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Radio telescopes: An Introduction to Techniques and Instrumentation (I) Gie Han Tan / ESO ALMA European System Engineer A schematic agenda • Basic radio interferometer θ τg=b.sinθ/c • Focus on element sub-systems b RF IF1 R I ADC Voltage multiplier L V1.cos(2πν(t−τg)) V2.cos(2πνt) LO1 Correlator Integrator (1) (2) r(τg) 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 2 Sensitivity of an interferometer • Continuum sensitivity (minimum detectable increase) is given by: 2k Tsys ∆S = ⋅ Aeff N ( N − 1) Bt • Primary design parameters that influence instrument sensitivity: – Effective aperture Aeff – System temperature Tsys – System bandwidth B – Number of elements N 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 3 Thermal noise • Thermal noise: – Thermal motion of electrons R in a resistor generate a (noise free) R(T) V(t) random voltage: V(t) <V2(t)> = 4.k.R.T.B – Available power is equal to (Nyquist relation): Pnoise = k.T.B k - Boltzmann’s constant T - physical temperature in Kelvin B - measurement bandwidth 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 4 Noise temperature • If a resistor produces more noise Noisy 2-port (e.g. amplifier) power then just thermal noise, Vn Rg its equivalent, noise temperature In is defined as: Vg(t) Tnoise = Pav / k.B • Noise of a 2-port: Rg Ideal noiseless 2-port Vn(t) Pnoise = <Vg2(t)+Vn2(t)>/4.R Vg(t) = k.(Tg+Tnoise).B 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 5 Noise contribution of a passive, lossy 2-port • Behaviour described by Kirchhoff’s law: – Lossy element attenuates the signal – Lossy element adds noise Tnoise = (1/ε - 1).Tphys lossy 2-port Tphys Rg Rg = Rin Rl = Rout Rl Pout = ε.Pin Vg(t) 0 ≤ ε ≤1 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 6 Noise in a chain of 2-ports • The noise temperature of a cascade of 2-ports, e.g. amplifiers or attenuators, is given by the Friïs formula: Tn 2 Tn 3 Tnm Tnoise _ tot = Tn1 + + + ..... + Gav 1 Gav 1 ⋅ Gav 2 Gav 1 ⋅ Gav 2 ⋅ .... ⋅ Gav ( m −1 ) Tn1, Tn2, Tn3, Tnm, Gav1 Gav2 Gav3 Gavm 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 7 System temperature contributors • System Temperature Tsys is defined as the equivalent noise temperature of the complete instrumental system, it includes the following terms: 1. Receiver noise Trx 2. Noise from the ground due to spill-over, strut scattering, reflector mesh leakage 3. Ohmic losses in the antenna 4. Atmosphere 5. Sky background Tsky eτ Tsys = (Trx + η ⋅ Tsky + (1 − η) ⋅Tground ) η η - forward efficiency (coupling to the sky) τ - atmospheric opacity 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 8 Atmospheric transmission • Reduced transmission, ε < 1, results in attenuation and extra noise (Kirchhoff’s law) Transmission at Chajnantor, pwv = 0.5 mm (1.0 mm) 1 0,9 0,8 0,7 atmosperic transmission 0,6 0,5 0,4 0,3 0,2 0,1 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 fre q (GHz) A T/WW 2 July 99 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 9 Sky temperature at the lower frequencies 1E+9 1E+8 Equivalent noise temperature [Kelvin] 1E+7 Cosmic noise towards 1E+6 Galactic pole Man made noise (quiet rural) 1E+5 Atmospheric noise (day) 1E+4 Atmospheric noise (night) 1E+3 Total antenna noise (day) 1E+2 1E+1 1E+0 1 10 100 1000 10000 Frequency [MHz] 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 10 Feed system • Primary functions: – Provide a transition between the free space EM field and a guided wave structure – Beam pattern matches to reflector antenna geometry – Separation of orthogonal polarisation signals 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 11 Feed system / Polarisation (1) • Dual polarisation: for a better sensitivity (most astronomical sources are randomly polarised) but also to measure polarisation in astronomical sources • Two choices: linear (X, Y) or circular (CW, CCW) • Common techniques to separate orthogonal polarisation signals: – Wire grid 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 12 Feed system / Polarisation (2) • Waveguide ortho-mode transducers (OMT) 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 13 ALMA feed system / Style 1 • Used for: – Band 1 (31,3 - 45 GHz) – Band 2 (67 - 90 GHz) • Feed system components: – Waveguide OMT – Circular, corrugated horn – PTFE lens 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 14 ALMA feed system / Style 2 • Used for: – Band 3 (84 - 116 GHz) – Band 4 (125 - 164 GHz) • Feed system components: – Waveguide OMT – Circular, corrugated horn – PTFE lens – Double mirrors 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 15 ALMA feed system / Style 3 • Used for: – Band 5 (163 - 211 GHz) – Band 6 (211 - 275 GHz) – Band 7 (275 - 370 GHz) – Band 8 (385 - 500 GHz) – Band 9 (602 - 720 GHz) – Band 10 (787 - 950 GHz) • Feed system components: – Grid polarizers – Corrugated horn / planar antennas – Mirrors 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 16 Low noise amplification • Practical low noise, amplification is only feasible up to approx. 100 GHz using III-V semiconductors (e.g. InP, GaAs) • Above 100 GHz a low noise, low loss mixer is used followed by a low noise amplifier at the, lower, intermediate frequency. 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 17 Frequency conversion • Conversion principle: – non-linear behaviour of a device x y=f(x) – expand transfer function into Taylor series y = c0 + c1 ⋅ x + c2 ⋅ x 2 + c3 ⋅ x 3 + c4 ⋅ x 4 + ....... • Mixing modes: – fundamental (second order term) – harmonic (third and higher order terms) • Common mixer devices in the microwave, (sub-)millimeter region: – transistors – diodes – SIS junctions 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 18 Mixing schemes (1) P • Double Side-Band mixing (DSB): – both lower and upper sidebands ∆f=fif are converted to IF 0 fif fl fLO fu lower upper f sideband sideband • Single Side-Band mixing (SSB): P – either lower or upper sideband is converted to IF ∆f=fif – sideband selection is done by appropriate filtering at the input of the mixer 0 fif frf flo frf lower upper f sideband sideband 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 19 Mixing schemes (2) • Sideband separating mixer: – lower and upper sidebands are each converted to a separate IF output 1 2 [cos 2π( fu − fLO )t + cos 2π( fLO − fl )t ] R I + cos2π(fu - fLO)t L cos2πflt + cos2πfut 1 cos2πfLOt Σ Σ cos2πfLOt - π/2 network 2 1 2 [cos 2π( fu − fLO )t L − cos 2π( fLO − fl )t ] R I -π/2 - cos2π(fLO - fl)t 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 20 Local oscillators • Amplitude and phase stability of a harmonic oscillation: – amplitude distortion (green) – phase distortion (red) V ( t ) = (V0 + v ( t )) ⋅ [cos 2πω0t + φ( t )] Y ω0 O X 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 21 Influence of phase instability • Phase stability of a hydrogen maser is expressed as Allan standard deviation • Phase instabilities cause limited S/N ratio 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 22 Local oscillator generation – Common frequency/time standards (deliver fixed reference frequency): • Quartz oscillators • Rubidium clocks • Hydrogen masers • GPS system – Variable frequency generation through synthesizer circuits: • Phase Locked Loop (PLL) • Direct Digital Synthesizers (DDS) – Multipliers: • Non linear element (e.g. Step Recovery Diode, varactor diode) generate higher harmonics 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 23 ALMA first Local Oscillator • LO sub-system based on a LO controller Cartridge 20.83 Hz Ref combination 125 MHz Ref R I DDS AMB of: L – PLL xN Loop filter φ-detector cold multiplier – DDS – mulitpliers I R VCO assembly x 2/3 L warm multiplier 34 - 52 GHz Opt Ref 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 24 A-D conversion (1) • Sampling in time domain: – Nyquist criterium: A signal of bandwidth -f is completely characterised by its instantaneous values at times tk for all integer values of k: 1 tk = k ⋅ 2∆f – In other words, the minimum sampling time is equal to: 1 ts = 2∆f P 0 ∆f ts f t 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 25 A-D conversion (2) • The frequency for which fs = 2-f is called the Nyquist frequency or Nyquist rate • Aliasing: – If the sampling frequency is lower then the Nyquist rate, the sampled signal can be distorted by so called alias products P P 0 ∆f fs 0 ∆f fs f f (Remember that a multiplication in the time domain results in a convolution in the frequency domain) 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 26 A-D conversion (3) • Passband sampling: – The alias products can be used to our benefit to accomplish sampling and frequency conversion simultaneously – For distortion free sampling the spectrum of the sampled signal must be limited to the interval n.-f to (n+1).-f, n being an integer, and equal to zero outside this interval • Quantization: – noise degradation due to limited number of quantization levels: N um ber of E ff ic ie n c y f a c t o r E ff ic ie n c y f a c t o r q u a n t iz a t io n le v e ls f s = f n y q u is t f s = 2 .f n y q u is t 2 0 ,6 4 0 ,7 4 3 0 ,8 1 0 ,8 9 4 0 ,8 8 0 ,9 4 • A to D conversion involves both sampling in the time domain as well as quantization of signal levels 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 27 ALMA receiver block diagram • Double super- heterodyne Front end IF sub-system principle RF 31 - 950 GHz R L I ADC IF1 • Fundamental 4 - 12 GHz To optical TX sub-system R I L Band mixing mode LO1 27 - 938 GHz selector 10:1 R L I ADC • SSB, DSB and Frequency multiplier N = 1 .. 8 sideband R L I ADC separating schemes R I ADC L • Baseband IF2 2 - 4 GHz sampling LO2 8 - 10 GHz / 12 - 14 GHz LO reference frequencies (27 - 122 GHz, 2 GHz, 25 MHz, 20 Hz) on optical fiber from central distribution 2001-04-11 Radio telescopes: An Introduction to Techniques and Instrumentation (I) 28