#94: RMS Voltage for Sine and square waves, and why your DMM might not work right!

This video discusses the meaning of RMS voltage, and runs through an example of sine waves illustrating the 0.707 "factor". Examples of AC square waves and digital PWM waves are also shown, along with cautions regarding the results obtained with DMMs, including True-RMS DMMs, which may not read the RMS values of digital waveforms correctly. Notes from the video can be found here:

[csimet]

You provide some of the best quick, simple explanations on these topics. While I knew about RMS measurements (both sine and square wave), I completely forgot about square wave DC offset and needed to verify that my two meters did not measure RMS voltage correctly. Great pointer!

[UncleDoug]

I am a new subscriber and love your videos, but I couldn't help but note a math error at 4:04. The square of 0.500 is 0.250, not 0.500 as written. I hate nit-picking, but this confused me (a little) the first time I watched the video and might have confused others. Again, thank you for your clear, concise explanations of complex topics.

[spelunkerd]

I thought your first video of this topic was excellent, but this one was even better. I watched the first video twice over, and got the message after thinking about it for a while. The video today was more logically and clearly presented -- you're a very good speaker.

[graemetait]

You refer several times to the 0.7071 factor which is the ratio of the RMS to peak value of a sine wave. However, in the comparison of the true RMS and non-true RMS meters on a square wave, what counts is the "form factor" of the waveforms, which is 1.111 for a sine wave, and 1 exactly for a square wave. Thus the non-true RMS meter (which is almost certainly responding to the average modulus of the waveform) reads high by a factor os 1.111, because it is calibrated to rad correctly for a sine wave.

[Jnglfvr]

Something not right at 6:02. If the non true-RMS meter is just assuming a factor of 0.707 (as if it were a sine wave) then it should be reading 0.707*1 volt = 0.707 V (on a 2 V peak to peak square wave) and not 1.113 volts. I just happened to do a series of tests just like this on my "true RMS" meter and on a 4 V peak to peak signal my meter read 1.394 V which is 2/sqrt(2). So my meter IS making the 0.707 assumption regardless of the shape of the waveform. The other things I discovered (as you mentioned) is that the meter gives identical readings whether or not there is an offset suggesting it is AC coupling the signal. Finally I found that at any frequency above about 1 kHz the readings become progressively more inaccurate. E.g., with a 4 V peak to peak sine wave at 1 K Hz meter reads 1.395 (2/sqrt(2)) but at 3 K Hz reads only 1 volt and at 5 k Hz reads a mere 0.268 volts. In all cases my oscilloscope calculates and displays the correct RMS voltage regardless of wave type, frequency or offset.

[MrTankera]

AWESOME Video!
Your simplistic approach makes me wonder why the RMS subject was not explained to me like that back in the days of my electronic classes...
Thanks a lot for verifying my reasons for spending the extra twenty dollars into the procurement of a True RMS DMM…Cheers!

[felixcat]

Some of the DMM's I've seen will give a voltage rating plus the duty cycle at the same time on the display. So if you are making a quick check of a chips output to see if its faulty it gives a better picture of what is happening in circuit without bringing out your scope.

[UncleDoug]

Again, sorry for the nit-picking. I really appreciate your videos. IMHO, no one does it better.

[anthem]

The square value written for your 150 degree increment is written as .500 vs .250 although i believe you summed it correctly.
Thanks for the great tutorials. 👍

[Jnglfvr]

You could have gotten the correct RMS voltages at 8:35 by switching the meters to DC mode. This would have correctly determined the DC offset. Your "true" RMS reading would then be sqrt(AC-RMS^2 + DC-RMS^2). It's a 2 step process for any DIMM that filters out the DC offset.

[schwinn]

@w2aew Thanks, once again, for these videos; This particular video helped to remind me that a True RMS meter (without the designation of True RMS AC + DC) would read incorrectly if a DC bias was applied to the signal - hope this makes sense.

[cny]

Awesomely lucid and clear presentation-as usual- Alan. Would love to see your take on PEP vs peak vs average input and output power in regards to amateur radio as the rules have changed over the years, in term of the various modulation modes and lastly how manufactures talk about these things. Seems like your discussion of RMS voltage could be a good entry point to what I see as a mildly confusing topic to new hams, generating debates on various forums tens of pages long! lol!

[adrianguyton]

Fantastic video, I really liked it.  However, I am a bit confused on the bit at 5:43. You said that "RMS voltage, on a square wave, is equal to the peak voltage for any duty cycle" and I was a bit surprised to hear that. Can you please explain why "for any duty cycle"?  Thanks. Regards.

[toddhardin]

Was going along with your notes - minor mistake at phase angle=150 degrees where the amplitude is .5V and the Vsquare corresponding reads .5V rather than .25V. With this correction the math comes out as it should.

*Supplemental: Clearly others have made the same comment and I neglected to show my appreciation for the video content, for which I thank you!

[TheCrazyStudent]

Ah, I see. That explains it. :) Thank you for taking the time to make all these videos. Your channel is truely a wonderful resource for anyone interested in electronics. And I have never really understood the concept of RMS voltage, so I was very happy to see a video from you on this topic. May I perhaps request a little follow up video where you deal with RMS for triangle waves and maybe even more complex waveforms as well?

[billwilliams]

Thank you for the help, I'm guessing GFCI have comparator circuits, a differential amplifier, phase lock loop to compare the hot and neutral currents? Normal Regular Circuit breakers don't compare the hot and neutral currents, they just trip at a certain threshold. I thought GFCI outlets were went only for connecting plugging in equipment like sterilzers machines, dishwashing machines, autoclave machines, etc that uses water, water tubes, electronic circuits boards because if the water gets on the circuit boards or on the AC wires the GFCI will trip or if you had your hand on the sink which is grounded and the units chassis was hot live chassis the GFCI will trip.

[rishabs]

Hi .. I just have a basic question. Why is everyone using the RMS ( which is a quadratic mean [ power of 2 ] ) ? Why not use a normal average ? I'm not quite convinced by the fact that because of the direction changes in AC voltage, the value will sum up to zero in a single cycle ( from 0:2*pi, say ), for an answer here. That's a theorotical answer. Practically, why not always take a Modulus(-ve value) and do a normal average. Since what we mean here is literally "voltage means work done", we can always ignore the -ve sign and flip the voltages which are below x-axis to the top of the x-axis and do a normal integral over the period of relevance. For a sine. this happens to be 2 square units from 0:pi  [ 1 square unit  ( 0 : pi/2  ) + 1 square unit ( pi/2 : pi )  ]. Converting the area of 2 from the sine curve to a rectangle, we get an amplitude of 0.6366 ( considering the rectangle width as pi ), which is infact the Vavg ( which is < Vrms ). This looks perfectly corrrect for me. In this case, why is Vrms preferred over Vavg ? Thanks !!

[NickMoore]

Very cool, I had a hard time explaining RMS to an apprentice a while ago, I'll have to get them to check out this video.

[DeeegerD]

Thanks again - watched this as a refresher as I just bought a Fluke 17B+ (non RMS) DMM.  You always add a bit more than I thought I knew (ie: duty cycles, etc...).  Now I feel better about spending a bundle on my other meter B&K Precision 393 (True RMS AC+DC).  Can never have too much info or too many meters :)  Just need to make sure you know what they can do!

[clems]

@5:30. This isn't clicking for some reason. The Vp =Vrms. How ?