Antennas Greg Taylor University of New Mexico Spring 2017 Astronomy 423 at UNM Radio Astronomy
Outline 2 Fourier Transforms Interferometer block diagram Antenna fundamentals Types of antennas Antenna performance parameters Receivers Dipole Antennas
stationary time series indefinitely long but statistical properties don t vary with time
assume that we are dealing with a fragment of an indefinitely long time series time, minutes time series, d duration, T length, N
one quantity that might be stationary is
Power T 0
Power T 0 mean-squared amplitude of time series
How is power related to power spectral density?
write Fourier Series as d = Gm were m are the Fourier coefficients
now use
now use coefficients of complex exponentials coefficients of sines and cosines equals 2/T Fourier Transform
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
Example: Atmospheric CO 2 (after removing anthropogenic trend) 4 CO2, ppm 2 0-2 -4 0 5 10 15 20 25 30 35 40 45 50 time, years
4 3 enlargement 2 CO2, ppm 1 0-1 -2-3 0 0.5 1 1.5 2 2.5 3 time, years
4 3 enlargement 2 CO2, ppm 1 0-1 -2 period of 1 year -3 0 0.5 1 1.5 2 2.5 3 time, years
power spectral density 3 log10 psd of CO2 2 1 0 0 1 2 3 4 5 frequency, cycles per year frequency, cycles per year
cumulative power 5 4.5 4 3.5 power 3 2.5 2 1.5 1 power in time series 0.5 0 0 1 2 3 4 5 6 frequency, cycles per year
Fourier Transforms 18
Fourier Transforms 19
20 Mixer Bandpass filter, IF amplifier Square law detector Software
E.g., VLA observing at 4.8 GHz (C band) Interferometer Block Diagram 21 Antenna Front End IF Back End Correlator
Importance of the Antenna Elements 22 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 apparent polarization of the source. Antenna pointing errors can cause time varying amplitude and phase errors. Variation in noise pickup from the ground can cause time variable amplitude errors. Deformations of the antenna surface can cause amplitude and phase errors, especially at short wavelengths.
General Antenna Types 23 Wavelength > 1 m (approx) Wire Antennas Dipole A e = Gλ 2 /4π Yagi Helix or arrays of these Wavelength < 1 m (approx) Reflector antennas Feed Wavelength = 1 m (approx) Hybrid antennas (wire reflectors or feeds)
Basic Antenna Formulas 24 Effective collecting area A(ν,θ,φ) m 2 On-axis response A e = ηa η = aperture efficiency Normalized pattern (primary beam) A(ν,θ,φ) = A(ν,θ,φ)/A e Beam solid angle Ω A = A(ν,θ,φ) dω all sky A e Ω A = λ 2
Aperture-Beam Fourier Transform Relationship 25 f(u,v) = complex aperture field distribution u,v = aperture coordinates (wavelengths) F(l,m) = complex far-field voltage pattern l = sinθcosφ, m = sinθsinφ F(l,m) = aperture f(u,v)exp(2πi(ul+vm)dudv f(u,v) = hemisphere F(l,m)exp(-2πi(ul+vm)dldm For VLA: θ 3dB = 1.02/D, First null = 1.22/D, D = reflector diameter in wavelengths
The Standard Parabolic Antenna Response 26
Primary Antenna Key Features 27
Types of Antenna Mount 28 + 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
Beam Rotation on the Sky 29 Parallactic angle
Reflector Types 30 Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam Waveguide Dual Offset (NRO) (ATA)
Reflector Types 31 Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam Waveguide Dual Offset (NRO) (ATA)
Effelsberg 100-m telescope near Bonn, Germany 32
Reflector Types 33 Dual Offset Unblocked Aperture (GBT)
VLA and EVLA Feed System Design 34
Example Feed Horn 35
Focal Plane Arrays 36 8 x 9 Array for 2-7 GHz Ivashina Et al.
Antenna Performance Parameters 37 Aperture Efficiency A 0 = ηa, η = η sf η bl η s η t η misc η sf = reflector surface efficiency η bl = blockage efficiency η s = feed spillover efficiency η t = feed illumination efficiency η misc = diffraction, phase, match, loss η sf = exp(-(4πσ/λ) 2 ) e.g., σ = λ/16, η sf = 0.5 rms error σ
Antenna Performance Parameters 38 Primary Beam πdl l=sin(θ), D = antenna diameter in wavelengths db = 10log(power ratio) = 20log(voltage ratio) For VLA: θ 3dB = 1.02/D, First null = 1.22/D contours:-3,-6,-10,-15,-20,-25, -30,-35,-40 db
Antenna Performance Parameters 39 Pointing Accuracy Δθ = rms pointing error Δθ Often Δθ < θ 3dB /10 acceptable Because A(θ 3dB /10) ~ 0.97 BUT, at half power point in beam A(θ 3dB /2 ± θ 3dB /10)/A(θ 3dB /2) = ±0.3 θ 3dB Primary beam A(θ) For best VLA pointing use Reference Pointing. Δθ = 3 arcsec = θ 3dB /17 @ 50 GHz
40 Antenna Pointing Design Subreflector mount Reflector structure Quadrupod El encoder Alidade structure Rail flatness Foundation Az encoder
ALMA 12m Antenna 41 Surface: σ = 25 µm Pointing: Δθ = 0.6 arcsec Carbon fiber and invar reflector structure Pointing metrology structure inside alidade
Antenna Performance Parameters 42 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
Off-Axis Cross Polarization 43 Cross polarized aperture distribution Cross polarized primary beam VLA 4.8 GHz cross polarized primary beam
Antenna Holography 44 VLA 4.8 GHz Far field pattern amplitude Phase not shown Aperture field distribution amplitude. Phase not shown
Other Concerns 45 Pointing errors, especially at high frequencies Gain curves Atmospheric opacity corrections
Practical concerns continued Opacity corrections and tipping scans Can measure the total power detected as a function of elevation, which has contributions T sys = T 0 + T atm (1-e τ 0a ) + T spill (a) and solve for τ 0. Or, make use of the fact that there is a good correlation between the surface weather and τ 0 measured at the VLA (Butler 2002): 46 and apply this opacity correction using FILLM in AIPS
Noise Temperature Rayleigh-Jeans approximation P in = k B T Δν, k B = Boltzman s constant When observing a radio source T total = T A + T sys Tsys = system noise when not looking at a discrete radio source T A = source antenna temperature T A = ηas/(2k B ) S = source flux (Jy) SEFD = system equivalent flux density SEFD = Tsys/K (Jy) Receivers Matched load Temp T ( o K) P in Receiver Gain G B/W Δν P out =G*P in VLA Sensitivities Band (GHz) η T sys 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 47
Hertz Dipole 48 A e = Gλ 2 /4π G=1.5 for Hertz Dipole G = 2.5 at 20 MHz for LWA G = 4.0 at 60 MHz for LWA
LWA Antenna 49
20 MHz 3D 50
E and H-Plane Antenna Pattern 51
Further Reading 52 http://www.nrao.edu/whatisra/mechanisms.shtml http://www.nrao.edu/whatisra/ www.nrao.edu Synthesis Imaging in Radio Astronomy ASP Vol 180, eds Taylor, Carilli & Perley