Transcript Slide 1

Performance of station
array configurations
Sparse vs. Dense, Regular vs Random
Jaap D. Bregman
AAVP Workshop,Cambridge, 2010-12-09
Overview
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Setting the Scene for SKA-Low
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LOFAR 20 – 240 MHz (sparse, regular & random)
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Station & Array Calibratability
Element & Sparse Array Beam
EM-coupling effects
Vivaldi Element & Array (dense regular)
Antenna Cost Extrapolation
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Some Antenna Basic
Why Sparse Arrays for F < 300 MHz
Peak sensitivities for SKA Low
Balancing Lowest against Highest frequency octave
Conclusions (combine)
Setting the Scene for SKA-Low
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Memo 125 defines SKA1 with 2 Synthesis Arrays
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70 – 450 MHz
0.3 – 10 GHz
2000 m2/K @ z = 10
1000 m2/K 0.45 – 3 GHz
Effective supporting surveys requires
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100 M€ for AA-Low
100 M€ for Dishes
30% of cost in Receivers, Beamforming, Correlation & Imaging
70% of cost in collecting area & Low Noise Amplifier
What could we do with 70 M€ in view of
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Limitations set by the Sky
Limitations set Antenna Theory
Limitations set by Ionosphere calibration
Limitations set by Station Beam calibration
Some Antenna Basic
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Array has set of N antenna element separated by a pitch P
When l/2 > P we are in the dense regime and Ae = N P2 = N lp2/4
A dense array has a projected area ~ cos(q) with zenith angle q
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A dipole above a ground plane has a beam pattern ~ cos(q) in H-plane
and ~ cos2(q) in E-plane,
A free dipole above ground has Ae = l2/W with beam solid angle W ~ 3
In the sparse regime are the pitch cells not fully filled so Ae < P2
and lsparse < (3/4)1/2 P
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A dipole with length L and height H above a ground plane has below resonance
impedance Z ~ 377 L H / l2 (real part)
The EM coupling between the elements in the dense regime increases the effective
impedance in a dense array, which is important to get appropriate matching to low
noise amplifiers
Why Sparse Arrays for F < 300 MHz
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Sparse Array stations have
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Aeffective < Aphysical
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Ae ~ N l2 / W
Tsky ~ l2.6
Sensitivity Ss ~ Ts / Ae ~ l0.6
Typical source flux So ~ l0.6
Source Count N(S > So) ~ So-1
Beam solid angle W = l2 / Ap
So constant detection sensitivity
But sources/beam ~ l-2
Expo-Shell configuration
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Exponential decreasing element
separation towards centre of station
LBA 50% subsets of LOFAR
Select 50% of elements to limit
sparseness at higher frequencies
30 MHz
subset
60 MHz
subset
LOFAR 20 – 240 MHz
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Two different sparse array configurations
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Two different dipole like elements
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Randomized expo-shell for 96 elements 20 - 80 MHz
24/48/96 Tiles with 16 elements on regular grid 120 - 240 MHz
Free standing thin wired short inverted V-dipole
Boxed Vertical bowtie as fat dipole
Both above ground plane
Descent receiver noise match
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LBA sky noise limited 30 - 60 MHz
HBA sky noise limited 120 - 180 MHz
Station & Array Calibratability
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VLA 75 MHz could not be selfcalibrated
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A single single source available in only a few fields
Ae/Ap = 0.15 is too small
Beam too wide, 25 m dish to small for ionosphere patch size
1.5 MHz bandwidt not enough with 10 sec to match ionosphere
LOFAR will do full ionosphere multi direction selfcal
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40 m remote stations allow multi direction at 120 MHz
30 m core stations could provide combined solution for core
56 m international stations still see partly resolved calibrators
10 MHz, 10 sec, allows for ~20 directions when Ae/Ap = 1.0
33 m station at 60 MHz Ae/Ap = 0.47 reasonable ionosphere needed
83 m station at 30 MHz Ae/Ap = 0.29 good ionosphere needed
Element & Sparse Array Beam
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Ignore EM Coupling
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Product of element beam and
“array factor”
Element beam is smooth
Array factor has side lobes
Array factor has grating lobes
Array factor independent of
direction where it is pointed to
Include EM Coupling
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True in very sparse arrays
True for arrays like WSRT
Not true for ATA
Effective Station beam
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Pitch < few wavelength
Element beam gets ~30 % bumps
Every element beam is “different”
Effective Station Beam
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Average element beam depends on
direction in which array is pointed
Also for element impedance to which
LNA needs to matched
Average element pattern has blind
angles for specific freq & directions
Especially for regular array
Array factor has grating lobes
Randomization reduces both effects
Vivaldi Element & Array
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Free Vivaldi is wide band
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At least 3 octaves
However narrow beam
Array of connected elements
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Good impedance P/2 < l/2 < 4 P
Constant Ae = Ap for l > P 3-1/2
Cos (q) “element” beam l/2 > P
Narrower “element” beam l/2 < P
In sparse regime Ae/Ap ~ l2
Array factor has grating lobes
No grating for q < 47o at l = P 3-1/2
Antenna Cost Extrapolations
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LOFAR Actuals
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Free LBA element (~2 m)
Container + Combiner + Cables
5*5 m2 Tile + Combiner + Cables
Embedded HBA element + delay
Production for ~5,000 LBA ~3000 HBA
€ 150
€ 500
€ 1800
€ 75
Extrapolated SKA Upper Bound Costs
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8 element cluster
16 element bowtie tile
32 element Vivaldi tile
64 element Vivaldi tile
6*6 m2
6*6 m2
6*6 m2
6*6 m2
k€ 1.7
k€ 3.0
k€ 4.5
k€ 6.0
(2 m separation)
Peak Sensitivity for 70 M€ in antenna arrays
Ap
1.5 km2
0.84 km2
0.59 km2
0.42 km2
Freq
Tsys
Ae8/Ts
Ae16/Ts
Ae32/Ts
Ae64/Ts
MHz
K
m2 K-1
m2 K-1
m2 K-1
m2 K-1
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9400
160
90
65
45
60
4000
375
210
150
105
85*
1600
940*
525
370
265
“Tiles” of 6*6 m2 with 8 or 16
dipoles and 32 or 64
Vivaldi elements
Frequency and element pitch
increment 21/2
Purple is receiver noise
dominated
Yellow is relevant EoRrange
120*
700
1070
1200*
840
600
170*
320
1170
1310
1840*
1315
Blue is actual LOFAR range
240*
160
1310
1840
2625*
Red is relevant Pulsar range
340
85
1735
2470
480
60
1750
* indicates max frequency with
3 sr element beam and
qmax = 47o to avoid
grating lobes
Balancing Lowest against Highest octave
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Tiles of 6*6 m2 with 64 elements have unprecedented sensitivity in 200480 MHz range or 2 < z < 6
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Free element clusters provide best sensitivity for EoR application
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Combining Vivaldi tiles in centre of a station with dipole clusters in
expense ratio 1:2 gives 720 m2/K at 85 & 400 MHz and 1220 m2/K at
170 MHz
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In “Dense” regime could tapering reduce the station side lobes
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In the sparse regime will grating lobes rise above the horizon when the
array is pointed toward large zenith angles and pick up sky noise and
disturbing sources.
Conclusions
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A full 1 km2 array could be realized
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Combine Vivaldi tiles and Dipole clusters in station
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Still 720 m2/K at 85 & 400 MHz
Peak sensitivity of 1220 m2/K at 170 MHz at octave “centre” of band
Calibratability limits practical ranges of sparse regime
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1 octave in Sky noise limited regime by W ~ l2
1/2 octave In receiver noise limited regime by additional Ae ~ l2
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Full instantaneous U,V-coverage for core possible
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Stay for EoR in “dense” regime
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Avoid grating lobes and blind angles
Apply taper to reduce side lobes
Reduces sensitivity for low frequency