  ### Author Topic: Testing DMMs RMS measuring capability  (Read 4817 times)

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#### The Electrician

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« on: December 14, 2012, 09:08:43 pm »
There has been discussion of "True RMS" meters, so I thought it would be handy to have a signal to test them.

RMS capability is most needed when waveforms are peaky; this means that the crest factor (ratio of peak to RMS) is high.  Many meters whose specs I've looked at allow a maximum crest factor of 3 for rated accuracy.

Peaky waveforms often occur in power supplies.  The current drawn by a capacitor input filter following a transformer/rectifier is usually rather peaky, but rarely exceeding a crest factor of 3.  This fact suggests that a rectifier waveform might make a good test signal.

This circuit generates some waveforms that can be used to verify meter performance: It's not necessary that the transformer be a 24 VAC output unit.  You might use a 12 VAC, or a 36 VAC unit.  The 1000 uF capacitor voltage rating should be appropriate for the transformer secondary voltage.  A 63 volt rating would be useable for most cases.  The resistors should be selected to be "matched" in the following sense: R1 and R2 should be as nearly identical  as possible--within .1% and R3 should be 10 times the value of R1 and R3; R1 and R2 don't have to be exactly 1k but they should match.  So, for example, R1 and R2 might be 1023 ohms; then R3 should be 10230 ohms.  Hopefully, you'll have a selection of nominally 1k and 10k resistors and you can then use the ohmmeter function of your DMM to pick out a matched trio of resistors.

Here is a scope capture showing the waveforms across R1 and R2.  The voltage across R1 is orange and across R2 is blue. The current through R1 is the same as the current through R2, except that the R2 current is full wave rectified.  The current through R3 has the same DC value as the current through R2.  Because we're looking at currents (via the voltage across resistors), we don't have to deal with the diode voltage drops.

Average responding meters are calibrated to read the RMS value of an undistorted sine wave.  This means that they measure the mean (average) absolute (full wave rectified) value (with any DC component removed before rectification) of an applied waveform and multiply that value by 1.1107 because this number is the ratio of the RMS to mean absolute value of a pure sine wave.

The voltage across R3 is proportional to the mean value of the rectified current; mean value because the capacitor does averaging.  If we measure the DC voltage across R3 and multiply that value by 1.1107, then divide by 10 (because R1 is 1k and R3 is 10k), that is the value an average responding meter will give for the voltage across R1.  So, in effect, we have a very peaky waveform whose value as read by an average responding meter is known.

The waveform across R1 has exactly the same "True RMS Ac+DC" value as the waveform across R2.  To check whether or not a "True RMS AC+DC" meter is performing the "AC+DC" function correctly, just measure the voltage across R1 and R2; they will be the same if the meter is correctly measuring "True RMS AC+DC".

To determine if a meter is measuring RMS at all, first measure the voltage across R3 with the meter in DC mode.  Then measure the voltage across R1 with the meter in AC mode.  If the reading is about 1/10 of the DC reading across R3 times 1.1107 (within the accuracy specification of the meter), then the meter is an average responding meter.  If the reading is about 40% to 50% higher than 1/10 the DC reading across R3, then the meter is a "True RMS" meter.  And, of course, to double check the "True RMS AC+DC" capability, compare the readings across R1 and R2; they should be the same (if the "+DC" option is turned on).

I wired up this circuit, picking out resistors for R1 and R2 with values 1000.6 and 1000.3 ohms and for R3, 10001 ohms.  My transformer had a 36 VAC secondary and I fed the transformer with a variac.  I adjusted the variac so that the DC voltage across R3 was 10.064 volts.  Then the voltage across R1 measured with a Fluke 187 in "True RMS AC only" mode was 1.485 volts; an average responding meter read 1.15 volts.  With the meter in "True RMS AC+DC" mode, it reads 1.485 volts across both R1 and R2.
« Last Edit: December 14, 2012, 09:11:34 pm by The Electrician »

#### SeanB ##### Re: Testing DMMs RMS measuring capability
« Reply #1 on: December 15, 2012, 04:47:40 am »
Very nice unit. Will be quite useful for checking.

#### BravoV

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« Reply #2 on: December 15, 2012, 05:08:59 am »
Thanks & bookmarked ! #### mazurov

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« Reply #3 on: December 15, 2012, 06:10:23 am »
The resistors should be selected to be "matched" in the following sense: R1 and R2 should be as nearly identical  as possible--within .1% and R3 should be 10 times the value of R1 and R3; R1 and R2 don't have to be exactly 1k but they should match.  So, for example, R1 and R2 might be 1023 ohms; then R3 should be 10230 ohms.  Hopefully, you'll have a selection of nominally 1k and 10k resistors and you can then use the ohmmeter function of your DMM to pick out a matched trio of resistors.

Unfortunately, this could be an issue. With modern ATE it is feasible to do 100% testing/selection of resistors; what it means for end-user is that if you have a pile of 5% resistors, for example, none of them will be within 1% of nominal value - all 1% ones are separated at the factory and then sold as 1% resistors. I just grabbed a tape of 1K 1% film resistors and started measuring with calibrated HP34401 in 4-wire mode. I stopped after 100 pieces -  not a single one of them was within 0.5%. Go figure.

On the other hand, 0.1% resistors are not that expensive. Single-quantity prices on Mouser are 18-30 cents.

#### The Electrician

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« Reply #4 on: December 15, 2012, 07:10:35 am »
You didn't read what I said carefully.  They don't have to be within .1% or even 1% if nominal value; they just have to be matched.  If they are 5% away from nominal that's fine; they just have to be matched.

Furthermore, if a person needs a resistor very close to 1k for example, and has available a 1023 ohm resistor, it's an easy calculation that paralleling it with a 44478 ohm resistor will get you an equivalent resistance of 999.9999 ohms.  Paralleling 1023 ohms with 43000 ohms gets you to 999.23 ohms.  But, for this project it isn't necessary to do more than match, which can be done with most DMMs to within .1% easily.

#### SeanB ##### Re: Testing DMMs RMS measuring capability
« Reply #5 on: December 15, 2012, 07:14:49 am »
You just need matched, and then a decade one of that. Within limits it does not matter the value, just the ratio is needed. Thus you can get a pair out of a pile of 5% units, and then go through a set of 10 times that value and match for the other one.

#### The Electrician

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« Reply #6 on: December 15, 2012, 11:45:45 am »
In connection with the discussion of RMS capable meters, the maximum crest factor for rated accuracy is relevant.  A while ago I decided to find out just what the crest factor for some waveforms would be and how likely it was that a crest factor of 3 would be approached or exceeded.  Some of my results are shown in this post.

My Tek scope has a power analysis software add-on that displays crest factor, and I used that to measure crest factor.  The crest factor of the waveform across R1 in the first post is 1.8

I set up a capacitor input rectifier filter and changed various parameters to try for a high crest factor.    One way to increase crest factor is to use a transformer with more current capability than needed for a given output power.  This causes the transformer ESR to be lower than would ordinarily be the case if the transformer were sized for the desired load.  Another change that increases crest factor is to use a large filter capacitor with low ESR.  The following image shows a high crest factor waveform (blue) obtained by these methods: The next waveform shows an even higher crest factor rectifier waveform: I have an IEEE paper describing very high crest factor waveforms generated when capacitor input rectifier filters are operated directly from the 120 VAC grid without a transformer, such as older television sets sometimes did.  The next image shows a grid-connected rectifier waveform: Finally, a grid connected rectifier waveform with circuit parameters adjusted to increase the crest factor: A typical capacitor input filter rectifier probably won't generate rectifier current pulses with crest factor exceeding 3 except in unusual circumstances.  A  rectifier with a power transformer of 500 VA rating or less will likely have sufficient ESR to keep the crest factor of the rectifier current pulses under 3.

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