Like the majority of digital oscilloscopes, the SDS1000X-E has an 8-bit acquisition system.
One division on the display happens to be equivalent to 25 LSB of the ADC.
So what vertical gain did you use to measure the 3 Vpp? It probably was at the optimum of 500 mV/div, then one LSB is equivalent to 20 mV. This would explain why you can see non-integrative measurements like peak-peak only in steps of 20 mV.
Why it measures 3.08 V or 3.10 V and not closer to 3.00 V (+/- 0.02 V), as suggested by your other measurements, that is another question. But we'll try to find an answer...
I pretty much expect that it would measure more accuratey with a direct coax connection or x1 probes.
Have you noticed that the measurement error on a x10 probe depends on the accuracy of both the probe and scope input impedance?
For most passive high impedance probes, accuracy of the input impedance is not specified. Your guess about the worst case error is as good as mine.
Then the input impedance of the scope itself. The specification says 2% - and that is the minimum additional error margin for such measurements.
Out of curiosity I've checked an old PP510 probe with the 12-bit SDS2000X HD. For this instrument, the input impedance accuracy is still only 2%, but at least the DC accuracy is specified as 0.5%, so it can easily compete with the average 3.5 digit DMM.
in x1 mode, we get 3.018 V amplitude; so the voltage of the calibrator output is only off by 0.6%. Even though its tolerance is not specified, this output is clearly produced by some 3.0 V logic circuit and modern voltage regulators are just accurate like that.
In x10 mode, we get 301.25 mV amplitude, so one might come to the wrong conclusion that the error is now even lower at only 0.417%. No, it is not, because the true calibration signal amplitude is
not 3.00 V! Yet the error because of tolerances in the impedances of both probe and scope do not appear to be nearly as bad as expected.
Have a look at the attached screenshots for more information on this test.
In any case, this little experiment should tell us several things:
- For calculating the total error margin, we need to take the probes into account
- Passive high impedance probes often do not have any specifications that allow the estimation of the additional error margin, but the tolerance of the scope input impedance is already high enough to rule out the guarantee for precise measurements with any probe other than x1
- Measurements statistics are your friend whenever accuracy is important. Always use the statistic mean values over a number of measurements
- Most important: select the right measurement for the task! Peak-Peak is not going to give the right answer to the question about the amplitude of a square wave, because it will include overshots, ringing and noise