From: David Woolley (david_at_djwhome.demon.co.uk)
Date: Tue Jun 03 2003 - 14:15:24 PDT
> Where can I find calculations for transmitter power into an antenna with
> a known beamwidth and all as a function of distance?
As well as the SETI League Excel spread sheets, there are worked examples
in the sci.astro.seti newsgroup FAQ.
>
> How much power would have to be injected into an aerial 100light years
> away, that dish having a beam of, say 1degree diameter?
In order to do what???
With the caveat that you can't actually have a beam that is a perfect
cone - they have fuzzy edges (so the power density at the centre may not
be exactly as described here, you are spreading the power over a cone
with a radius at the base of (range * tan (0.25)). For a relatively
small angle, tan (theta) is approximately theta in radians, or pi / 720,
in this case. To get the range, you multiply the speed of light, just
under 300,000,000 m/s by one hundred years (approximately 100 * 365.25 *
86400).
Now decide what the power density in watts per square meter that you
want (for signal detection this depends on the receiver noise figure
(including antenna and ground noise), the effective size of the receive
antenna (for dishes this is normally less than its real size), the
bandwidth, the centre frequency (sky noise is frequency dependent), the
time over which you want to average the signals, and the proportion of
false detections that you can tolerate). Multiply this by the area of
the base of the cone (pi * radius ^ 2), and you will have the transmit
power that would produce your desired receiver power density in an ideal
1 degree diameter cone beam.
However, I can't imagine that anyone would consider using anything as
wide as a 1 degree beam for a serious SETI transmission, and it
would be illegal, in most countries, to send one as an indiviual.
Without working it out properly from first principles, or defining all
the assumptions, I think you would need about 10MW input at 1.42 GHz,
to produce a signal at a reasonable confidence level when using Arecibo
to receive it, and if transmitting at about the smallest practicable
bandwidth. You would be talking of about a few terrawatts for an Argus
system to get a good confidence detection (10,000 penalty for area,
a little over 10x penalty for using 10 Hz bandwidth, and some extra
penalty, in most cases, for a system noise level of rather more than
45 K).
On the other hand, Arecibo to Arecibo at 2.2GHz is possible, using
its real feed power of 1MW, to somewhat over 100 LY.
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