A few questions about TRUE RMS

[zapta]

1. What is true RMS? My understanding is that it is DC voltage that will result with same power when applied to same resistance but am not sure.  (I do understand the mathematical definition of RMS, I wonder what it means and why it is important).

2. Why multimeters provide RMS measurement for AC only? I would think it would be useful for DC voltages as well, for example PWM.

3. When dealing with household electrical projects, is true RMS really required or an average measurement is sufficient? (what can be the error between them in % in common house hold scenarios?)

4. How true RMS meters work? (I think I understand how average measurement works, e.g. by a rectifier and some low filter).

Thanks,

Z.

[c4757p]

You are correct, power from 120 V RMS = power from 120 V DC. It just comes from Ohm's law and P=VI.

A true RMS DMM should have no trouble responding to pulsed DC, though you will have to manually add the offset. Some have an AC+DC mode that does this.

I can't really think of a reason why you would need one for household electrical work.

They literally compute sqrt(mean(v^2)). Some use an analog circuit making use of a logarithmic amplifier. Some newer ones sample the voltage and compute digitally. It is also possible to actually measure power delivered thermally, but that is uncommon.

[PA4TIM]

AC in Volt is allway RMS except when stated that it is not.
It is the same Voltage that you need for heating up a resistor when using DC.

Everey meter should be able to measure the correct AC voltage, but to bad, that never was the reality. The meters that did this were called RMS meter or later under marketing pressure TRMS meters.
But then the cheapys allso started to make TRMS meters. To bad many have a very narrow bandwidth, crestfactor.

There are AC coupled TRMS meters and TRMS meters that also have a AC +DC mode. (I haver 4 meters who do that and two upto 1 MHz and high crest factors)

You can however measure AC and DC separate and do the math if your meter does not do it for you.

There are several ways. Today most times this is done by special IC's. Look at the site of Analog Devises. They have a (very) thick pdf only about measuring TRMS. In the earley days they often used a measurement based on heating.

[Lightages]

1. What is true RMS? My understanding is that it is DC voltage that will result with same power when applied to same resistance but am not sure.  (I do understand the mathematical definition of RMS, I wonder what it means and why it is important).

RMS is Root Mean Squared. There are better resources to explain the math than I can provide here. Yes, it basically means the equivalent power into a resistive load. This can be measured by applying the voltage to a known nonreactive load and measuring the heat produced.

2. Why multimeters provide RMS measurement for AC only? I would think it would be useful for DC voltages as well, for example PWM.

Many multimeters do provide AC+DC True RMS. Some provide a way of switching from AC only to AC+DC.

3. When dealing with household electrical projects, is true RMS really required or an average measurement is sufficient? (what can be the error between them in % in common house hold scenarios?)

It depends. If you are just trying to get a rough measure of the output of a transformer, then an averaging meter will do. If you are trying to measure a reactive load or trying to determine things like power factor or measure music waveforms then True RMS is a must.

4. How true RMS meters work? (I think I understand how average measurement works, e.g. by a rectifier and some low filter).

True RMS calculations are done a few different ways. Most meters use a chip that is made specifically to do the calculations and then pass on the equivalent DC voltage to the main meter processor.

Here are a couple of resources
http://en.wikipedia.org/wiki/Root_mean_square
http://www.analog.com/en/special-linear-functions/rms-to-dc-converters/ad636/products/product.html

[zapta]

Thanks guys for the informative answers. I think I get it now.  I have two follow up questions if I may

1. The true RMS meters that use heat, do they take the heat from the input signal (effecting the measurement and difficult to have multiple ranges) or do they have high impedance and internal buffer that feed the heat load?

2. I tried to make sense of the match of measuring true RMS by adding the DC bias to the true RMS of the AC decoupled signal but could not make it to work.  Here is an example

Let S0  be the measured signal: 10% duty cycle pulse between 0V and 10V.
AverageDC(S0) = 1v.
TrueRMS(S0)=sqrt(0V*0V*0.9 + 10V*10V*0.1) = 3.3V

Let S1 be S0 after AC coupling. S1 = AcCoupling(S0) = S0 - AverageDC(S0) = S0 - 1V. This is 10% duty cycle pulse between -1V and 9V.

TrueRMS(S1) = Sqrt(-1V*-1V*0.9 + 9V*9V*0.1) = Sqrt(9VV) = 3V.

If we add the AverageDC(S0) to TrueRMS(S1) we get 3V + 1V = 4V which is not the same as TrueRMS(S0) = 3.3V.

I think that the problem is that we are mixing average measurement (the AC decoupling which subtracts the average DC level) with RMS measurement.

[c4757p]

I misspoke when I said "add" the offset, I should have said "consider" or "adjust for" or something like that. You're right, it doesn't quite work that way.

If I'm not mistaken:

[macboy]

Thanks guys for the informative answers. I think I get it now.  I have two follow up questions if I may

1. The true RMS meters that use heat, do they take the heat from the input signal (effecting the measurement and difficult to have multiple ranges) or do they have high impedance and internal buffer that feed the heat load?

We are measuring voltage not power. Generally, they have a high input impedance (unless it is an RF range instrument, which might have a 50 ohm input). The input voltage is buffered and fed to a resistor to generate heat. This has a temperature sensor. Usually what is done is that there is an identical resistor and temperature sensor which is fed by an internally generated DC voltage and controlled by a control loop which balances the two; it makes the power dissipated in the DC-fed resistor equal to the power dissipated in the (external signal) AC-fed resistor. Then the DC voltage is measured and displayed. It's simple really but very difficult to pull off.

[c4757p]

Even better, if you'd rather be convinced that it holds true for all AC waveforms:

Edit: Fixed a missing factor of two. Thanks, zapta!

[G0HZU]

I have an old school Racal 9300 true rms meter here that has a very elegant method of measuring true rms.

It operates from about 5Hz to 20MHz and uses a series of precision attenuators followed by a multiplier stage (squared) followed by an integrator (mean) and then a final stage to display rms. It also has a complex 'offset error' cancelling system and I have used one of these as my gold standard true rms meter here and at work for many years.

I think my Fluke 45 bench DVM uses an AD637 chip for the true rms function but I think it only works up to about 100kHz and I would always trust the 9300 more than the Fluke for signals that contain noise.

[zapta]

Even better, if you'd rather be convinced that it holds true for all AC waveforms:

Hi cp. I am not a math wiz but tried anyway to follow your formulas and got stuck at line 7. When you go from line 6 7o line 7, do you say that (AC + DC)^2 = AC^2 + AC*DC + DC^2 ?  Is there a 2 missing somewhere?

[c4757p]

Ah, yes! Thank you, I missed that.

It doesn't make a difference, though, since the integral of AC is zero and that whole term drops out, so don't worry about it.

Edited above.

[zapta]

Thanks cp. So the way to combine the DC level and the AC RMS is a geometric mean of the two. Makes sense. I plugged it in my example above and it gave the correct answer. Mystery solved ;-)

[mikes]

Everey meter should be able to measure the correct AC voltage, but to bad, that never was the reality. The meters that did this were called RMS meter or later under marketing pressure TRMS meters.

"True RMS" is not a marketing term, it's a feature. Many meters which claim simply "RMS" are only accurate for sine waves, and that's good enough for many uses. With a true RMS meter, the shape of the waveform doesn't matter, and that may be needed in some cases.

[Dave]

With a true RMS meter, the shape of the waveform doesn't matter, and that may be needed in some cases.

The waveform shape matters even with true RMS meters.
The key here is crest factor. If your meter has a poor crest factor, you may get incorrect readings with waveforms that have large, but short spikes.

[Robomeds]

Perhaps I'm wrong but I have assumed that RMS and True RMS were marketing terms for the same things.  IE they don't assume a sign wave when reporting AC voltage.  I think the cheap meter just rectify and average the AC wave and assume a scaling factor that results in the same value as the ideal true RMS value. 

My understanding of all RMS meters is they effectively integrate the voltage over time (either via heating or sampling or charging etc) and again report the voltage with out needing to assume a sinusoidal wave form.

Finally, there are the AC+DC RMS meters which add both the AC and DC wave forms just in case there is a DC offset.   

[PA4TIM]

Everey meter should be able to measure the correct AC voltage, but to bad, that never was the reality. The meters that did this were called RMS meter or later under marketing pressure TRMS meters.

"True RMS" is not a marketing term, it's a feature. Many meters which claim simply "RMS" are only accurate for sine waves, and that's good enough for many uses. With a true RMS meter, the shape of the waveform doesn't matter, and that may be needed in some cases.

The wave form does matter: crest factor

And it is a marketing term because AC volt is defined as RMS. So if a meter has a reading in  AC Volt, it is rms, there is no other way. If the volt has no extra like peak-peak, avarage, mean etc it is volt and so by nature rms.
An example: The HP3400 maual states it is a rms meter, this to differentiate it from meter that only have an ACV scale but measure f.i. avarage or peak. So that was a form of marketing (not in a negative way )

[mikes]

The waveform shape matters even with true RMS meters.
The key here is crest factor. If your meter has a poor crest factor, you may get incorrect readings with waveforms that have large, but short spikes.

If crest factor matters, then it's not true RMS.

[c4757p]

Sure it is. Even a true RMS meter will have a bandwidth, and anything approaching that will be measured incorrectly. That's like saying your DMM doesn't really measure voltage because it can't measure megavolts, or your spectrum analyzer doesn't really measure RF because it doesn't measure terahertz...

[macboy]

Everey meter should be able to measure the correct AC voltage, but to bad, that never was the reality. The meters that did this were called RMS meter or later under marketing pressure TRMS meters.

"True RMS" is not a marketing term, it's a feature. Many meters which claim simply "RMS" are only accurate for sine waves, and that's good enough for many uses. With a true RMS meter, the shape of the waveform doesn't matter, and that may be needed in some cases.

The wave form does matter: crest factor

And it is a marketing term because AC volt is defined as RMS. So if a meter has a reading in  AC Volt, it is rms, there is no other way. If the volt has no extra like peak-peak, avarage, mean etc it is volt and so by nature rms.
An example: The HP3400 maual states it is a rms meter, this to differentiate it from meter that only have an ACV scale but measure f.i. avarage or peak. So that was a form of marketing (not in a negative way )

You are neglecting the fact that cheap meters that are not "True RMS" are in fact average-responding (average of rectified voltage input), but calibrated to the RMS of a sine wave. So the displayed reading will be the correct RMS value for a pure sine, but way off for a triangle, saw-tooth, or most real-life waveforms.

[PA4TIM]

No, I'm not neglecting that. I wrote that before and that does not change it. AC Volt is always RMS if not stated that it is not. Just because people do not read manuals or manufacturers lie they invented the term  TRMS. Most cheap meters today are no meters, they are indocators. And that does not justify the fact that Vrms is double up. It is like saying 1 kilo kOhm, or . This is becoming a just as stupid discussion as audio people can have over RMS Power,  or writing VSWR as 1:1.5 instead off VSWR = 1.5, or Return Loss as -25dB instead of 25dB.  This are all double statements.

[nctnico]

To add to the confusion:
When measuring DC its custom to use the average value. All analogue DC panel meters will show the average value (current or voltage). Now it gets interesting when DC isn't DC but it consists of pulses. In that scenario any attempt to calculate the power will be wrong. So even when measuring DC (be it pulsating) you'd need a true RMS meter to be able to calculate the power dissipated in the load / drawn from a source.

I wouldn't rule out the cheap meters. Maybe in the old days those cut corners but my cheap VC8145 bench multimeter can show DC, AC or true RMS for pulsating currents and voltages.

[PA4TIM]

http://vicimeter.en.alibaba.com/product/518095781-212886966/VC8145_4_7_8_bench_digital_multimeter_DMM_80000_digit.html

Are you kidding, it only goes up to 50 kHz and no crestfactor given !. Even my old PM2505 does better as 50 kHz. (my Keitley 2000 was still accurate at 1 MHz !!!! Not that I care much, I rarely measure AC with a meter.

[zapta]

The RMS thing good be a good topic for an EEVBlog video. Explaining what it is, why we care about it (sometimes), and comparing average and TRMS meters with various signals shapes.

[KedasProbe]

If you want to see RMS values of different signals you can see them here:
The scope screen shows DC, RMS DC+AC and RMS AC  (assume -10mV DC is actually 0V)

[perkabrod]

Why does my Brymen BM257 multimeter read 2.5 V when I measure a 5V PWM signal at 50% duty cycle?
According to theory and simulation it should read 3.54 V

sqrt(0.5 * (5^2 + 0^2)) = 3.54 V

My meter reads 2.5 V both when dialed to AC and DC