Radio telescopes An Introduction to Techniques and by gregoria

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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)



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             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




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                              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
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                            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



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  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




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                 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




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         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
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               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



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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]


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                                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
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             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




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             Feed system / Polarisation (2)
• Waveguide ortho-mode transducers (OMT)




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             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




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             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




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             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

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                 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.

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                      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
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                       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


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                              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




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                           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




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             Influence of phase instability
• Phase stability of a
  hydrogen maser is
  expressed as Allan
  standard deviation
• Phase instabilities
  cause limited S/N
  ratio




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                      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




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             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




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                         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

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                           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)
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                                 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
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             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


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