Here are the values for full, 250MHz, and 20MHz, with a 50-ohm input and shielded BNC connector...
This is very strange. I did not recall a noise level well above the specs during the tests with my MHO98.
It turns out that the AC RMS measurement results of the noise floor are possibly not accurate when the time/div is higher than some threshold. I did my tests with 10us/div, and the results are very different.
I repeated the test with this setup in the thread: single channel, 4Gsps, 50Mpts, 1mV/div, 20MHz bandwidth limit, 50-ohm input, BNC connector shielded.
When the time/div is lower or equal to 25us/div (using vernier timebase control), the measured AC RMS noise is around 26uV. However, it jumps to 117uV if the time/div is greater than 25us/div and stays at this level.
Then, I dumped the captured data and calculated the AC RMS values myself. For the 50Mpts data from memory, the calculated AC RMS value is 26uV for both timebase settings. For the 1kpts data form screen, the calculated value is 83uV for 20us/div and 91uV for 50us/div. This can be explained by the "peak-detection" downsampling (creating 1k bins of the captured data for the displayed duration and alternately calculating the minimum and maximum values) of the captured data, which causes a non-linear increase of signal power if aliasing occurs.
In conclusion, I can not reproduce the results of the on-screen measurement function and the results are possibly wrong when time/div is greater than 25us/div. I think this has something to do with the undocumented preprocessing of the captured data before display and measurement.
There is a reason why we measure at at least 1ms/DIV.
Time base defines what lowest frequency will exist in a whole capture.
If our whole capture is 500µs long (50µs/div) then, for instance, in that capture there cannot be any signals that have frequency that is lower than what fits into that captured time.
And one single period of low frequency signal will not be enough to reliably estimate how often that low frequency component appears/repeats.
So let's say you need to have at least 10x periods to reliably detect the signal..
That means that you need to have 10ms of data to measure contribution of 100Hz frequency component to some accuracy.
Measuring at 50µs/div means that you are not measuring at all anything less than 2 kHz and you are not measuring right contribution to noise energy on anything less than 10-20kHz..
Hence, when you are doing 20 MHz LPF and by virtue of short time base additionally HPF anything from 1/f region, you are going to have very optimistic noise estimates.
1ms/div proved to be good enough estimate of scope noise performance without being too long timbase. That allows you to run some averages and get good data.
That being said,
there might be problem with Stdev measurement itself.
I used to have DS1000Z that had similar problems with RMS measurements and that was the reason I sold it. If I cannot trust the measurements, it is not measurement instrument.
Funny enough, similar problems were reported few years ago at release of new Rigol DHO series, where people also had random large variation in results. I called for deeper investigation then, but was viciously attacked for it. Denial was strong. So I let it be. Maybe this is simply that same problem that was never fixed.