Re: [amsat-bb] Coverage Area of 10Ghz

[Dr Thomas A Clark <clark@xxxxxxxxxxxxxxxxxxxx>]

James KD4DLA wrote:
> 
> Just wondering if someone could answer a couple of questions for me?
> 
> I am wondering what the coverage area (footprint) for three centimeter 
> (10 Ghz) dish(0.6 meters in size with a 0.45 F/D ratio) feed putting out 
> 1 watt mounted pointing straight down on the International Space Station
> would be? Would this be the same as on two meter and seventy centimeters.

Well, here is how to do a "back-of-the-envelope" calculation to answer
your questions. In the following there are some small simplifications
in the trigonometry, but they only introduce errors at levels of 25%.

Regarding dish beamwidth, dish diameter and wavelength are all that 
are important -- the xmtr power level and f/D are irrelevant.

A 60 cm diameter dish at 3 cm wavelength is 20 wavelengths in size.
Therefore the beamwidth of the dish (full width @ half max) will be 
about (3/60) = (1/20) radian or about 3 degrees.

Let's consider the satellite in question 500 km away. A (1/20) radian 
beam will have a footprint of about (500/20) = 25 km in size.



> Also wondering how bad the doppler shift would be using different modes 
> (SSB, CW, FM)? Also on two point four, three, and five point seven GHZ?

Again this is pretty simple to calculate and the answer doesn't depend 
on the mode. 

A satellite in earth orbit has a speed (tangential to the orbit) of 
about 7 km/sec. It's not be surprising to see that when it is at the 
horizon and rising upwards, we see a good fraction of this velocity 
"head on" -- lets call it about 4 km/sec.

For your 3 cm wavelength case, this means that the satellite is moving
towards you with a speed that amounts to about 

       (4 km/sec)
    ------------------   =   133,000 wavelengths/second
     (3 cm wavelength)

which means that the downlink signal has a Doppler offset of 133 kHz
high in frequency.

When it is setting it is moving 4 km/sec away from you, so it has a
Doppler offset of about 133 kHz low in frequency.

Therefore from rise to set the frequency has "swooshed" by about 266 kHz
in a time of about 15 minutes or about 1000 seconds for a LEO satellite
like ISS. Therefore you would have to move your receiver's dial at a
rate 
of about 266 kHz/1000 seconds or about 266 Hz/second. 

Since SSB gets to be unintelligible when you a off frequency by more
than 
a couple of hundred Hz and your SSB radio has filters with a bandwidth
of 
only ~3 kHz, you would have to keep tuning the dial very rapidly!!!!!

While on the topic of the satellite's speed, I noted earlier that the
footprint of a 60 cm dish would be about 25 km in size. Since the
satellite's tangential velocity is about 7 km/sec, a spot on the earth
zip thru bthe beam in 3-4 seconds.

You asked about how this scales with frequency -- the answer is
that all these effects scale directly. Since 2.4 GHz is about a
quarter of 10 10 GHz, the Doppler effects scale down by a factor of
4, and the beamwidth of the antenna is 4 times bigger.

Hope that helped -- 73, Tom
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