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Radio Antennas, Feed Horns, and Front-End Receivers

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Radio Antennas, Feed Horns, and Front-End Receivers Radio Antennas, Feed Horns, and Front-End Receivers Bill Petrachenko, NRCan EGU and IVS Training School on VLBI for Geodesy and Astrometry March 2-5, 2013 Aalto University, Espoo, Finland Radiation Basics – Power Flux Density -2 -1 Spectral Power Flux Density, Sf (Wm H ), is the power per unit bandwidth at frequency, f, that passes through unit area. [Subscipt f indicates spectral density, i.e. that the parameter is a function of frequency and expessed per unit bandwidth (Hz-1)] Sf can be used to express power in bandwidth, δ f , passing through area, δ A , i.e.: P = S f ⋅δA⋅δf Sf is the most commonly used parameter to characterize the strength of a source; it is often referred to simply as the Flux Density of the source. Because the typical flux of a radio source is very small, a unit of flux, the Jansky, has been defined for radio astronomy: 1 Jy = 10-26Wm-2Hz-1 The power from a 1 Jy source collected in 1 GHz bandwidth by a 12 m antenna would take about 300 years to lift a 1 gm feather by 1 mm. Radiation Basics – Surface Brightness -2 -1 -1 Surface Brightness, I f (θ , φ ) (Wm Hz sr ), is the Spectral Power Flux Density, Sf, per unit solid angle (on the sky) radiating from direction, ( θ , φ ) . (aka Intensity or Specific Intensity) Because I f varies continuously with position on the sky, it is the parameter used by astronomers for mapping sources. I f is related to Sf according to S = I dΩ f ∫ f ΔΩ Radiation Basics – Brightness Temperature Source Power generated per Flux decreases as 1/R2 unit solid angle increases proportional to R2 since the since power per unit area R is diluted as the distance area of the source (in the from the source increases. solid angle) increases as the distance from the Observer source increases. These two opposing effects cancel so that I f is independent of the distance from the source and hence a property of the source itself. For a Black Body in thermal equilibrium and in the Rayleigh-Jeans limit (i.e. h ν << kT which is good for all radio frequencies) of the Plank Equation, 2 ⎛ f ⎞ 2kTB (θ,φ) I f ()θ,φ = 2kTB ()θ,φ ⎜ ⎟ = ⎝ c ⎠ λ2 where k=1.38x10-23 (m2 kg s-2 K-1) is the Boltzmann Constant Brightness Temperature, T B ( θ , φ ) , has become a proxy for I f (θ , φ ) regardless of whether or not the radiation mechanism is that of a thermal Black Body. Radiation Basics – Radiative Transfer Thermal For a Black Body, i.e. a perfect absorber, 2 Incident ⎛ f ⎞ T I f = 2kTB ⎜ ⎟ ⎝ c ⎠ (see previous page) For an imperfect absorber 2 Scattered ⎛ f ⎞ Transmitted I f < 2kTB ⎜ ⎟ ⎝ c ⎠ T I f ∝ absorption coefficient Absorption is a Lose-lose Oxygen effect: - the desired signal For the atmosphere is attenuated Imperfect absorption is - thermal noise is added why zenith atmosphere to system noise at x-band is 3°K and Water vapour not 300°K Radiation Basics - Polarization The Polarization vector is in the instantaneous direction of the E-field vector Linear Polarization Circular Polarization Random Polarization Probability of E-field direction Most geodetic VLBI sources The most efficient detection of linear and circular polarization have nearly circular distributions, signals is with a matched detector. i.e. are nearly unpolarized. Regardless of the input signal, all of the radiated power can be detected with two orthogonal detectors, either Horizontal and Vertical linear polarization or Left and Right circular polarization. With random polarization this is the only option for detecting all the power. Linear Detector Circular Detector e.g. dipole e.g. quadrature combination 90° +/- of dipole outputs Antenna Basics •ARadio antenna is a device for converting electromagnetic radiation in free space to electric current in conductors •An Antenna Pattern is the variation of power gain (or receiving efficiency) with direction. Antenna pattern: Dipole antenna Antenna pattern: Parabolic antenna • Reciprocity is the principle that an antenna pattern is the same whether the antenna is transmitting or receiving. – Transmitting antennas are generally characterized by gain – Receiving antennas are generally characterized by effective area Antenna Gain - Characterizes a Transmitting Antenna P(θ ,φ ) Antenna gain is defined as, G () θ , φ = , where Piso P()θ,φ ~ power per unit solid angle transmitted in direction, (θ,φ) P P ~ power per unit solid angle transmitted by an isotropic antenna, P = in iso iso 4π For a lossless antenna, P = P , hence G = 1 and GdΩ = 4π out in lossless ∫ Sphere An isotropic antenna is a hypothetical lossless antenna radiating uniformly in all directions, i.e. G iso ( θ , φ ) = 1 . [Note: An isotropic antenna is a useful analytic construct but cannot be built in practice.] G(θ,φ) The beam solid angle of an antenna is defined as Ω = d Ω hence A ∫ Sphere Gmax 4π ΩA = Gmax Effective Area – Characterizes a Receiving Antenna The total power received into area, A e ( θ , φ ) , and bandwidth, BW , is ⎛ S f ⎞ P()θ,φ = ⎜ ⎟Ae ()θ,φ BW Note: S includes all radiated flux. For an ⎜ 2 ⎟ ⎝ ⎠ unpolarized source, only one half the flux is received per polarized detector. Hence 2P(θ,φ) ⎛ S ⎞ ∴ A ()θ,φ = ⎜ ⎟ e the use of ⎝ 2 ⎠ in the equations. S f ⋅ BW At a particular frequency, A e ( θ , φ ) can be rewritten 2Pf (θ,φ) Ae ()θ,φ = S f -1 where Pf (WHz ) is the power received per unit frequency The noise power (per Hz) generated by a resistor at temp, T, can be written P f = kT . Pf = kT Note: It is common to use T as a proxy for Pf , especially in low power/noise situations. Average effective area Antenna Side Resistor Side Black Body cavities I T1 T2 P = A θ,φ f dΩ f ∫ e () Sphere 2 R Pf = kT 2 2kT ⎛ f ⎞ P = ⎜ ⎟ A dΩ f 2 c ∫ e ⎝ ⎠ Sphere Rayleigh-Jeans At thermodynamic equilibrium, T1=T2 and no current flows between antenna and resistor Antenna Side must equal Resistor Side 2 2kT ⎛ f ⎞ ∴ A dΩ = kT ⎜ ⎟ ∫ e 2 ⎝ c ⎠ Sphere 2 ⎛ c ⎞ 2 A dΩ = ⎜ ⎟ = λ2 λ ∫ e ⎜ ⎟ Ae = Sphere ⎝ f ⎠ 4π For an isotropic antenna λ2 A ()θ,φ = A = e e 4π Effective Area Gain From reciprocity Ae (θ,φ)∝ G(θ,φ) From earlier results λ2 A = and G =1 e 4π Combining these λ2 A ()θ,φ = G ()θ,φ = G()θ,φ ⋅ A e 4π iso This allows us to calculate the receiving pattern from the transmitting pattern and vice versa. Main beam Sidelobes High Gain Antenna (Gmax>>1) e.g. Parabolic Reflector Antenna Stray radiation It was already shown that, in a Black Body cavity, the received spectral density is I (θ,φ) P = A θ,φ f dΩ = kT f ∫ e () Sphere 2 For a high gain antenna, A e (θ , φ ) is concentrated in the main beam; hence I (θ,φ) P = A θ,φ f dΩ = kT f ∫ e () Ω−Beam 2 which implies that I f () θ , φ need only cover the main beam for this result to be true. If a source is smaller than the main beam, I Ω P = A f dΩ = kT Source f ∫ e Ω−Beam 2 ΩBeam Main beam Sidelobes High Gain Antenna (Gmax>>1) e.g. Parabolic Reflector Antenna Stray radiation Spectral Power Flux Density, Sf, Relations If the source is larger than the beam I A S Ω PReceived = A f dΩ = e f Beam f ∫ e Ω−Beam 2 2 ΩSource If the source is smaller than the beam I A S PReceived = A f dΩ = e f f ∫ e Ω−Source 2 2 Parabolic Reflector Antenna Secondary reflector (aka Sub-reflector) Sub-reflector support legs Feed Horn Antenna positioner Feed Horn Support Structure Primary reflector Pedestal (aka antenna tower) The antenna reflectors The feed horn converts concentrate incoming E-M E-M radiation in free radiation into the focal space to electrical point of the antenna. currents in a conductor. The antenna positioner points the antenna at the desired location on the sky. Aperture Illumination The ‘Feed Horn’ is itself an antenna with a power pattern that ‘illuminates’ the reflector system. Although the terminology derives from signal transmission, the feed works equally well, in a radio telescope, as a receiving element. Over-illumination: The feed pattern extends well beyond the edge of the dish. Too much ground radiation is picked up from outside the reflector. Under-illumination: The feed pattern is almost entirely within the dish. There is minimal ground pick-up but the dish appears smaller than it is. Optimal-illumination: This is the best balance between aperture illumination and ground pick-up. The power response is usually down about 10 dB (10%) at the edge of the dish. Aperture Illumination Beam Pattern The beam pattern of the antenna is the Fourier Transform of the aperture illumination (assuming that the aperture is measured in units ofλ). λ FFT Aperture illumination Beam pattern Depending on the details of the aperture illumination, the Half Power Beam Width (HPBW) is approximately λ HPBW ≈ D where D is the diameter of the reflector. The beam becomes narrower as dish becomes larger or λ becomes shorter. (λ becoming shorter is the same as the frequency becoming larger). Aperture efficiency The antenna effective area, A e , can be compared to the antenna geometric area with the ratio, η A , being the antenna efficiency, i.e. Ae =η A Ageo π where, for a circular antenna, A = D 2 .
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