# 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

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
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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

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)
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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
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

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

• SSB, DSB and                                   Frequency
multiplier
N = 1 .. 8

sideband                                                                                      R
L

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

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