Antennas. Greg Taylor. University of New Mexico Spring Astronomy 423 at UNM Radio Astronomy

Transcription

1 Antennas Greg Taylor University of New Mexico Spring 2017 Astronomy 423 at UNM Radio Astronomy

2 Outline 2 Fourier Transforms Interferometer block diagram Antenna fundamentals Types of antennas Antenna performance parameters Receivers Dipole Antennas

3 stationary time series indefinitely long but statistical properties don t vary with time

4 assume that we are dealing with a fragment of an indefinitely long time series time, minutes time series, d duration, T length, N

5 one quantity that might be stationary is

6 Power T 0

7 Power T 0 mean-squared amplitude of time series

8 How is power related to power spectral density?

9 write Fourier Series as d = Gm were m are the Fourier coefficients

10 now use

11 now use coefficients of complex exponentials coefficients of sines and cosines equals 2/T Fourier Transform

12 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

13 Example: Atmospheric CO 2 (after removing anthropogenic trend) 4 CO2, ppm time, years

14 4 3 enlargement 2 CO2, ppm time, years

15 4 3 enlargement 2 CO2, ppm period of 1 year time, years

16 power spectral density 3 log10 psd of CO frequency, cycles per year frequency, cycles per year

17 cumulative power power power in time series frequency, cycles per year

18 Fourier Transforms 18

19 Fourier Transforms 19

20 20 Mixer Bandpass filter, IF amplifier Square law detector Software

21 E.g., VLA observing at 4.8 GHz (C band) Interferometer Block Diagram 21 Antenna Front End IF Back End Correlator

22 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.

23 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)

24 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

25 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

26 The Standard Parabolic Antenna Response 26

27 Primary Antenna Key Features 27

28 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

29 Beam Rotation on the Sky 29 Parallactic angle

30 Reflector Types 30 Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam Waveguide Dual Offset (NRO) (ATA)

31 Reflector Types 31 Prime focus Cassegrain focus (GMRT) (AT) Offset Cassegrain Naysmith (VLA) (OVRO) Beam Waveguide Dual Offset (NRO) (ATA)

32 Effelsberg 100-m telescope near Bonn, Germany 32

33 Reflector Types 33 Dual Offset Unblocked Aperture (GBT)

34 VLA and EVLA Feed System Design 34

35 Example Feed Horn 35

36 Focal Plane Arrays 36 8 x 9 Array for 2-7 GHz Ivashina Et al.

37 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

38 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

39 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 50 GHz

40 40 Antenna Pointing Design Subreflector mount Reflector structure Quadrupod El encoder Alidade structure Rail flatness Foundation Az encoder

41 ALMA 12m Antenna 41 Surface: σ = 25 µm Pointing: Δθ = 0.6 arcsec Carbon fiber and invar reflector structure Pointing metrology structure inside alidade

42 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

43 Off-Axis Cross Polarization 43 Cross polarized aperture distribution Cross polarized primary beam VLA 4.8 GHz cross polarized primary beam

44 Antenna Holography 44 VLA 4.8 GHz Far field pattern amplitude Phase not shown Aperture field distribution amplitude. Phase not shown

45 Other Concerns 45 Pointing errors, especially at high frequencies Gain curves Atmospheric opacity corrections

46 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

47 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

48 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

49 LWA Antenna 49

50 20 MHz 3D 50

51 E and H-Plane Antenna Pattern 51

52 Further Reading Synthesis Imaging in Radio Astronomy ASP Vol 180, eds Taylor, Carilli & Perley