Performance of station array configurations

Sparse vs. Dense, Regular vs Random

Jaap D. Bregman

AAVP Workshop,Cambridge, 2010-12-09

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Overview

• Setting the Scene for SKA-Low – Some Antenna Basic– Why Sparse Arrays for F < 300 MHz

• LOFAR 20 – 240 MHz (sparse, regular & random)– Station & Array Calibratability – Element & Sparse Array Beam– EM-coupling effects

• Vivaldi Element & Array (dense regular)• Antenna Cost Extrapolation

– Peak sensitivities for SKA Low– Balancing Lowest against Highest frequency octave

• Conclusions (combine)

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Setting the Scene for SKA-Low

• Memo 125 defines SKA1 with 2 Synthesis Arrays– 100 M€ for AA-Low 70 – 450 MHz 2000 m2/K @ z = 10– 100 M€ for Dishes 0.3 – 10 GHz 1000 m2/K 0.45 – 3 GHz

• Effective supporting surveys requires– 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– Limitations set by the Sky– Limitations set Antenna Theory– Limitations set by Ionosphere calibration– Limitations set by Station Beam calibration

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Some Antenna Basic• Array has set of N antenna element separated by a pitch P• When /2 > P we are in the dense regime and Ae = N P2 = N p2/4• A dense array has a projected area ~ cos() with zenith angle • A dipole above a ground plane has a beam pattern ~ cos() in H-plane

and ~ cos2() in E-plane, • A free dipole above ground has Ae = 2/ with beam solid angle ~ 3• In the sparse regime are the pitch cells not fully filled so Ae < P2

and sparse < (3/4)1/2 P

• A dipole with length L and height H above a ground plane has below resonanceimpedance Z ~ 377 L H / 2

(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

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Why Sparse Arrays for F < 300 MHz• Sparse Array stations have

– Aeffective < Aphysical– Ae ~ N – Tsky ~ – Sensitivity Ss ~ Ts / Ae ~ – Typical source flux So ~ – Source Count N(S > So) ~ So-1

– Beam solid angle / Ap– So constant detection sensitivity– But sources/beam ~

• Expo-Shell configuration– Exponential decreasing element

separation towards centre of station– LBA 50% subsets of LOFAR– Select 50% of elements to limit

sparseness at higher frequencies

60 MHzsubset

30 MHzsubset

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LOFAR 20 – 240 MHz

• Two different sparse array configurations– Randomized expo-shell for 96 elements 20 - 80 MHz– 24/48/96 Tiles with 16 elements on regular grid 120 - 240 MHz

• Two different dipole like elements– Free standing thin wired short inverted V-dipole– Boxed Vertical bowtie as fat dipole– Both above ground plane

• Descent receiver noise match– LBA sky noise limited 30 - 60 MHz– HBA sky noise limited 120 - 180 MHz

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Station & Array Calibratability

• VLA 75 MHz could not be selfcalibrated– 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– 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

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Element & Sparse Array Beam• Include EM Coupling

– Pitch < few wavelength– Element beam gets ~30 % bumps– Every element beam is “different”

• Effective Station Beam

– 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

• Ignore EM Coupling

– True in very sparse arrays– True for arrays like WSRT– Not true for ATA

• Effective Station beam

– 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

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Vivaldi Element & Array

• Free Vivaldi is wide band– At least 3 octaves– However narrow beam

• Array of connected elements– Good impedance P/2 < < 4 P– Constant Ae = Ap for > P 3-1/2

– Cos () “element” beam > P– Narrower “element” beam P– In sparse regime Ae/Ap ~

– Array factor has grating lobes– No grating for < 47o at = P 3-1/2

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Antenna Cost Extrapolations

• LOFAR Actuals– Free LBA element (~2 m) € 150– Container + Combiner + Cables € 500– 5*5 m2 Tile + Combiner + Cables € 1800– Embedded HBA element + delay € 75– Production for ~5,000 LBA ~3000 HBA

• Extrapolated SKA Upper Bound Costs– 8 element cluster 6*6 m2 k€ 1.7 (2 m separation)– 16 element bowtie tile 6*6 m2 k€ 3.0– 32 element Vivaldi tile 6*6 m2 k€ 4.5– 64 element Vivaldi tile 6*6 m2 k€ 6.0

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Peak Sensitivity for 70 M€ in antenna arrays

“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

Blue is actual LOFAR range

Red is relevant Pulsar range

* indicates max frequency with 3 sr element beam and max = 47o to avoid grating lobes

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

43 9400 160 90 65 45

60 4000 375 210 150 105

85* 1600 940* 525 370 265

120* 700 1070 1200* 840 600

170* 320 1170 1310 1840* 1315

240* 160 1310 1840 2625*

340 85 1735 2470

480 60 1750

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Balancing Lowest against Highest octave• Tiles of 6*6 m2 with 64 elements have unprecedented sensitivity in 200-

480 MHz range or 2 < z < 6

• Free element clusters provide best sensitivity for EoR application

• 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

• In “Dense” regime could tapering reduce the station side lobes

• 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.

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Conclusions• A full 1 km2 array could be realized

• Combine Vivaldi tiles and Dipole clusters in station– 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– 1 octave in Sky noise limited regime by ~

– 1/2 octave In receiver noise limited regime by additional Ae ~

• Full instantaneous U,V-coverage for core possible

• Stay for EoR in “dense” regime– Avoid grating lobes and blind angles– Apply taper to reduce side lobes– Reduces sensitivity for low frequency