The difference in measured noise of the two instruments might come down to how accurate the 20 MHz bandwidth limit is. It is not a guarantied specification and can easily vary at least 10%.
Yes, I suspect that spec is pretty loosey-goosey. Never actually measured it though.
Just measuring what is in front of me, my 2232 is 18.5MHz and my 2247A is 17MHz with single pole responses.
I've noticed that the low-level RMS figures on my DSO are exaggerated because of the DC offset, but I didn't actually know there was a separate RMS with the DC removed. I have a DMM that does this all quite neatly, but I never looked for it on my scope. So I watched it and learned something, anyway.
Most DMMs do the RMS calculation with an AC coupled RMS to DC converter before the ADC; this also removes any DC offset generated internally before the RMS to DC conversion. DMMs which also feature the AC + DC RMS measurement combine an AC RMS measurement and average DC measurement like I described above.
It could of course be done all at once digitally with a sampling ADC like an oscilloscope but offhand I do not know of any DMM only instruments which do it this way. DSOs which include DMM functionality like the Fluke Scopemeter series might.
Knowing the bandwidth is important when looking at RMS values, but less for more normal mode. For quick measurement the FFT on noise should tell.
Integrated spot noise is easier to compare though and sufficient for many applications. In measurement applications, it may be the only specification which matters which is why operational amplifiers usually include it at low frequencies as well as the noise density specification.
How accurate the 20 MHz number is depends on how it is realized. Chances are the filter could be digital and could thus be relatively accurate in frequency. There are still different possible 20 MHz LP filter functions to choose from and noise BW and -3 dB BW are generally not the same.
Most are still part of the analog signal path and single pole filters so they follow the 0.35 rule and have a noise bandwidth 1.6 times the -3dB bandwidth. There are some exceptions that I know of but you would only know it by making a careful measurement, checking the schematics, or in one case from Tektronix, the specifications actually say. These all have Bessel responses of course. (1)
All of the modern DSOs I have tested either had completely separate analog and DSP bandwidth limiting. In the last modern Tektronix DSO I evaluated, the bandwidth limit function explicitly specified if the selected filter was implemented in hardware or DSP and they had very different responses; the DSP filters were not simply copies of the hardware filters. Based on my measurements, the hardware filters were single pole and the DSP filters were Butterworth filters for maximally flat response.
(1) The exceptions I know of offhand include:
Tektronix 7A13 - 5MHz 2 pole Bessel
Tektronix 7A22 - 100Hz to 1MHz single pole (not an exception but interesting)
Tektronix 7A26 - 20 MHz 2 pole Bessel (interesting because it is electronically switched)
Tektronix 465 series - 20MHz 2 pole Bessel
Tektronix 11A33 - 20MHz and 100MHz 4 pole Bessel (given in the specifications)
Later models starting in 1982 which replaced the 465 series implemented single pole filters. I suspect this was because the single pole response was more useful for comparative noise measurements and noise measurements became more important; it helps if the noise bandwidths all match. I thought maybe the change might have been because single pole filters are easier to switch with semiconductors but the 7A26 example above shows that this is not the case.
When doing this noise measurement, shouldn't you ground the input to prevent stray noise from entering the input? If not, please explain why. Thanks.
Whether the difference is significant depends on the bandwidth because higher bandwidth oscilloscopes have higher bandwidth front ends with both higher spot noise and higher total noise while the noise from the input termination remains the same for 1 megohm inputs. See my answer below.
Shorting the input should be done for the comparison.
For the open input case much of the noise comes from the 1 M input resistance (resistor to ground) and the input capacitance set the bandwidth - not so much the 20 MHz filter. So it is not such a surprise to get rather similar results from different scopes: this is about the noise of 1 M shunted with some 20 pF.
I agree, the input should be shorted for measurement consistency but it did not matter in this case; see below. A 50 ohm terminator works fine to short out the input. But do not rely on a DSO's ground coupling function unless it is verified to work properly or even exist because some lie; I am not saying it was Rigol but ... it was Rigol.
I get a noise bandwidth of 12.75kHz so the 1 megohm input resistance contributes 14.7 microvolts RMS noise. That increases the measured noise by 3% so it is insignificant in this case.
On a good 100 MHz oscilloscope, that added noise would be significant and could be almost half of the total noise. On a bad one, it would not be noticed. On something like a 1MHz Tektronix 7A22, it would be overwhelming even though its 47 picofarad input capacitance more than halves the noise bandwidth.
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