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SKA Antenna Selection ­ Economics and the Field of View
John Bunton,
CSIRO Telecommunications and Industrial Physics, Australia

Introduction
In designing a radiotelescope there is always a conflict between performance and economics. This poster shows that feed numbers are a major constraint in limiting the field of view. Using this constraint leads to a flow chart, which shows possible paths to a practical solution.

A full version of this paper available at http://www.atnf.csiro.au/SKA/techdocs/Antenna_selection.pdf


Theory
For any antenna the maximum effective aperture Aem in m2 and the beam solid angle A in steradians are related to the wavelength in metres by:

2 = Aem

A

(can be derived by squaring Beamwidth = wavelength/diameter)

If the SKA were made of N identical antennas then each would have an effective area of 1,000,000/N square metres. The above relationship can be rewritten as:
2 Ф 0.3 Ж 1,000,000 Г В= . A with f in GHz ГfВ N Х Ь

A =

N

11,100,000 f 2

steradians

The beam solid angle is approximately equal to the product of the half power beam width in the two principle planes HP and HP. The field of view FOVHP is equal to the area of the ellipse defined by HP and HP. This gives: . A N FOV HP HP HP = steradians 4 4 14,100,000 f 2 And if the total instantaneous field of view is FOV then: Number of feeds per antenna FOV/FOVHP 14,100,000 FOV.f 2/N Multiplying this by the number of antennas N shows that Total number feeds innthe SKA 14,100,000 FOV.f f2 Total number feeds i the SKA 14,100,000 FOV.
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This result is independent of antenna technology and at 1GHz full sky coverage requires 88,000,000 feeds growing to 8,800,000,000 at 10GHz. It would seem full instantaneous sky coverage is not possible at GHz frequencies, thus:

At GHz frequencies economics dictate that the SKA have a restricted Field of View
FOV is the area of sky where the SKA can have high sensitivity instantaneously, about 10,000 deg2 for phased arrays and about 1 deg2 for small parabolic reflectors at 1 GHz. Later beamforming can reduce this total. N specifies the number of primary receptors each consisting of an LNA and feed

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Astronomy and Field of View
The scientific impact of the SKA can be improved not only by increasing its Ae/Tsys but also by increasing its field of view. A good example of this is the Parkes Multibeam, which increased the field of view of the Parkes dish by a factor of 13, allowing a survey to be completed in an order of magnitude less time. The extreme in increasing field of view is the phased array, which can allow any part of the sky to be accessed. With sufficient backend processing 100's or 1000's of observations can be conducted simultaneously. In terms of astronomy throughput a 10 independent beam instrument is equivalent to a single beam instrument that has Ae/Tsys three times higher. In general, the number of useable beams that can be achieved with a given antenna technology is proportional to the field of view which leads to the conclusion:

To maximise the astronomy throughput it is desirable that the SKA maximise the Field of View
But this conflicts with feed number limitations. These two conflicting requirements leads to the Flow chart shown below which systematically explores options for maximising the field of view while at the same time keeping in mind many of the economic constraints imposed by the various antenna technologies. The major contenders for full field of view are phased arrays and Luneburg lenses. These are followed by designs with a large field of view such as log periodic antennas and cylindrical reflectors, which with suitable beam forming can provide multiple beams over a 1000 square degrees area of the sky. Finally there are the parabolic/spherical reflector designs. The small parabolic reflectors typically have a single useable beam. The large reflectors will use a focal plane array but even so the total field of view will be smaller than that of the small reflector. Typically all parabolic/spherical reflector designs will support only a single user at a time. The other designs can support multiple users.

The flow chart below describes possible paths to a practical solution
The chart includes feed numbers for the phased arrays these are proportional to maximum frequency squared. For parabolic designs the size is inversely proportional to the minimum frequency leading to a minimum feed number that is proportional to minimum frequency squared. A cylindrical reflector antenna is part reflector and part phased array so the feed numbers are proportional to the product of maximum and minimum frequency. This also applies to a Luneburg Lens with line feed.
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Antenna Selection Flow chart
Begin selection of SKA antenna Technology Front ends and beamformer within budget

Yes ~35,000,000(fmax)2 feeds Elevation limit

Phased arrays

No

Luneburg Lens Options Filled focal plane array within budget
No

Luneburg Lens fabrication within budget

Yes

Yes

Full Field of View No mechanical steering

40,000,000 to 80,000,000(fmax)2 feeds Field of View 100-3000 deg Driven Azimuth, ~70 deg of elevation
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One mechanical drive
No

Yes

5,000,000fmax.fmin to 15,000,000(fmax)2 feeds

No

Multiple mechanical drives common axis
No

Yes

Multiple beams over full sky Multiple beams per line feed Multiple line feeds

No

Independent drives per feed

Yes

Multiple beams over full sky High mechanical complexity

2,000,000 to 20,000,000(fmin)2 feeds

FOV 30-60 degrees

Yes

Front ends, feeds and steering within budget

Yes

Log periodics, horns, etc

~20,000,000(fmax)2 feeds No

FOV 100x10fmin/f degrees

Yes

Cylindrical reflector & line feed within budget ~8,000,000 fmax.f

Yes feeds

Cylindrical reflector

min

No Yes FOV 10 degrees at fmin ~2,000,000(fmin)2feeds Small Parabolas small GMRT, 1hT

Elevation limit No Large reflectors LAR, FAST

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Single Patch on Sky

Part Sky Instantaneously

4,000,000 to 40,000,000 fmax.fmin feeds

All Sky Instantaneously


Conclusion
Phased arrays are too expensive at GHz frequencies but are the design of choice at lower frequencies. At higher frequencies, the Luneburg lens would form the basis of an ideal instrument because of its extreme flexibility in forming a field of view. Its major problem is dielectric loss which limits its maximum frequency and the unknown costs and technical challenges in building and supporting the lens. Cylindrical reflector antennas are also a good choice as a large field of view is desirable in maximising the astronomy throughput of the SKA although the 100 by 1 degree FOV at 1GHz is less than ideal. Cylindrical reflectors have become a viable option, at this time, because Moore's Law has made the implementations of a full beamformer cost effective. The reflector is low cost and designs such as the Doublet (see paper these Proceedings) are very robust and can be made very rigid. This allows operation at very high frequencies. At present no work is being conducted into the feasibility of non-reflector reducedfield-of-view antennas such as log-periodic, horn or helical antennas. However, the degree of field of view reduction they can give is not great. This probably makes them uneconomic, at high frequencies, due to the high antennas numbers needed to give the required collecting area. Small parabolas and the Canadian Large Adaptive Reflector have fields of view of about 1 deg2 at 1GHz which probably limits these designs to a single astronomy program at any one time. But when the instrument is dedicated to imaging the throughput will be similar to the imaging beam of a multibeam instrument. Current correlator costs possibly precludes full imaging on multiple beams at any one time. All large reflectors have elevation limits caused by foreshortening in the case of the Canadian LAR and blockage in the case of the Chinese FAST proposal. For a complete sky coverage both these instruments would probably require a Northern and Southern hemisphere instrument. Phased arrays also have elevation limits, which could be overcome by building paired instruments inclined at complementary angles.

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