Which should have the most accurate RMS measurement?

[pwnell]

I currently have access to the following equipment:

Rigol MSO5104 oscilliscope with Migsic DP10007 differential probe in x100 mode
Fluke 365 true RMS clamp meter (new) [1.5 % ±5 digits so for 125V it means 122.6 - 127.3]
Fluke 175 true RMS multimeter (20 years old) [±(1.0% + 3) so for 125V it means 124.5 - 126.5]
Brymen BM235 True RMS DMM (< 1 year old) [ 0.03% + 2d so for 125V it means 124.7 - 125.2 - not sure why the brymen would be 100 times more accurate than the fluke...]
IotaWatt with JW-95001-NA AC adapter

I am trying to get the most accurate measurement of RMS line voltage but do not know which number to trust most.  Since my voltage is fluctuating it is hard to get a comparative number, but tis is roughly how they seem to measure:

Rigol: 125.23 V (RMS)
Fluke 365: 125.2 V
Fluke 175: 125.0V
Brymen BM235: 124.9V

Which would be most accurate in principal?

[bdunham7]

Not only do you have fluctuation and noise to deal with, you need to consider what bandwidth you want to include in your measurement.  Distortion shows up as higher-frequency energy content and all of those meters become less accurate quite quickly as the frequency increases.  Except the scope, but that will be the least accurate of the whole bunch and I would not count it in the mix--although it does appear to be close in this instance.

The specs for those meters are all 1% or worse (the Brymen is a little better at exactly line frequency, but your spec is wrong as well as your math) but all will likely perform somewhat better than spec.  The two most accurate would be the 175 and the BM235, but all three meters agree to a lot less than their tolerances--so you already have far better results than you have any right to expect from specifications.  The differences may be a result of calibration or simply due to the frequency content of the signal vs. the frequency response of the meter.  As to which is the closest, there's nothing there that would allow you to even guess.  125V +/- 0.5V is probably a reasonably guess as to what you know. 

[pwnell]

Thank you for your detailed response.

I got the spec for the Brymen from the manual on Dave’s site but see now that I confused line frequency and AC V from reading too quickly. It is 0.7% +3d.

Also where is my math wrong? I thought 2% +- 5 digits mean if the display reads 125.0 it can be 125.0 - 125.0*2/100 - 0.5 to 125.0 + 125.0*2/100 + 0.5.

Why would the oscilloscope be the worst if it has full access to the waveform and is way faster than the multimeter? If I can resolve details at picosecond level surely it can perform the math to accurately calculate RMS on a non perfect sinusoidal waveform? What am I missing here? Not questioning you, just want to understand.

[bob91343]

I am curious as to why accurate rms is important.  Or, for that matter, rms at all.  I have consistently found that the old fashioned average responding meters are more accurate than I need.  Most gear is sensitive to other parameters than rms if you are measuring or comparing output signals or power supplies.  The only parameter I can see that depends on rms is efficiency.

[pwnell]

I want to calibrate my IoTaWatt device to accurately calculate power consumption. For that I need accurate rms  voltage.

[bdunham7]

Also where is my math wrong? I thought 2% +- 5 digits mean if the display reads 125.0 it can be 125.0 - 125.0*2/100 - 0.5 to 125.0 + 125.0*2/100 + 0.5.

Why would the oscilloscope be the worst if it has full access to the waveform and is way faster than the multimeter? If I can resolve details at picosecond level surely it can perform the math to accurately calculate RMS on a non perfect sinusoidal waveform? What am I missing here? Not questioning you, just want to understand.

That math looks right, but you calculated wrong in your examples.  Look at the 175 for example and plug the numbers in again.  The tolerance would be 125.2 * .01 + 0.3 or ~1.6, so 125.2 +/- 1.6 is 123.6 to 126.8, if I did the math right.

The scope is the worst because they typically have poor absolute DC performance, both scale and offset.  Then you have to add in both scale and offset from the differential probe.  After that, they're great!  And yours appears to be spot-on, actually.

[pwnell]

I based my tolerance calculations on 125V, not 125.2. But you are right - I messed up the lower tolerance somehow.

As to the oscilloscope - assuming the line voltage has no dc offset, surely it can calculate the Fourier transform of the waveform, calculate the cumulative rms of each harmonic up to some threshold to get the required accuracy and be done with it?

[bdunham7]

As to the oscilloscope - assuming the line voltage has no dc offset, surely it can calculate the Fourier transform of the waveform, calculate the cumulative rms of each harmonic up to some threshold to get the required accuracy and be done with it?

It's not even that hard--it just has to calculate the square of a subset of the samples and then average them and take the square root.  The inaccuracy with scopes comes from the very limited accuracy of the samples themselves.

[bob91343]

No you don't need accurate rms voltage to calibrate a wattmeter.  Unless your power factor is unity.  Harmonic content will affect true rms reading but doesn't necessarily contribute to power.

This is not a simple subject.  If you are running a motor, harmonics will creat heat but not mechanical energy.  If you are running resistors or light bulbs, harmonics will contribute.  If you are rectifying the wave, all bets are off, especially if you are running a switch mode load.

I don't know how the power is computed in your wattmeter but that's important in its calibration.  Very few wattmeters react properly to harmonics, especially higher order.  A dynamometer is good but only up to a not-too-high frequency.

We tend to take modern technology for granted but I am skeptical.

[james_s]

Why would the oscilloscope be the worst if it has full access to the waveform and is way faster than the multimeter? If I can resolve details at picosecond level surely it can perform the math to accurately calculate RMS on a non perfect sinusoidal waveform? What am I missing here? Not questioning you, just want to understand.

Oscilloscopes are not precision measuring devices, especially in terms of the vertical axis. Typically they have only 8 bits of vertical resolution, a scope is optimized for showing you an accurate visual representation of a signal, not for giving you a precise RMS voltage measurement. A multimeter has access to the waveform too, it just uses a different technology to calculate the RMS reading.

[SiliconWizard]

Why would the oscilloscope be the worst if it has full access to the waveform and is way faster than the multimeter? If I can resolve details at picosecond level surely it can perform the math to accurately calculate RMS on a non perfect sinusoidal waveform? What am I missing here? Not questioning you, just want to understand.

Oscilloscopes are not precision measuring devices, especially in terms of the vertical axis. Typically they have only 8 bits of vertical resolution, a scope is optimized for showing you an accurate visual representation of a signal, not for giving you a precise RMS voltage measurement. A multimeter has access to the waveform too, it just uses a different technology to calculate the RMS reading.

Absolutely.
As to multimeters, look up the spec sheet to see which one is the most accurate. You did. What else do you need?

Note that "accuracy" is not the only story here - you'd need to know the rated bandwidth. From what I've seen, it's spec'ed up to 800 Hz for the Brymen. Not sure what it is for the Fluke ones.
But accuracy depends on the frequency range. Usually, the higher the frequency, and the lower the accuracy for a RMS measurement.

[David Hess]

Good RMS converters have better accuracy than all of those except the Brymen BM235 so that one is likely the most accurate.

[Conrad Hoffman]

You might find the manual for the old Clarke-Hess 255 power meter interesting. It give you some hints about what affects accuracy and how high a bandwidth you really need. http://manuals.repeater-builder.com/te-files/MISCELLANEOUS/CLARKE%20HESS%20255%20Instruction.pdf

[pwnell]

Thanks for all the feedback.

[TimFox]

I had a problem with a low-power rectifier circuit exhibiting unexpected fluctuations (negligible load current) and found surprisingly high random variation in the AC line voltage over roughly 100 msec  to 10 sec time scales, even without my house air conditioning running.

[bob91343]

Over the years, power quality has been improving.  There are major exceptions.  The voltage keeps going higher.  The reliability is exceptional.

Nothing is perfect.

[TimFox]

I was just commenting on the practical problems involved with using the power line as a reference for AC measurements.

[bob91343]

Right.  The power line is a poor reference for calibration.  Maybe Heath used it sometimes.  I know they used a D cell I think as a reference.  As a result there are probably many meters that are not properly calibrated.  As a further result, the world hasn't stopped turning because of it.

There is a group of technical people who agonize over these things.  They are called Volt Nuts.  Sometimes I am one of them.  As well as a parallel group called Time Nuts.  I asserted my informal membership in the latter group tonight by measuring the error in frequency of my TS-440S transceiver.  I was pleased to learn that its error is about 1.5 ppm.  So I won't pull the cover to adjust it.