How can I test if a DMM is reading in true RMS ?

[Wytnucls]

Glad you finally got it. Don't worry, it confuses a lot of people, even professionals.
I'm surprised Dave hasn't done a tutorial over this subject, it is so fundamental.
Maybe there is too much math involved. 

[Lightages]

What adds to the confusion is that some multimeters have the option for AC TRMS and AC+DC TRMS.

[SeanB]

True RMS should not care about DC as long as the peak is within the dynamic range of the converter input. It should give the correct result if you put in pure DC, or with an input of half Dc and AC on top of it. I have some TRMS converter chips around, old AD devices. Need +-15V rails, but do not care as long as the input is in range, crest factor of up to 13 AFAIKR on a 2V pp signal.

[ejeffrey]

True RMS should not care about DC as long as the peak is within the dynamic range of the converter input. It should give the correct result if you put in pure DC, or with an input of half Dc and AC on top of it. I have some TRMS converter chips around, old AD devices. Need +-15V rails, but do not care as long as the input is in range, crest factor of up to 13 AFAIKR on a 2V pp signal.

Almost all hand-held multimeters only use the RMS-DC converter in AC coupled mode. A few offer both AC coupled and AC+DC true RMS.  Wytnucls claims that the former is incorrect and means 'it provides incorrect readings in the presence of a DC offset.'  I think that is a bit pedantic, but as always it is true that you have to understand what your meter is measuring.  It is a true RMS reading with a bandwidth from ~1 Hz up to the BW limit of the meter.  That is a perfectly reasonable thing to measure, but it is *not* the heating power of the signal if applied to a resistor, which is a common description of RMS vs averaging.

[Wytnucls]

True RMS should not care about DC as long as the peak is within the dynamic range of the converter input. It should give the correct result if you put in pure DC, or with an input of half Dc and AC on top of it. I have some TRMS converter chips around, old AD devices. Need +-15V rails, but do not care as long as the input is in range, crest factor of up to 13 AFAIKR on a 2V pp signal.

You are wrong.
Most TRMS converters have the option to take the DC offset into account. The 61E converter has it, but Uni-T elected not to implement it on this particular meter. I'm not sure what converter Fluke uses on the 87V, but the meter also only measures TRMS accurately if there is no DC offset.
Few meters have the AC+DC option, which is paradoxically quite common on bench meters.

All meters measure TRMS correctly for a sine wave with no DC offset.
Meters with the AC+DC option are the only ones giving a correct value for TRMS, if there is the smallest DC offset on the sine wave.

All meters measure TRMS correctly for a 50% square wave with no DC offset, except meters lacking a TRMS converter.
Meters with the AC+DC option are the only ones giving a correct value for TRMS, if there is the smallest DC offset on the square wave.

With pure DC, with meters set on the AC range, only the meter with AC+DC measures TRMS accurately.

[alm]

I think you're being pedantic here. RMS voltage is the root mean square of the instantaneous voltage. The RMS of the voltage is the RMS of the whole signal, and the RMS AC voltage is the RMS of the AC (with some lower and upper frequency). It's trivial to add up RMS AC and DC with the formula I gave earlier, AC+DC is just a convenience function, assuming the DC function has a decent NMRR. Some meters even give you the formula in the manual. Are you also going to complain that measuring a 10 MHz RF signal does not indicate the thermal heating power?

[Wytnucls]

Call me whatever you want, but the problem remains:
Your fancy TRMS meter only gives you accurate TRMS readings if the signal being measured has no DC offset, unless it has the AC+DC feature.
Anything can be calculated with a formula, TRMS included, but it is not as trivial as you make it out, depending on the shape of the wave. Quite often, you won't even know if the AC voltage or AC current being measured has a DC offset, until you look at it with an oscilloscope.
Most people are not aware of the limitations of their TRMS meters, as this thread proves and they seldom have a calculator taped to the back of their Fluke meter for DC offset TRMS calculations.

To compound the problem, in the case of the 61E, TRMS measurements for a strictly AC square wave are wrong too!
It is only accurate for a duty cycle of 50%. The errors are not trivial either: up to 25% less than TRMS with a 20% or 80% duty cycle (tested at 100Hz 5Vpp). The 71D gives the same wrong readings when in AC mode only, but measures correctly in AC+DC mode.

[IanB]

I don't think it's being pedantic at all. RMS is RMS. There is no "sort of RMS" or "partly RMS". If the meter doesn't measure true RMS correctly, including any DC offset, then it is not a true RMS meter. There is no point calling something what it isn't. Maybe several "true RMS" meters are actually "false RMS" meters, but if so that fact should be publicized. Let's reserve true RMS for those meters that measure the signal many times per second, square it, sum the measurements over an interval, and display the square root of the mean.

[alm]

RMS(x) is sqrt(mean(x^2)). RMS does not define what this x is: this may be voltage, current, temperature, velocity, only the z component of the velocity or only the 1 Hz - 10 kHz part of the voltage signal. RMS(V_AC) is a real RMS value, nothing sort of RMS about it.

Just tried an experiment with a function gen, a true RMS DMM without AC+DC feature, and a DMM with. Function gen is set to 1 kHz sine with 200 mV RMS amplitude, 100 mV DC offset. In DC mode, the DMM without AC+DC reads 99.7 mV in DC mode and 200.4 mV in AC mode, or 223.8 mV AC + DC according to the equation I gave. The AC+DC meter reads 0.22375 mV. Could you give an example of a signal where this procedure would fail? It would require two measurements and some arithmetic, that's the only issue.

A change in duty cycle from 50% adds a DC offset, it's not a strictly AC signal. Does it show an increase in DC voltage if you increase the duty cycle?

[Wytnucls]

"Let's reserve true RMS for those meters that measure the signal many times per second, square it, sum the measurements over an interval, and display the square root of the mean." IanB

I agree with Ian, as this is what the AC+DC meter does, giving you an instant  true RMS value on the screen and coping with a small variation in DC offset easily.
A change in duty cycle is not a change of DC offset, by the way. The voltage hasn't changed at all.
There is a bodge solution, like you describe, but it requires pen and paper and a calculator, exposing the user to mistakes. It is so much easier to use a proper AC+DC meter, since they are available.
That is also assuming that the meter AC readings are correct in the presence of a DC offset, which there are not in the case of the 61E, introducing an extra 1% error. This could be insignificant for most applications, but an error nonetheless.

So, pedantic or not, if true RMS is important to you, buy a meter capable of AC+DC calculations.

[alm]

"Let's reserve true RMS for those meters that measure the signal many times per second, square it, sum the measurements over an interval, and display the square root of the mean." IanB

The meters I'm talking about do that, the inputs are just AC coupled, as you would expect in VAC mode. I would be very annoyed if they would respond to DC voltages in VAC mode, this would make them useless for tasks like measuring power supply ripple.

I agree with Ian, as this is what the AC+DC meter does, giving you an instant  true RMS value on the screen and coping with a small variation in DC offset easily.

An AC+DC mode is convenient, I agree that it is annoying to get out your calculator and measure two values, especially for fluctuating signals. AC coupled RMS measurements are not wrong or misleading, however, as you seem to imply. If you're asking for VAC, then it should not take DC voltage into account.

A change in duty cycle is not a change of DC offset, by the way. The voltage hasn't changed at all.

An AC signal has a mean of zero. What happens to the mean voltage as you change the duty cycle?

That is also assuming that the meter AC readings are correct in the presence of a DC offset, which there are not in the case of the 61E, introducing an extra 1% error. This could be insignificant for most applications, but an error nonetheless.

This sounds like a flaw.

[T4P]

Yes exactly, you expect RMS AC readings when you switch to VAC and not both ... that's proper RMS! You selected VAC so you should get VAC not the other way round! Pfft. 

[Wytnucls]

The AC+DC option is just that, an option. The meters I talk about can give true RMS for AC only, if required, although I hear some Fluke meters are stuck on AC+DC for mV.

I never implied that AC coupled measurements are not useful. I just said that working out true RMS for a signal with a DC offset without an AC+DC multimeter or an oscilloscope that doesn't have DC coupling, is a chore.

An AC signal has a mean of zero for a sine wave, otherwise it can be any voltage that reverses over time. My function generator certainly doesn't think that the DC offset changes with duty cycle on a square wave. My oscilloscope on the other hand, when AC coupled, moves the base to keep the surface areas in balance (energy?), when the duty cycle changes, so it looks like you are right when it comes to the definition of RMS(AC).

Here is a Fluke write-up on the subject:
http://www.fluke.com/fluke/usen/community/fluke-news-plus/ArticleCategories/DMMs/True-rms+Facts.htm

[BravoV]

Here is a Fluke write-up on the subject:
http://www.fluke.com/fluke/usen/community/fluke-news-plus/ArticleCategories/DMMs/True-rms+Facts.htm

Thank you, a really nice reference ! 

[The Electrician]

If the meter doesn't measure true RMS correctly, including any DC offset, then it is not a true RMS meter. There is no point calling something what it isn't.

The terms one finds used to describe the capabilities of available meters are "True RMS" and "True RMS AC+DC".  Perhaps "True RMS" should be "True RMS AC only", but in the year 2012 it's clear by inference that when they say "True RMS", they really mean "True RMS AC only".

There is a point in describing a meter as "True RMS" even if it's not able to include the DC component of a waveform in its measurement when on the AC range of the meter.  This because it's possible to get the "True RMS AC+DC" value of a waveform from such a meter by measuring the DC component with a separate measurement and doing the V_AC+DC = sqrt(V_AC² + V_DC²)  computation.

If the meter is a "True RMS AC only" (called "True RMS" by manufacturers), this two part measurement is capable of giving the "True RMS AC+DC" value of the waveform.  If the meter isn't even "True RMS" (meaning that it's an average responding meter), that measurement won't be possible at all.  That's why there's a point in describing a meter as "True RMS"; we need only understand that it's a marketing gimmick.

Now, it would be my preference that the very designation RMS should mean a value for a waveform that includes the total waveform in the measurement/computation, AC and DC components both.  But, in fact, because of marketing practices, some meters are only capable of measuring the RMS value of the AC part of a waveform when on the AC range.  Such a meter can still measure the "True RMS AC+DC" value of a waveform with two measurements, which an average responding meter can't do.  The buyer should understand what the manufacturers mean when they describe a meter as "True RMS" or TRMS, without the "AC+DC" addendum.

A good example of where it is absolutely necessary to be able to measure an RMS value which includes the DC component of the waveform is determining copper losses in a full wave capacitor input filter power supply, where the transformer secondary is center tapped (a two diode configuration).  The current in each half of the center tapped winding has a substantial DC component because there is a single diode in series with the half winding; the current in that half winding is therefore unidirectional.  With a "True RMS AC only" (called "True RMS" by manufacturers) you could make the measurement; with an average responding meter, you couldn't.

This means that it's not a good idea to use a 0->5v square  logical signal to test it.

Such a waveform will work just fine; simply put a 1 uF film capacitor in series with it to eliminate the DC component of the waveform.

The answer to your original question is that probably the simplest way to determine if a meter is truly responding to the RMS value of the AC part of a waveform is to use a square wave without a DC component.  If you have a  bipolar square wave, with a positive excursion of 1 volt and a negative excursion of -1 volt, the RMS value of that waveform is 1 volt RMS, regardless of the duty factor.  An average responding meter will calculate the average value of the absolute value of that waveform (the full wave rectified version) and multiply by the number  1.1107, which would give the correct RMS value of an undistorted sine wave.  That same average responding meter would give a value of 1.111 volts for the square wave I described.

If you use a logic square wave with a maximum positive value of V volts (5 volts maybe), minimum value of zero volts, and remove the DC component with a capacitor, you will have a DC free square wave with a peak value of V/2 volts  (2.5 volts maybe).  A "True RMS AC only" meter will read that waveform as 2.5 volts; an average responding meter will read 2.5*1.111 = 2.777 volts.

You could even use the CAL output from a scope.  Put a big film cap in series with it and measure with your meter.  If the P-P voltage of the calibrator output (as measured by the scope) is V volts, then a "True RMS AC only" meter will  read V/2 volts, but an average responding meter will read V/2*1.111 volts.

NOTE WELL.  This assumes that the duty factor of the calibrator out is a 50% duty factor square wave.  If it's not, use the following to compensate.  (When you remove the DC component of a square wave, the positive and negative excursions change with changes in duty factor.)

Assume we have a square wave with a positive excursion of 1 volt and a negative excursion of -1 volt, with adjustable duty factor.  If the DC component is removed with a capacitor,  and the RMS value of the DC free waveform and the average of its absolute value (what a non RMS meter would measure) are calculated, we would get table shown in the first image.  The first column is the duty factor in percent.  The second column is the RMS value and the third column is the average of the absolute value.  If you have a square wave with peak values other than 1 volt, use numbers in the table as compensating factors.

The second image shows the same information in graphical format with the duty factor along the horizontal axis.  The red curve is for the RMS value and the blue curve is for the averaged absolute value.