Author Topic: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?  (Read 957 times)

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Offline EEVblog

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EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« on: June 24, 2019, 04:39:34 am »
What's all this AC RMS and Standard Deviation measurement stuff on your oscilloscope anyhow?
And how does it differ from "normal" RMS measurement?
Another trap for young players.
Dave made an oopsie in the 1GHz Siglent scope review, did you spot it?

« Last Edit: June 24, 2019, 04:45:34 am by EEVblog »
 
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Offline David Hess

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #1 on: June 24, 2019, 11:35:00 am »
Wow Dave, thanks for covering this.



You can convert between AC RMS and AC + DC RMS easily enough.  The square of the AC + DC RMS is equal to the sum of the squares of the AC RMS and DC mean value:

(AC + DC RMS)^2 = (AC RMS)^2 + (DC mean)^2

This is very handy for multimeters which lack an AC + DC RMS measurement mode but it applies to oscilloscopes just as well.  So if your oscilloscope only measures AC + DC RMS and lacks the standard deviation measurement:

AC RMS = Sqrt( (AC + DC RMS)^2 - DC mean)^2 )



Those roughly 40 microvolt RMS noise measurements over 20 MHz are about what I expected.  They are twice what a good 100 MHz oscilloscope would deliver over the same bandwidth because the 1 GHz input amplifier has a higher spot noise, especially CMOS ones, but I would also bet they have a lot more flicker noise which becomes more important at lower bandwidths.  Wide bandwidth CMOS front ends which seem to be common now have incredibly high flicker noise.

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%.



Note that the RMS and standard deviation measurements depend on the bandwidth but not significantly on the sample rate and record length.  Aliased signal components fold over into the measurement bandwidth so they get included.  Old sampling voltmeters took advantage of this to make RMS measurements into the GHz range with a sample rate of only 50 kSamples/second or so.

Low sample rates and record lengths will result in more uncertainty in the measurement reflected in a higher standard deviation of the standard deviation.  Ha!
 
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Offline sibeen

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #2 on: June 24, 2019, 11:46:46 am »
You learn something everyday, even when you're an old fart.  :-+

On the Keysight 3000T series it's called AC RMS (Std Deviation). I do a lot of power measurements, mainly fairly high power and three phase systems so I don't really ever use a scope for these and it's normally something like a Fluke 435 or equivalent, but it's interesting to be informed of the other options if I ever get stuck.
 

Offline EEVblog

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #3 on: June 25, 2019, 03:35:41 am »
You learn something everyday, even when you're an old fart.  :-+

I thought it would be interesting to cover, as I suspect a lot of people don't know about this, but not many views it seems. Perhaps they see the title and think "I know what RMS is"?  :-//
 

Offline EEVblog

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #4 on: June 25, 2019, 03:39:08 am »
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.
 

Offline Dundarave

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #5 on: June 25, 2019, 04:33:45 am »
I thought it would be interesting to cover, as I suspect a lot of people don't know about this, but not many views it seems. Perhaps they see the title and think "I know what RMS is"?  :-//

Or see that nasty looking root/sigma term and think it's going to require some active concentration just to follow along...
 

Online Fungus

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #6 on: June 25, 2019, 05:06:30 am »
How many bee's dicks are there in one fag paper...?  :popcorn:


 

Offline bdunham7

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #7 on: June 25, 2019, 05:19:30 am »
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. 

I think it didn't garner views because we're all busy debating which advanced features ought to be included on the next 500MHz $200 DSO.
 

Online Circlotron

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #8 on: June 25, 2019, 05:21:44 am »
I haven't seen the video yet but I like the nod to Bob Pease in the title.
 

Offline Towger

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #9 on: June 25, 2019, 07:28:50 am »
How many bee's dicks are there in one fag paper...?  :popcorn:
I thought it was Dave's attempt at being more child friendly :-).  But the Yanks have managed to change the meaning of the word.  Many years ago a friend was in the USA, went into a shop and asked for a 'pack of fags'. It did not go down well. 
 

Offline Kleinstein

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #10 on: June 25, 2019, 08:16:40 am »
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.

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.
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.
 

Offline Gary350z

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #11 on: June 25, 2019, 08:19:55 am »
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.

Edit:

I think I found the answer in this document by Keysight Technologies.

Evaluating Oscilloscope Vertical Noise Characteristics
http://literature.cdn.keysight.com/litweb/pdf/5989-3020EN.pdf

Page 3

"Table 1 and Table 2 shows RMS noise floor measurements of six competitively priced
oscilloscopes with bandwidths ranging from 500 MHz to 1 GHz. Each scope was terminated
into 50‑Ω
and was set up to acquire waveforms with no input signal connected, using each
scope’s maximum specified sample rate."
« Last Edit: June 25, 2019, 01:12:05 pm by Gary350z »
 

Offline Kleinstein

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #12 on: June 25, 2019, 08:42:07 am »
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.
 

Offline David Hess

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #13 on: June 25, 2019, 04:38:49 pm »
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.

Quote
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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Offline thm_w

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #14 on: June 25, 2019, 10:25:28 pm »
On the Keysight 3000T series it's called AC RMS (Std Deviation). I do a lot of power measurements, mainly fairly high power and three phase systems so I don't really ever use a scope for these and it's normally something like a Fluke 435 or equivalent, but it's interesting to be informed of the other options if I ever get stuck.

Good that one manufacture got it right. As soon as Dave said "AC RMS" then it became immediately obvious what the measurement is doing.
Calling it standard deviation just causes confusion when you see it being used multiple times on the screen, and having different meanings. Hell look on wikipedia for "standard deviation" there is only the one statistics meaning, nothing else.

Rigol calls it Variance. But then that is confusing as well as I'm not sure if it matches the statistical definition: https://en.wikipedia.org/wiki/Variance
 

Online SparkyFX

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #15 on: June 26, 2019, 01:27:46 am »
I thought it would be interesting to cover, as I suspect a lot of people don't know about this, but not many views it seems. Perhaps they see the title and think "I know what RMS is"?  :-//
It is interesting to cover ... otherwise i´d be a bit confused why it would contain DC offset, then eyeballed it somehow, because i would not even know. Double checking numbers is always a good idea to spot such goofs.

The educational type content collects its views over time, given proper keywords included and all, but hardly will go viral.
Those videos add to your reputation.
Support your local planet.
 

Offline EEVblog

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #16 on: June 26, 2019, 02:15:50 am »
Rigol calls it Variance. But then that is confusing as well as I'm not sure if it matches the statistical definition: https://en.wikipedia.org/wiki/Variance

AC RMS/Standard Deviation is the square root the Variance, I think I mentioned that in the video.
 

Offline EEVblog

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #17 on: June 26, 2019, 07:46:34 am »
Rigol calls it Variance. But then that is confusing as well as I'm not sure if it matches the statistical definition: https://en.wikipedia.org/wiki/Variance

AC RMS/Standard Deviation is the square root the Variance, I think I mentioned that in the video.

The Rigol formula for variance does do the square root, but it's divided by N, not N-1 like sample standard deviation.

« Last Edit: June 26, 2019, 07:49:39 am by EEVblog »
 
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Offline Kleinstein

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #18 on: June 26, 2019, 08:26:21 am »
...
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.
Some of the good Bench-top DMMs do the RMS the digital way, e.g. the Keysight 34460-34470. AFAIK it started with the HP3458, that still has both options of analog RMS chip and the digital way.  With the ADC and µC prices and power consumption coming down, one might even have this in some cheap handheld DMMs.
 

Offline balage

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #19 on: June 26, 2019, 12:01:33 pm »
Some of the good Bench-top DMMs do the RMS the digital way, e.g. the Keysight 34460-34470. AFAIK it started with the HP3458, that still has both options of analog RMS chip and the digital way.  With the ADC and µC prices and power consumption coming down, one might even have this in some cheap handheld DMMs.

My 34461 can also calculate the standard deviation. It is not clear for me how does a slow drift in the measured values affect the std. deviation measurement. I mean when I measure something and the baseline of the noise is drifting. What do you think?
 

Offline Kleinstein

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Re: EEVblog #1223 - What's All This AC RMS Stuff Anyhow?
« Reply #20 on: June 26, 2019, 01:45:46 pm »
A drifting baseline is a kind of very low frequency signal. It would essentially add the power from the drifting part to the standard deviation.
 


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