# Electronic Circuits and Projects Forum

1. ## About "True RMS AC+DC" meters

Questions often arise in the forum about RMS measurements, what is RMS, what is "true RMS", what is "True RMS AC+DC", why is RMS used, does my meter measure RMS?

If we pass a DC current through a resistive load, the load will heat. If we reverse the direction of the current, but keep its value the same, the same amount of heating will occur; there's no such thing as negative heating in resistors caused by reverse current flow.

Consider the attached image; the orange trace shows an AC waveform. If we pass an AC current like that through a resistor, the resistor will heat during the positive lobe of the waveform, and it will also heat the same amount during the negative lobe (assuming the negative lobe has the same waveshape and amplitude as the positive lobe, just reversed in polarity) because heating in a resistor doesn't depend on the direction of the current, just its amplitude.

So, if we reversed the negative lobes, making them positive lobes (as shown by the purple waveform in the image), we would have a current wave that would cause the exact same heating in the resistor as the orange waveform because the purple lobes are the same size and shape as the orange lobes (polarity doesn't matter for causing heating).

We know that power dissipated in a resistor is given by the formula P = I^2*R. The current value is squared and multiplied times the resistance. The fact that the current value is squared is consistent with the fact that heating doesn't depend on the direction of the current. A negative number squared is a positive number, as is a positive number squared, so when we square the value of the current we get a positive result regardless of the current direction.

When we have an AC waveform, the current is changing magnitude and reversing direction constantly, and it all causes heat in a resistor. The fact is, the instantaneous heat dissipated in a resistor by an AC current is changing constantly as the current changes magnitude; 120 (or 100 in Europe, etc.) times a second. But we want a single number that tells us how much heat, ON AVERAGE, will be generated in a resistor if we pass that AC current through a resistor, rather than a bunch of numbers (a mathematical function) that change during a cycle of the AC current.

What we can do is calculate the power that is dissipated at every instant during one cycle of the AC waveform, and average that power over the entire cycle. Then divide that power by the resistance value and take the square root. That will give us the value of a DC current that would cause the same heating in the resistor; this is what RMS means.

RMS means "root mean square"; square the instantaneous current (or voltage) value, take the mean (average), and then take the square root.

Now back to meters. Have another look at the first image. The orange waveform is the output from a small transformer connected to the grid. The waveform is supposed to be a sine wave, but we can see that it is somewhat distorted; it's a little flattened on top and bottom. If we set our DMM to measure AC volts, we will get a number (I measured 28.33 VAC). The purple waveform is the full wave rectified version of the orange waveform; the negative lobes have been made positive. As I explained above the purple waveform should cause the same heating in a resistor as the orange waveform, so if I measure the purple waveform with my DMM it should read the same as the orange waveform

If I set my meter to measure AC volts and measure the purple waveform, I get 12.92 VAC, but I was expecting to get 28.33 VAC. Why don't I get the same reading?

The reason is that a complex voltage (or current) wave may contain a DC part as well as an AC part.

Look at the orange waveform in the image; at the left side of the image is an orange number 1; that is the reference level (zero volts) for the orange waveform. Anything above that level is a positive voltage and below it is a negative voltage. We see that the orange waveform is symmetrical; it spends just as much time above the reference as below it. That means that its average value is zero; the positive parts are balanced by equal negative parts.

On the left side of the image, we see a purple number 3; that is the reference level for the purple trace. Voltages above that level are positive and below it, negative. There are no parts of the waveform that go below that line, so the purple waveform is always positive. If we ask ourselves what the average value of the purple waveform is, we see that it must be positive, because there are no negative values to balance out the positive.

The average value of a voltage (or current) waveform is by definition its DC part. The orange waveform has an average value of zero; it contains no DC part. The purple waveform has an average value which is not zero. It never goes negative so it has a non-zero DC part.

The existence of the DC part of the purple waveform is why my meter measured 12.92 VAC and not 28.33 VAC. I was only measuring the AC part of the waveform. But, this is an incorrect way to determing the heating capability of the waveform, because the DC part can cause heating as well as the AC part.

If I set my meter to measure DC volts, and measure the orange waveform, I get 0.00 volts. With the meter still set to measure DC volts and measuring the purple waveform, I get 25.26 volts.

But I'm still not getting 28.33 volts; if the purple waveform has the same heating value as the orange waveform shouldn't there be some way to get the same measurement for the two?

There is. I need to have a meter that can measure "True RMS AC+DC". What this means is that the meter takes into account the AC part of the waveform AND ALSO the DC part of the waveform. On my Fluke 187, I can choose whether the meter measures only the AC part or if it measures both the AC and DC parts together. If I set the meter to AC+DC, the reading of the purple waveform is 28.34; close enough to 28.33 measured for the orange waveform.

There is a way to get the correct RMS value for the purple waveform even if your meter doesn't have "True RMS AC+DC". If your meter is only "True RMS", but without the "AC+DC" functionality you need only measure the waveform in AC volts mode, then in DC volts mode. Combine the two readings by taking the square root of the sum of the squares of the VAC and VDC readings. Above I got 12.92 VAC and 25.26 VDC for the purple waveform. If I calculate
SQRT(VAC^2 + VDC^2), I get 28.37, which is plenty close enough to 28.33 measured for the orange waveform. We conclude that the orange waveform and the purple waveform have the same RMS value.

Sometimes you may want to measure only the AC part of a waveform, and most meters will allow this. The Fluke 187 (and similar "True RMS AC+DC" meters) allows you to select AC, or AC+DC when measuring. Some "True RMS AC+DC" meters may always measure the DC part together with the AC part, not allowing the choice of turning off the measurement of the DC part; I don't know of any such meters, but they may exist. If so, it's easy to get rid of the DC part of the measurement; just put a 1 uF capacitor in series with the test leads and the DC part will be blocked.

So far, I've only talked about waveforms (grid voltage) that are fairly good approximations to a sine wave. For a perfect sine wave the RMS value is .707 times the peak value, but this is not true for other waveshapes.

What if we need to measure the heating effect of a current wave that isn't a sine wave? For example, the very peaked current drawn by a rectifier/capacitor power supply circuit. The current the rectifier supplies to the filter capacitor is usually very peaked, and the heating this current causes in the copper wires comprising the transformer windings is determined by a simple I^2*R formula, PROVIDED that the current I is measured with an RMS responding meter. If the rectifier is a full bridge rectifier, the current in the secondary winding is AC only, but very peaked, and a "True RMS AC+DC" metering function is not needed, only "True RMS". But if a full wave rectifier using the center tap of the secondary is used, there will be a DC component in each half winding current waveform, and to accurately measure the heating in the winding, the DC component must be taken into account.

Finally, a meter claiming "True RMS" functionality (but not "True RMS AC+DC") means that the meter correctly deals with a non-sinusoidal waveform, such as the peaked current in a rectifier, but may not correctly take into account the DC part. It may do so, but it may not. If the meter is actually measuring "True RMS AC+DC" (but the manufacturer didn't say so), it will correctly measure a DC voltage while in the "True RMS" mode. The meter can be checked for this by simply setting the meter to measure AC RMS volts and measuring a simple AA dry cell, or other DC source. You should get the same voltage reading that you get on the DC setting.

Nowadays, manufacturers are aware that the "AC+DC" functionality is a desireable thing, and they say so if their meters can do it. There may be some earlier meters that actually measure the DC component in RMS mode, but didn't say so in thier advertising; as I explain above it's easy to check if a meter can do this.

If the meter claims to be "True RMS AC+DC", then in that mode it will correctly measure the voltage of a dry cell or other DC source. A meter able to measure "True RMS AC+DC" is what is needed for correct RMS measurement of all complex waveforms, whether or not they contain a DC part.

So, always be aware that if you want the full heating effect ("True RMS AC+DC" value) of a complex voltage or current waveform, you need to make a measurement that includes the DC part as well as the AC part.

2. Hi,

I had a set of formulas for calculating the RMS value of many different wave forms i'll have to look for them, but im sure there is much on the web too.

One thing i always meant to do was to measure the RMS values of current and voltage in rectifier diodes where there is significant capacitive filtering that makes the current wave shape almost like that of a pulse. I have plenty of spice data and even a special program for calculating these things, but it would be nice to have some real life measurements.
I got my first AC+DC meter about 2 years ago even though i have used them before. I should break it out and do some small experiments with low power supplies like 12v, 1 amp or something like that to start.
Have too many other things going right now though.

3. I think it's important to note the frequency of the waveform is quiet important, most True RMS meters (AC only or DC+AC) are going to have a limited frequency range in which they can obtain true RMS numbers. If the frequency components are high enough a DSO would be required to obtain the true overall values.

4. Hi,

Yes good point. I think mine goes up to around 300kHz and it has separate calibration numbers for the higher frequencies, but not all meters will go that high and are meant for 50/60Hz.

I think it's important to note the frequency of the waveform is quiet important, most True RMS meters (AC only or DC+AC) are going to have a limited frequency range in which they can obtain true RMS numbers. If the frequency components are high enough a DSO would be required to obtain the true overall values.
Maybe I should have said explicitly that I was concerned with grid frequencies, 50 or 60 hertz. If a DMM is specified to measure true RMS, and has an accuracy specification for grid frequency waveforms, it will necessarily have adequate frequency response to meet the accuracy specification.

6. If a DMM is specified to measure true RMS, and has an accuracy specification for grid frequency waveforms, it will necessarily have adequate frequency response to meet the accuracy specification.
The Electrician, that is an assumption which may not hold true. Depending on the type of load and conditions the distortion from a sine wave can contain frequency components outside of the meters specification. The simplest example I can think of is the use of phase angle power control of high powered loads.

The Electrician, that is an assumption which may not hold true. Depending on the type of load and conditions the distortion from a sine wave can contain frequency components outside of the meters specification. The simplest example I can think of is the use of phase angle power control of high powered loads.
Whether or not there may be some harmonics outside the meter specification is not the issue. The issue is whether the failure to include those harmonics will result in an error greater than the meter specification.

It's not too hard to calculate how many harmonics must be included to achieve a certain error specification.

Doing the calculation for a phase control waveform that turns on at 90° with an infinitely fast turn-on edge rate, I get the following approximate results:

Code :
Desired error spec      Highest Harmonic needed

2.5%                              7th
1.5%                              13th
1%                                19th
.5%                               45th
.2%                               105th
.1%                               201st

Low end handheld DMMs, such as Forum beginning project builders might use and which are true RMS typically have a bandwidth of 1 kHz, but their error spec is typically a rather poor 2% or so. They will measure the phase control waveform with an error within their spec given their bandwidth.

The better handheld DMMs typically have bandwidths from maybe 20 kHz to 100 kHz and that's enough to achieve errors of around .2% which is typical of those DMMs.

I would think the DMM manufacturers would be aware that waveforms such as phase control waveforms might be the very sort where true RMS capability would be needed to get an accurate measurement, and would specify an accuracy the meter could achieve for such a waveform, given the meter's bandwidth.

One might reasonably think that if 1% of the energy in a waveform is outside the meter's bandwith, an measurement error of something like 1% might be expected. If 10% of the waveform's energy is outside the rated bandwidth, we might expect something like a 10% measurement error.

If 90% of the waveform energy is outside the meter's bandwith, then the measurement error will likely be very large, but such waveforms are not what the meter is intended for.

The meter specs for most actual meters of various accuracies that I checked are such that the meter will measure a phase control waveform, and similar waveforms one might find in a 60 Hz environment, with an error commensurate with the meter's bandwidth. I think a 60 Hz environment is what these meter's true RMS capability is intended for.

If a person wants to accurately measure a high audio frequency complex waveform, then something other than a low cost DMM may be needed.

The examples I discussed are grid frequency rectifier waveforms, and these DMMs can easily measure such waveforms, and even phase control waveforms, within the meter's error specification.

8. Hi,

Yeah i think the general rule is that the more standard below 200 dollars meter would be ok for most waveforms at 50/60Hz or maybe even up to 400Hz, but definitely not for audio work. It might suffer for very low conduction angles but that's not too bad really.

Those kinds of meters generally can not even measure an AC signal above 1kHz using the 'regular' AC setting because they are really made for line frequencies anyway. Remember in the old days a VTVM was used for higher frequency stuff. Havent seen one of those around for a thousand years now :-)

9. Originally Posted by MrAl
Hi,

Yeah i think the general rule is that the more standard below 200 dollars meter would be ok for most waveforms at 50/60Hz or maybe even up to 400Hz, but definitely not for audio work. It might suffer for very low conduction angles but that's not too bad really.

Those kinds of meters generally can not even measure an AC signal above 1kHz using the 'regular' AC setting because they are really made for line frequencies anyway. Remember in the old days a VTVM was used for higher frequency stuff. Havent seen one of those around for a thousand years now :-)
They can presumably measure a sine wave up to the specified bandwidth within the specified error even though their main intended use is for grid frequency waveforms.

For example, the EXTECH 470 has a specified error of 1.5% up to 400 Hz and 2.5% up to 1 kHz. This means that sine waves can be measured up to 1 kHz with no more than 2.5% error. This could be useful. And, it can be used for sine waves above 1 kHz if the user determines the error at higher frequencies. I just use a source with known output level, such as a function generator.

Sceadwian's mention of using a DSO for higher frequencies is well taken. That's what I usually do, although you probably can't get .1% accuracy! Fortunately, I don't usually need .1% accuracy for the kind of waveforms I would use the scope to measure.

For grid frequency waveforms an old panel meter of the moving iron type can be used to get an RMS measurement. The waveforms associated with grid frequency rectifier waveforms are usually rather smooth without sharp edges, hence not containing a lot of high frequency harmonics. However, the crest factor limitation may come into play for very narrow current pulses. I'm going to make some measurements of crest factor for rectifier waveforms.

We older guys no doubt have many resources for measurements. Most of us probably have several DMMs, a couple of scopes, thermocouple RF ammeters, moving iron panel meters, wattmeters, variacs, function generators, current probes, etc., etc.

But, on the forum I try to keep in mind that the beginners who want to build a power supply don't have those resources or the money to spend on them. This thread was aimed at helping them understand the need for a certain minimum measurement capability.

10. Originally Posted by The Electrician
They can presumably measure a sine wave up to the specified bandwidth within the specified error even though their main intended use is for grid frequency waveforms.

For example, the EXTECH 470 has a specified error of 1.5% up to 400 Hz and 2.5% up to 1 kHz. This means that sine waves can be measured up to 1 kHz with no more than 2.5% error. This could be useful. And, it can be used for sine waves above 1 kHz if the user determines the error at higher frequencies. I just use a source with known output level, such as a function generator.

Sceadwian's mention of using a DSO for higher frequencies is well taken. That's what I usually do, although you probably can't get .1% accuracy! Fortunately, I don't usually need .1% accuracy for the kind of waveforms I would use the scope to measure.

For grid frequency waveforms an old panel meter of the moving iron type can be used to get an RMS measurement. The waveforms associated with grid frequency rectifier waveforms are usually rather smooth without sharp edges, hence not containing a lot of high frequency harmonics. However, the crest factor limitation may come into play for very narrow current pulses. I'm going to make some measurements of crest factor for rectifier waveforms.

We older guys no doubt have many resources for measurements. Most of us probably have several DMMs, a couple of scopes, thermocouple RF ammeters, moving iron panel meters, wattmeters, variacs, function generators, current probes, etc., etc.

But, on the forum I try to keep in mind that the beginners who want to build a power supply don't have those resources or the money to spend on them. This thread was aimed at helping them understand the need for a certain minimum measurement capability.
Hi,

Yes but many meters dont have a spec for high frequency AC, even just AC alone without considering RMS.

Also, a meter + frequency generator isnt just a meter anymore. If we can add test equipment to the batch then why not also include a 2000 dollar oscilloscope and say we can use the meter up to 5 megahertz if we check it with the scope.

The point is about the meter alone, not the meter plus various other test equipment. If we had other calibrated test equipment we could use a 15 cent diode and 10 cent capacitor and make our own AC meter that goes up to 1 megahertz easy. As a matter of fact, myself and a group of other onliners built this very device several years back to measure ripple frequency output of a DC switching power supply. We used a Schottky diode and a couple of ceramic caps and some small value resistors. Once calibrated, it would go up into the megahertz quite easily but all we needed to reach was 300kHz.

I have an old Weston meter with a face that is about 12 inches in diameter. Not sure what year it was from.

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