Cylindrical Antenna for a

SETI All-Sky Search

John Bunton CSIRO Telecommunications and Industrial Physics, Australia john.bunton@tip.csiro.au

Abstract

A simplified figure of merit (FOM) is described which allows a direct comparison between the number of detectable extra-terrestrial civilisations at a given transmit power for different antennas. The small beam size of large parabolic reflectors precludes all-sky surveys, but a north-south cylindrical antenna can cover the whole sky every 24 hours. For the same front-end cost, the FOM for such a transit all-sky survey is an order of magnitude larger than for a survey with a 64x64-element phased array.

Simplified Figure of Merit

The power gain or directivity of an antenna is proportional to the effective area times the square of the frequency of operation. Increasing the directivity by a factor of 4 doubles the distance at which a source with a given Effective Instantaneous Radiated Power EIRP can be detected.

Within the disk of the galaxy, the total number of stars is proportional to the cube of the distance to furthest detectable civilisation. This drops to the square of the distance for distances exceeding the thickness of the disk. It rises rapidly again at a distance corresponding to the centre of the galaxy. At this last distance, the numbers lie on a line formed by extrapolating the cube law relationship derived for the number of stars at distances less than the thickness of the disk of the galaxy. Thus, a single cube law relationship holds for all-sky surveys within the disk of the galaxy and for distances including the centre of the galaxy.

Table 1 Relative antenna performance for given EIRP

	Reference antenna	Larger antenna
Effective Diameter	1	d
Frequency	1	f
Directivity	1	(f.d)^2
Maximum range	1	f.d
Stars/square degree	n	n.(f.d)^3
No of square degrees	1	1/( f.d)^2
Total stars	n	n.(f.d)

Where f and d are frequency and effective diameter normalised to the frequency and diameter of reference antenna and n is the number of stars per deg² detectable by the reference antenna for a given EIRP at that star.

Increased directivity reduces the beam area making the number of detectable stars proportional f.d, the product of frequency and diameter, instead of the cube of f.d. The relationships are summarised in Table 1. The parameter f.d can be used as a Figure of Merit (FOM) defining the effectiveness of a single antenna beam. This parameter can be expressed in a number of different ways:

The FOM of an antenna beam is also dependant on the Tsys of the antenna. Choosing area in metres² and wavelength in metres gives a quantitative FOM

As an example, a 100m² antenna with a Tsys of 25K has a has a FOM of 40 at a wavelength of 10cm.

All-Sky Searches can be done by Transit Instruments

An all-sky phased-array survey from a single site can, in fact, only observe sources within a large but limited declination range, and, for those sources, observe them for a limited hour angle. If the hour angle coverage is reduced all sources are still observed every day but for a reduced amount of time. In the limit, the instrument becomes a full declination transit instrument, which leads to the conclusion.

Phased Array and Cylindrical Reflector

with Identical FOM at Transit

When oriented NS a cylindrical reflector generates beams that are identical to the transit beams of a phased array with the same length and effective width. The difference between the two is that full electronic beamforming in the phased array has been replaced by reflector beamforming in one direction. Used as a transit instrument the cylindrical reflector is considerably cheaper than a phased array because considerably fewer feeds, LNAs and front-end electronics systems are needed. In addition, the beamforming is cheaper. However, the phased array can form many more beams, giving it, in principle, vastly superior performance. For a valid comparison, the front-end costs must be equalised.

FOM for Phased Array and Cylindrical Reflector

with Identical Front End Costs

If a phased array has N x N feeds, then for an equivalent front-end cost, a cylindrical reflector is N times longer with N² feeds in the line feed. This increases the number of transit beams by N and reduces the declination beam width by N. Compared to the N element line feed, the total FOM, summing over all beams, has increased by NÖN. This is a direct increase in FOM as the source dwell time within a beam has not changed, thus maintaining sensitivity for all detection modes.

For the phased array full use of its capabilities is achieved by forming all beams. Since the beam area increases with zenith angle, the total number of beams is less than N² and the average FOM of each beam is less than that for the transit beams. Thus, forming all beams in a phased array increases the total FOM by less than N when compared to just forming all the transit beams. Therefore, for equal numbers of feeds and effective widths we conclude: