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Front-end, Back-end, correlators
in Radiastronomy
Enzo Natale
IRA - INAF Firenze
First MCCT-SKADS Training School September, 23-29 2007, Medicina
Topics
• Description of a cryo receiver
- Feed horn / coupling to the antenna
- Polarizer / OMT
- Low Noise Amplifier
- IF processor
• Receiver sensitivity
• How many receiver?
- Dense focal plane array
- Array of receivers
Layout of a cryogenic receiver
Dewar
Feed horn
Trasformation from free space to guided propagation
Performances
Return loss
: > 30 dB
Insertion loss
: <0.2 dB
Off axis crosspol
: < -35 dB
Bandwidth
: 30% or larger
• Mode launching section (return loss - crosspol)
• Flare section (taper - antenna illumination)
Optical coupling to the antenna
The illumination efficiency (optical coupling) of the antenna is the ratio of
the gain of the antenna to that of a uniformely illuminated aperture and is
determined by the illumination function or “edge taper”, i.e. the level of
the illumination at the edge of the reflector compared to that of the center.
Edge taper Te = P(0) / P(re )
Te (dB) = -10 log10 (Te )
For gaussian illumination function
re / w = (Te (dB) ln 10 / 20)0.5
re : reflector radius
w: 1/e radius of the beam
Normalized
Copolar and
Crosspolar
beam pattern at 22 GHz
Horn for 18-26 GHz Multibeam
Taper 9 dB at the edge of the
subreflector (9.5°)
Multibeam horn at the Gregorian focus of
SRT
(simulation with GRASP by R. Nesti)
Maximum gain Gi = (4 p/ l2 ) Ag
Ag : geometrical area of the antenna
G/T ratio
G/T = G/(TA + TR) ;
TA : antenna temperature
TR : receiver temperature at window
Tatm = 265 K
t = 0.1
f
= 22 GHz
Gaussian beams
To evaluate the performances achievable at the focus of a large antenna
( D >> l ) we report here some results based on the approximation of the
electromagnetic field distribution in terms of Gaussian beam modes.
(Goldsmith: Quasioptical System, IEEE Press, 1998).
w0 waist (1/e)
l
wavelength
r
radial distance
w(z) beam radius (1/e) at z
z
distance from the waist
R curvature radius of the beam
In this approximation, it can be shown that, for not too large flare angle a a
feed horn with aperture radius a and slant length R produces a gaussian beam whose waist
radius is w = 0.644 a located inside the horn at a distance z approximatelye qual to 1/3 of
the horn length. In these conditions about 98 % of the power radiated by the horn can be
associated with the fundamental Gaussian beam mode.
Using the standard formulae for Gaussian beam mode propagation , it is
simple to compute the antenna illumination (the edge taper) and consequentely the
full width to half maximum (FWHM) beam width in the sky of a in-focus system and
unblocked aperture:
Ortho Mode Transducer (OMT)
Differential Phase Shifter (DPS)
The feed horn is sensitive to both linear and circular polarizations
Linear polarizations are separated by the OMT
Circular polarizations needs to be converted in linear (DPS)
DPS
Passive 18 - 26 GHz Front-end
Feed horn
Coupler
DPS
Waveguide to SMA
converter
Turnstile junction
(Navarrini, Plambeck IEEE MTT 45, Jan. 2006)
Planar OMT
(Engargiola,Navarrini, IEEE MTT 53, May 2005)
Low Noise Amplifiers
Typical performances of a cryogenic LNA
Gain
: >= 30 dB
Gain flatness : ~ 1 - 2 dB
Input return loss : < 15 dB
Bandwidth
: 30% or larger
Power Out @ 1dB Compression : +5dBm
Working temperature : ~ 20K
Noise temperature : ~ 18 - 30 K 18 - 26 GHz
~ 30 - 50 K 36 - 50 GHz
Devices : GaAs, InP High Electron Mobility Transistors (HEMT)
and Heterostructure FET (HFET)
: GaAs, InP
Integrated circuits
1/f
noise
(DG / G)2 = N A f-a
N number of active devices
A constant (i.e. ~ 3.6 10-8 Hz-1 for InP HEMT )
a ~ 0.9 -1 (0.5!)
4 - 8 GHz
2 stages GaAs HEMT
Noise T : 5K
(Alma Memo 421)
LNA block diagram
(inclusion of coupler + calibration source at the input?)
MMIC amplifier
chip
mounted
Hybrid amplifier
IF Processor
Receiver type : superheterodyne
IF processor
• accurate definition of the receiving band
• conversion of the RF band to IF band for easy interfacing to the back-end.
The mixer
RF
I
LO
RF = E sin (2pnst +f)
I = a (RF + LO)2 =
LO = V sin (2pnLOt )
• @ E2 + V2
• @ sin[2 (2pnst +f)]
• @ sin [2 (2pnLOt )]
• @ E V sin[2p(ns - nLO)]
• @ E V sin[2p(ns +
nLO)]
I = I0 [exp(q Dv /k T ) - 1]
For small Dv :
I @ a (Dv)2
Receiver Sensitivity
Tsys ON = Tbg + Tatm + Topt + Trec + Tsource
Tsys OFF = Tbg + Tatm + Topt + Trec
Tbg = 2.7 K CMB*atm
Tatm = atmospheric emiss.
Topt = spillover
Trec = receiver
Tsys ON ~ Tsys OFF
s(t) = k B G Tsys
If the noises are white :
D Trms = Tsys (B t)-0.5 (radiometric noise) (Kraus)
Tsource = Tsys ON - Tsys OFF = xs (ON source)(t) - x r (OFFsource)(t) = X(t)
sX(t) = a D Trms
a depends on the modulation type
But in real detecting system (receiver + atmosphere + ..) the low frequency
noise is not white:
• 1/fa (a ~ 1) electronics ( gain variation, ..)
• 1/fa (1< a ~ 2) drift, atmosphere
Power spectral density
18 - 26 GHz receiver
B ~ 400 MHz
t ~ 1 msec
Measuring system
In this case:
1/f2 noise
1/f noise
White noise (radiometric)
Allan plot
1/f2 noise
White noise
18 - 26 GHz receiver
B ~ 400 MHz
t ~ 1 msec
1/f noise
Measuring system
Allan time
Mitigation of the 1/fa noise
• “high” (>> 1/Allan time) modulation frequency
- ON Source / OFF Source
- On The Fly
- Two beams Dicke (equalized channels)
• gain stabilization (no effect on the atmospheric noise)
- Dicke receiver ( Modulation between sky end
- Correlation receiver
- Noise injection receiver
reference source)
Dicke receiver
D T / Tsys = ( D G / G) (Ta - Tn )/ Tsys (Kraus, 1966)
For balanced systems Ta = Tn
D T / Tsys = (2 / B t)0.5
Noise injection receiver
s1 = kGBTsys
during toff
s2 = kGB(Tsys + Tn) during ton
Tn = x Tsys
D T/ Tsys = (2 / Bt)0.5 (1 + 1/x + 1/x2 )0.5
W = (D T/ Tsys ) / (2 / Bt)0.5
= (1 + 1/x + 1/x2 )0.5
Tsys = Tn s1/(s2 - s1)
(D T/ Tsys)2 = (1/Bt) (1 + (s22 + s12)/(s2 - s1 )2 )
How many receivers?
Maximize observing efficiency of an antenna
Focal Plane Array
• Dense FPA (mainly for n < 10 GHz)
• Array of single pixel receiver
Dense array
• Small array elements
: about 0.5 l
• Optimization of the beam properties -> high efficiecy
low spillover
• Multi beam capabilities
-> increase FOV
survey speed
• Electronic synthesis
-> flexibility
• Operating frequency
-> up to ~ 8GHz
PHAROS (PHased Arrays for Reflector Observing System)
Vivaldi array
13x13 elements
pitch 21 mm
Optimized for:
• prime focus 0.3-0.5 f/D
• 4 - 8 GHz
Antennas, LNA, beam
former cryocooled
(PHAROS System Specification, Dec 2006)
PHAROS antenna (3D model)
Beam former
Window problems :
• mechanical (16 mm plexiglas)
• thermal (radiation power due to the ambient ~ 45 Watt)
Array of single pixel receivers
Current technology capabilities still prevent the use of dense arrays at frequencies
higher than say 10 GHz.
The only possibility is to build-up array by assembling together a certain number
of single channel (dual polarization) receivers..
For the sake of simplicity we briefly describe the structure of an hypothetical multibeam
for the 36 - 50 GHz band for Medicina antenna.
Antenna:
D = 32 m feq = 97 m F = feq /D = 3.04
Optical coupling efficiency :
edge taper Te (dB)= 9 dB
~ 80%
FWHM = (1.02 + 0.0135 Te (dB) ) l /D = 45 arcsec @ l = 7 mm
Beam at primary (wa ) : 0.5 D / [Te (dB) ln(10) /20]0.5 (from the definition of edge taper)
The illuminator (feed horn) must have
have w0 = l feq / p wa
13.8 mm
located in the antenna focus
Horn radius R = w0 /0.644 = 21.4 mm
~Fl
Sampling
: 0.5 l F (in the focal plane)
Nyquist limit
Actual sampling : 2 l F
Undersampling 4
In practice
+
: Nyquist positions
circle : horn position
undersampling 5
18 - 26 GHz Multibeam
Correction of field curvature (Petzval surface)
Best focus position
from the in axix focus
(distance from the optical axis)
Medicina antenna l = 7mm D = 500 mm
Configuration
Antenna
gain [dB]
#1 Feed in the Cassegrain 82.09
focus
#2
Feed shifted in the
80.90
focal plane
#3
Feed placed in the
81.54
best-focus point
Antenna
efficiency
[%]
78.53
59.67
69.07
Conclusions
Multi beam to increase the observing efficiency
- new solutions for “simpler” front-end
- integration of cal. source in the LNA
- IF integration
(Low cost ?) Integrated receiver (MMIC)