylor, Astr 423 at UNM
VLA 4.8 GHz
Far field pattern amplitudePhase not shown
Aperture field distributionamplitude.Phase not shown
Antenna Holography
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G. Taylor, Astr 423 at UNM
Other Concerns
• Pointing errors, especially at high frequencies• Gain curves• Atmospheric opacity corrections• Ionospheric effects: scintillation, isoplanatic patch size
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G. Taylor, Astr 423 at UNM
Practical concerns continued• Opacity corrections and tipping scans
– Can measure the total power detected as a function of elevation, which has contributions
Tsys = T0 + Tatm(1-et0a) + Tspill(a)and solve for t0.– Or, make use of the fact that there is a good correlation between
the surface weather and t0 measured at the VLA (Butler 2002):
and apply this opacity correction using FILLM in AIPS
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G. Taylor, Astr 423 at UNM
Noise Temperature
Pin = kBT Dn ,kB = Boltzman’s constant
When observing a radio source Ttotal = TA + Tsys
Tsys = system noise when not looking at a discrete radio source
TA = source antenna temperatureTA = hAS/(2kB) S = source flux (Jy)
SEFD = system equivalent flux density SEFD = Tsys/K (Jy)
ReceiverGain GB/W Dn
Matched load Temp T (oK)
Pout=G*PinPin
Rayleigh-Jeans approximation
Band (GHz) h Tsys SEFD
1-2 .50 21 236
2-4 .62 27 245
4-8 .60 28 262
8-12 .56 31 311
12-18 .54 37 385
18-26 .51 55 606
26-40 .39 58 836
40-50 .34 78 1290
VLA Sensitivities
Receivers
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G. Taylor, Astr 423 at UNM
Hertz Dipole
Ae = Gl2/4p G=1.5 for Hertz DipoleG = 2.5 at 20 MHz for LWAG = 4.0 at 60 MHz for LWA
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G. Taylor, Astr 423 at UNM
LWA Antenna
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G. Taylor, Astr 423 at UNM
20 MHz 3D
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G. Taylor, Astr 423 at UNM
E and H-Plane Antenna Pattern
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G. Taylor, Astr 423 at UNM
Further Reading
http://www.nrao.edu/whatisra/mechanisms.shtmlhttp://www.nrao.edu/whatisra/www.nrao.edu
Synthesis Imaging in Radio Astronomy ASP Vol 180, eds Taylor, Carilli & Perley