G0MJW we do have a link budget with is in very good agreement with the observed performance. But as you feared, this has too much NDA'ed information in it and for the sake of staying clean, I will not publish any numbers myself (sorry for being paranoid).
However, if anybody else is generating a spreadsheet which can be verified by the QO100 community, there is nothing we can do about...
OK - understood. Not everything in the spreadsheet will be under NDA though. I see the noise floor at ~10dB. Assuming antenna gain of 45 dB and a noise temperature of 400k I have a G/T of 19 dB. PSK Beacon SNR is 31.5 dB. This is according to SDR Console, I don't know if it is right but as long as it is consistent it does not matter.
To equal that SNR in the same bandwidth with a similar signal, I need to transmit about 200mW.
This is where errors start to creep in as I find if I TX at this level I am a lot weaker than some other stations who are apparently sending at the same level as the beacons.
My dish gain on 2.4 GHz is (assuming Willi's simulation is correct) is 32.5 dB so an EIRP of 25.5 dBW is what I need to reach the beacon level. It should be mostly the same for everyone else.
Now we could say at this point job done. To have a sensitivity such that the transponder noise is equal to the antenna noise one needs a dish with 7 dB less gain (not exactly, close enough though) other things being equal. -7 dB equates to 1/5th of the area, about 1.1m. The equal noise is an arbitrary target by the way but a fair one.
There are some improvements to the ground station that could be made, I assumed 50% efficiency and a noise figure of 3 dB and about 120k dish temperature. Realistically, this could be improved to 200k with a lower noise figure and better side-lobes with 70% dish efficiency. That's probably the limit without going to extremes. That would allow another 3 dB and a 75cm dish.
Part 2 after lunch