RMS Power?


I often see power specifications like "100W RMS".  There is no such thing as RMS power.  Of course, you can calculate RMS value from any curve, including power curve, but it won't represent anything.  "Real" power representing heat dissipated in resistive load is "Average Power"   Pavg=Vrms*Irms.   In case of sinewaves Pavg=0.707Vpeak * 0.707Ipeak = 0.5Ppeak,  or Ppeak = 2Pavg. 

Term "RMS Power" or "watts RMS" is a mistake, very common in audio.
A4cbbf0f e24a 481b bac9 8318cf2147eekijanki
Post removed 
Nobody interested?  Really?
The term refers to the fact that if you are to calculate the output power, then the AC voltage used in the calculation must be RMS volts.

To do this, first find the peak to peak AC voltage that is the output of the amplifier into a known load such as 8 ohms (usually non-inductive).

Then divide by 2 to get the peak voltage. Then multiply by 0.707 to obtain the RMS voltage. Then perform the power formula on the result.
That’s true, but it is called average Power in every engineering textbook. Unit of watt already signifies power convertible to heat - a "real" power.

Pavg = 0.5Ppeak

Taking RMS of power curve would bring different, totally irrelevant result.

With sinewaves sin(x) for power would be squared sin^2(x)
|1. Square: (sin^2 (x))^2 = sin^4(x)
2. Mean: Integral of sin^4(x) over 0-pi is 3/8
3. Root: SQRT(3/8) = 0.61

Prms = 0.61Ppeak

This number does not represent anything useful.

Faulty term watts rms or rms power came most likely from around 1975 FTC standard for power rating. FTC realized, that they goofed up and 25 years later in 2000 they corrected it .
Here’s what Wiki thinks (it’s very long)
https://en.wikipedia.org/wiki/Talk%3AAudio_power

One line in the text ...
For most, just comparing the RMS power number is useful

I guess to some - But it’s been a while since I paid any attention to the RMS numbers on amps or speakers - I go to the store and audition. You can quickly tell if the amp has enough oooomph (or not)

I really think there are a lot more "pressing things" to get this worked up about - world peace, climate change, famine, disease, etc......

After all it’s just a number!
- It’s used by many in the audio business as " the norm"

And y’ain’t gonna change that any time soon!

If I remember correctly there was a moment a few years back, when some companies used Peak or Continuous power ratings, but it appears that things have reverted back to good old RMS!

But I would like to thank Kijanki for letting us know "watts" what
- or is that whats "Watt" :-)

Hmmm - I think I’ll elect to - NOT loose any sleep over it.

Just sayin !


Wiliewonka - whoever wrote this doesn’t understand it. There is no such thing as rms power. There is only one power that produces heat and it is average power. He says that in his opinion it should be integral over time period of the v(t)*i(t) , instead of Irms*Vrms, but he doesn’t realize that it is exactly the same.

For sinusoids:
Pavg=0.707Vpeak*0.707Ipeak=0.5VpeakIpeak=0.5Ppeak

but integrating over period of time:

Pavg= Vpeak*sin(x) * Ipeak*sin(x)= Ppeak*sin^2(x)
Integral of sin^2(x) over 0-pi is 0.5 hence Pavg=0.5Ppeak

It is called Average Power since it is an average of all instantaneous V*I.
If I remember correctly there was a moment in time when some companies used Peak or Continuous power ratings, but it appears that things have reverted back to RMS
Again - there is no such thing as RMS Power. There is a momentary power, average power, real power, reactive power, total power but no RMS power.




The reason for introducing Wrms has more to do with distortion measurements. At some point at least in the US, requirements for producting THD+N along with power and pre-heating requirements occured and this settled down. The Wrms came out of that.

For a while amplifier manufacturers could measure watts any damn way they wanted to, so some used the Vpk-pk as the source for the wattage measurements, and never mind the distortion at all.

So Wrms is more of a commercial standards thing than a purely electrical one, and implies that it is a sine wave with THD+n below rated.

Have fun arguing it though.

Best,

E
Erik, They could say Average Power - power equivalent to power produced by DC voltage of 0.707Vp.
There are no two different power values - average and rms as it is with voltage. There is only one power - Average Power.

I’m pretty sure that when you visit websites of all major amp makers like Pass Labs, Jeff Rowland etc - you won’t find terms "rms power" or "watts rms".

I don’t have big hopes for changing anybody’s mind on this forum (even FTC stayed ignorant for 25 years).

Wliliewonka - It is "watt" and not "Watt" (units start with small letter - but I’m sure you don’t care). You can go back to sleep now.
kijanki,
Even though I am completely ignorant on the subject, I can fully understand why the incorrect term bugs you. I'm glad that there are people like you around to make us aware of these things.
I'm expecting Almarg to jump into this any minute...
Faulty term watts rms or rms power came most likely from around 1975 FTC standard for power rating. FTC realized, that they goofed up and 25 years later in 2000 they corrected it .
http://www.n4lcd.com/RMS.pdf
I think Roy Lewallen explained it very well:
http://eznec.com/Amateur/RMS_Power.pdf
In his summary:
The equivalent heating power of a waveform is the average power.
The RMS power is different than the average power, and therefore isn’t the equivalent heating power. In fact, the RMS value of the power doesn’t represent anything useful.
The RMS values of voltage and current are useful because they can be used to calculate the average power.

Thank you roxy54.  Almarg is much better in explaining technical merits. I'm just trying to contribute something being grateful for all things I learn here.  
imhififan, Thank you for posting.  Example of the wrong average power calculation in the second article is very interesting.  Using averaged values of voltage and current produced error of 50%.  It is very common error.  People who design test and measurement equipment (often big companies) make this mistake all the time.  For instance, when calculating mechanical power, they take average (filtered) values of speed and torque and multiply them, instead of taking instantaneous values of both, multiply and average (filter) the product - mechanical power.  For constant torque and speed it does not make a difference, but as soon as oscillatory component appears error becomes significant.  Even single percent error is very important for efficiency calculation.  Of course it has nothing to do with audio, but shows that "Power" is a muddy subject.
Thanks for the nice words, Kijanki. But you’ve explained it well, IMO, as did the summary quoted above by Imhififan. And I of course agree with your point.

As you indicated, the references to RMS power or watts RMS that are often seen are actually references to average power, which are calculated as the product (multiplication) of RMS voltage and RMS current (assuming voltage and current are in phase with each other). And as you and the reference provided by Imhififan both said, RMS power is certainly something that can be calculated for a given power waveform, but it would be a different number than average power, and it would be a quantity that has no relevance or usefulness. While average power, being proportional to heat generation, is relevant and useful.


Widespread usage of incorrect terminology doesn’t make it correct. Just as widespread misuse of the English language doesn’t make it correct. For example, many people would say that they could care less about this topic, even though that is the opposite of what they mean :-)

Best regards,
-- Al


@almarg 

Widespread usage of incorrect terminology doesn’t make it correct. Just as widespread misuse of the English language doesn’t make it correct. For example, many people would say that they could care less about this topic, even though that is the opposite of what they mean :-)
IMO you have to be pragmatic about these things. The industry isn't going to shy away from 'RMS power' anytime soon. Its a 'charged term' that has a life of its own.

Other examples of charged terms:

'output impedance' is not the measure of the actual impedance of the output circuit, its the measure of the servo (feedback) gain of that circuit. Otherwise we would have a problem with Kirchoff's Law. Put another way, if adding loop negative feedback really lowered the output impedance of an amplifier, the result would be that the amp could make more power into lower impedances. But the fact is that the only way to do that is to add more output devices, more heatsinks (or bigger output transformers) and so on. But adding loop feedback definitely lowers output impedance! That is because 'output impedance' is a charged term.

'Conservative' (political term) refers to a person that will drive a Prius rather than a Ford Excursion, will work to protect the forest rather than log it, will work to reduce global warming etc, but most people think it means the opposite. 

(the latter is an example of how messed up our politics are that liberals are conservative and conservatives are liberal...)

We deal with charged terms that mean other than what we are saying all the time. Its part of what makes the human experience so fun :)
Post removed 

Output impedance term can be complex. Perhaps we should rate it in ohms RMS for clarity? :)



@kijanki -

Wliliewonka - It is "watt" and not "Watt" (units start with small letter - but I’m sure you don’t care). You can go back to sleep now.

Peace - I really have no quarrel with you.

Might I suggest that since you have so eloquently demonstrated the incorrect use of the term - that you try contacting at least one of the offending manufacturers and ask them why they still elect to use this invalid term.

"We" might all agree that it is incorrect. But it does no good to preach to the choir.

Perhaps some feedback from the industry could shed some light as to why they continue this practice?

Without it, the reasoning behind it's continued use is just conjecture.

Regards... 
Williwonka, Peace!  I'm sorry for the tone of my comments toward you.  
Changing industry might not be possible, but we can start with our forum.
@kijanki - all is OK! - I sort of asked for it :-)
When it comes to watts, there never seems to be enough to satisfy some, regardless of how it's measured.
Ultimately, if you can't stay in the same space with it, it ought to be enough.  Unless you're hooked on the smell of things starting to fry.  Then I'd suggest you might need a therapist instead of more wattage.

Just teasing,  but MHO...;)
In Radiography (x-ray), the characteristics of the beam are controlled by varying the kVp across the x-ray tube and the mA in the filament.
The actual dosage to the patient is really dependant on the mA and kV rms, as is the amount of contrast in the image; analogous to dynamic range in audio.
The kV rms varies greatly with the quality of the power supplied to the input of the transformer and even more with the form of rectification. Since the degree of rectification varies so greatly with various audio technologies from tubes to op amps to class D, maybe RMS is at least as meaningful as peak.

....or maybe radiography and audio have nothing in common and I'm full of s#!t. Happens all the time.
The kV rms varies greatly with the quality of the power supplied to the input of the transformer and even more with the form of rectification.
What is "quality of power"? Do you mean amount?
Is "form of rectification" - full wave or half wave?
Since the degree of rectification varies so greatly with various audio technologies from tubes to op amps to class D, maybe RMS is at least as meaningful as peak.
What is "degree of rectification" and how is it related to op-amps or class of the amplifier? RMS of power does not represent anything useful. Your kVrms * mArms is just power.
...or maybe radiography and audio have nothing in common and I’m full of s#!t.
You’re not. Asking questions is important.
While it's interesting that the term RMS power is a misnomer, it is at least consistent. We are still at least comparing apples to apples. I suspect that's all most consumers care about. As long as I know everyone is using the wrong term in the same way, knowing that one amp is rated at 25 wpc rms and another is rated at 80 wpc rms, that is providing me, the consumer, useful information. 
Zavato, amp is rated 80watt and marked 80watt rms by mistake.  In watt rms it would be 97.6 watt.  Vrms*Irms=Pavg  NOT Prms.

@kijanki  I often see power specifications like "100W RMS".  There is no such thing as RMS power.  Of course, you can calculate RMS value from any curve, including power curve, but it won't represent anything.  "Real" power representing heat dissipated in resistive load is "Average Power"   Pavg=Vrms*Irms.   In case of sinewaves Pavg=0.707Vpeak * 0.707Ipeak = 0.5Ppeak,  or Ppeak = 2Pavg.

Term "RMS Power" or "watts RMS" is a mistake, very common in audio.

Where is the mistake in RMS power?

RMS is a measurement that allows one to determine the peak value of a sine wave that will produce the same heating in a resistive load as a DC voltage. So if run a heater or incandecent bulb off 120 DC or 120 RMS AC the heat and light will be the same. The peak voltage of that sine wave will be 1.414 X 120 about 170 volts. By the way the average of a 170 volt sine wave is 0.637 X 170 or 108 volts. This is all well documented and accepted. 

What is it you are going on about anyway? I make 100 Watt amplifiers and I know how to measure them.They produce 28.28 Volts RMS into a 8 ohm load. 

Perhaps you missed the fact that at the peak the instaneous power is very large and not related to the average voltage.
Hi Roger,

To use your example of 28.28 volts RMS into 8 ohms, corresponding to 100 watts, the corresponding RMS current is 28.28/8 = 3.54 amps.

Assuming a sine wave, the peak voltage is 28.28 x 1.414 = about 40 volts.

The corresponding peak current is 3.54 x 1.414 = 40/8 = about 5 amps.

The corresponding instantaneous peak power is 40 x 5 = 200 watts.

What Kijanki is saying is that the term "RMS power," if strictly interpreted, would imply 200 watts peak x 0.707 = 141.4 watts RMS. But of course what is really being referred to when that term is used is the product of RMS voltage and RMS current, which as you indicated is 100 watts in this example.

So the widespread use of the term "RMS power" is, strictly speaking, a misnomer. That is Kijanki’s point, with which I agree.

Regards,
-- Al
@almarg Hi Roger,

To use your example of 28.28 volts RMS into 8 ohms, corresponding to 100 watts, the corresponding RMS current is 28.28/8 = 3.54 amps.

Assuming a sine wave, the peak voltage is 28.28 x 1.414 = about 40 volts.

The corresponding peak current is 3.54 x 1.414 = 40/8 = about 5 amps.

The corresponding instantaneous peak power is 40 x 5 = 200 watts.

What Kijanki is saying is that the term "RMS power," if strictly interpreted, would imply 200 watts peak x 0.707 = 141.4 watts RMS. But of course what is really being referred to when that term is used is the product of RMS voltage and RMS current, which as you indicated is 100 watts in this example

So the widespread use of the term "RMS power" is, strictly speaking, a misnomer. That is Kijanki’s point, with which I agree.

Your first calculations in getting the peak voltage, current and power are indeed correct.

200 watts is the peak power however 100 watts is the RMS power. Thanks for not using the word average which does not apply. I will explain another way.

Kijanki needs a math lesson. 0.707 is the proper factor for the voltage and the current as you have demonstrated. One must however use that factor for both voltage and current. If you want to apply it to the already calculated peak power one must multiply that by 0.707 x 0.707=0.5 Correct?

Thus RMS power is 0.5 x peak power. It is incorrect to multiply power by 0.707 just once. One has to do it twice

If you read the OP’s last line he actually got it the 0.5 right but he called it average. I really dont see what he is going on about. A power amp behaves just like the power supplied to your home. You can use a power amps to run motors at various speeds and all sorts of things. This is basic electronics..
From Wikipedia "Audio Power"

As described above, the term average power refers to the average value of the instantaneous power waveform over time. As this is typically derived from the root mean square (RMS) of the sine wave voltage,[6] it is often referred to as "RMS power" or "watts RMS", but this is incorrect: it is not the RMS value of the power waveform (which would be a larger, but meaningless, number).[7][8][9][10] (The erroneous term "watts RMS" is actually used in CE regulations.[11]) This is also referred to as the nominal value, there being a regulatory requirement to use it.

Al, leave it (he is not going to get it).
Hi Roger,

All of us, certainly including Kijanki who is very knowledgeable technically, completely understand and are in complete agreement about the technical aspects of what is being discussed, i.e., the "basic electronics" and the math you referred to.

What he is going on about is simply the terminology that is being used.

And his point is that strictly speaking what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time. Which would be 141.4 watts in your example, while of course 100 watts (the product of RMS voltage and RMS current) is what is actually being referred to when that phrase is used.

Regards,
-- Al
@kijanki  Al, leave it (he is not going to get it).

Thats really rude, however

Would you please be so kind as to supply a link to what you want me to read, there are several articles on Wicki. 

OH, dont worry, I will get it or apologize for not getting it. 
@almarg  And his point is that strictly speaking what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time. Which would be 141.4 watts in your example, while of course 100 watts (the product of RMS voltage and RMS current) is what is actually being referred to when that phrase is used.


First when someone starts an OP with "there is no such thing as RMS power" whats that mean?

RMS Power doesn't vary as a function of time, instaneous power does. 

Im still waiting for the link to Wickipedia. Do you have it. Im just on pins and needles here.
Hi Roger,

I found the Wikipedia page from which Kijanki quoted (the link opens near the paragraph he quoted):

https://en.wikipedia.org/wiki/Audio_power#Continuous_power_and_%22RMS_power%22

RMS Power doesn’t vary as a function of time, instaneous power does.

To be sure it’s clear, I absolutely did not say that "RMS power" varies as a function of time, although I can see how my statement might have been misread. I said that...

... what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time.

(The "waveform defines how power varies as a function of time"; the RMS value of that waveform of course does not define how power varies as a function of time).

Again, what Kijanki has been addressing is terminology, nothing more.

Regards,
-- Al
@kijanki @almarg

Like to make it hard done you. I looked at all the references listed in the Wicki article. They can easily be clicked on above.

Half of them are referring to average power as a speaker sees it so as not to overheat the voice coil. That is indeed time averaged and all is well there.

However a speaker is not an amplifier. If you are betting on reference #8 being valid I will take $100 on that bet. Its pure fiction. http://www.hifi-writer.com/he/misc/rmspower.htm

Besides the admission at the top Most of what follows is an edited version of an email sent to me in April 2003 by the editor of Australian HI-FI. It was so well expressed I want to see it published, somewhere. So here it is.

Unfortunately the precise authorship has been lost due to rigorous cleaning of computer archives and trashed hard disks. I am told that much of it was probably from ’an electronics professor at Uni of NSW’, originally written as a letter to The Guide, an insert into The Age newspaper. Should the lost electronics professor seek to claim authorship (or even banish his words from this site), I would plead with him or her to email me at scdawson (at) hifi-writer.com.

Do you agree with this statement... By contrast, RMS (root mean square) power, would have to be defined as the square root of the time average of the square of the instantaneous power, since this is what ’RMS’ means.

FIrst thing wrong with that sentence is that if you take the square root of something you squared you get the same thing back. And what is the square of the instantenous power anyway.

Could a math major please come help us out. This is getting no where.

Though I love and contribute often to Wickipedia this article needs a lot of help. Did you not read the banner at the top of the article..


This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)This article may require cleanup to meet Wikipedia’s quality standards. (June 2011)This article possibly contains original research. (October 2008)


Please read this also. https://en.wikipedia.org/wiki/Talk:Audio_power

This is a "start class" article, please read the following https://en.wikipedia.org/wiki/Wikipedia:Content_assessment

Evidently you guys have not vetted this article at all. Heres another complaint I found on the talk page..   


 One thing this article does poorly is differentiate between speaker and amp ratings. Both are given "RMS" and "PMPO" ratings, but the conditions are different. The peak power of an amps is directly limited by their voltage rails and the minimum impedance of the loudspeaker. It is impossible to have a higher peak instantaneous power than this (unless due to reactance?) But for loudspeakers, the peak instantaneous power is not as clearly defined, and has to do with destruction of the speaker. — Omegatron04:48, 25 October 2007 (UTC)

Hi Roger,

I haven't read any of the Wikipedia article besides the paragraph Kijanki quoted in his post, and I don't consider whatever flaws the article may have to be relevant to Kijanki's point about terminology, especially given the further explanations of his point that I have provided.

I provided a link to the article simply because you requested it, and I was able to find it quickly.

Regards,
-- Al 
@almarg 
To be sure it’s clear, I absolutely did not say that "RMS power" varies as a function of time, although I can see how my statement might have been misread. I said that...

... what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time.

(The "waveform defines how power varies as a function of time"; the RMS value of that waveform of course does not define how power varies as a function of time).


The paragraph above appears to me contradictory. First you say the waveform defines how power varies as a function of time. That would be instaneous power or instaneous heating, agreed? The RMS also defines how power varies as a function of time and defines its DC heating value. We needed that when Tesla won the "war of the currents" over Edison. How else were we to specify the voltage of the required sine wave.

As to the WIckipedia article i did find it and its many flaws. If you have the time, rather than defend kijanki do some reading yourself. There are 18 complaints about this article on the talk page of which 13 and 14 pretty much kill the whole thing. If kijanki learned this from articles like this then he is in the same mistaken camp. Shall we leave him there?

Would you care to tell me why an amplifier producing 100 watts RMS is any different than an AC generator producing 100 watts RMS. We are talking about sine waves here, that is all. 
 
And then please where 141 watts comes from. What kind of inbetween power is that to be called?
@kijanki . FWIW some respected manufacturers quote power output as for example 200 watts RMS. I am with atmosphere - the term is used,usefully, in the trade, for amplifiers. This is not hard for you to verify. Interesting post thanks. 
That would be instaneous power or instaneous heating, agreed?

Yes.

The RMS ... defines its DC heating value.

Yes.

The RMS also defines how power varies as a function of time ...

Well, if the waveshape is known, for example if it is known to be a sine wave, then of course one can determine the amplitude of that waveform from the RMS value. But I don’t see how my statement that you were referring to is contradictory, as you claimed. My statement, once again, being as follows:

... what the words "RMS power" literally mean is the RMS value of a waveform that defines how power varies as a function of time.

Honestly, I think you may be misreading my statement.

Would you care to tell me why an amplifier producing 100 watts RMS is any different than an AC generator producing 100 watts RMS.

The 100 watts is the same in both cases, of course. I have never said anything that is in any way to the contrary, and as far as I can recall neither has Kijanki.


And then please where 141 watts comes from. What kind of inbetween power is that to be called?

As I have said, it is the RMS value of a sinusoidal power waveform having a peak value of 200 watts.

There are 18 complaints about this article on the talk page of which 13 and 14 pretty much kill the whole thing. If kijanki learned this from articles like this then he is in the same mistaken camp. Shall we leave him there?

The fact that the article has numerous flaws has nothing to do with the subject matter of this thread. And Kijanki is a very experienced engineer who doesn’t need any such help.


I have nothing further to say on this matter.


Regards,
-- Al

@almarg 
And then please where 141 watts comes from. What kind of inbetween power is that to be called?

As I have said, it is the RMS value of a sinusoidal power waveform having a peak value of 200 watts.


Well its not. We have agreed that a 100 watt RMS amplifier supplies 40 volts peak into an 8 ohm load. 40 x 40 / 8 = 200 last time i checked. 

As Monty Python says... say no more, say no more.
Post removed 
Al, I was right (he is not going to get it). RMS value of ANY sinusoidal waveform, having peak at 200 (of any unit) is 141 (of the same unit). 100W would be an average power value corresponding to VrmsxIrms and equal to half of peak power for sinewave (and equivalent to amount of DC power producing the same amount of heat). Guys, please, this is EE101.

@kijanki Al, I was right (he is not going to get it). RMS value of ANY sinusoidal waveform, having peak at 200 (of any unit) is 141 (of the same unit). 100W would be an average power value corresponding to VrmsxIrms and equal to half of peak power for sinewave (and equivalent to amount of DC power producing the same amount of heat). Guys, please, this is EE101.

Lets be a little careful here for those trying to understand this conversation. "RMS value of ANY sinusoidal waveform, having peak at 200 (of any unit) is 141 (of the same unit). Does that apply to watts? Are 200 peak watts the same heating value as 141 watts. They are the same units? I know you dont think so but one could easily interpret any to mean any. Granted going on its fine. Whats all this about average power? Whats the definition. I saw you 3 step calculus but, sorry I dont get it and I did fine in Calculus.

Yes RMS power is half the peak power, but you call it average power without informing us what average power is to you.  Al, who you appear to agree with. thinks 141 watts is the average power of 200 watts peak. He has said so. Still what is this average power? We are talking about a sine wave going on and on. 

Average power as used by most in audio means the average over a long time, playing music and not letting the voice coil get too hot. This is the definition I find most often for average power. I dont see how it applies to amplifiers except for the heat sinking.

RMS power is continuous sine wave in this discussion. Why say it is wrong. Whats wrong with it?

Come on kijanki, lets get this ironed out for everyone else who by now doesnt know what we are talking about. It is important. The early replies to you OP had no idea what to say.

I do think we agree yet use of the term average to describe heating is generally used as RMS. Do you really want to say this. " Prms = 0.61Ppeak "? not 0.5 . P rms= V rms x I rms. does it not. is so .7 x .7 =.5

I am writing a paper on how the FTC got involved, its not the way most people think and its not bad.


Al, who you appear to agree with. thinks 141 watts is the average power of 200 watts peak. He has said so.

No, I have not said that. I have said that 141 watts is the RMS value of a sinusoidal power waveform having a peak of 200 watts. "RMS" in the sense of a mathematically calculated root-mean-square. And in saying that I certainly recognize that the heating which occurs in that example corresponds to 100 watts, not to 141 watts.

On the other hand, though, in citing the 141 watt figure I overlooked the fact that the product of a sinusoidal voltage and a sinusoidal current is not sinusoidal, since it never goes negative in the case of a resistive load. And correspondingly positive power is being delivered to the load at all times, other than at the zero crossings. So I believe the 141 watt figure should be, per one of Kijanki’s posts early in the thread, 0.61 x 200 = 122 watts.

Also, Roger, a **much** better paper on the subject than the Wikipedia writeup Kijanki referred to is the one Imhififan linked to in a post early in the thread:

http://eznec.com/Amateur/RMS_Power.pdf

That author’s conclusions:

It should be noted that the term “RMS power” is (mis)used in the consumer audio industry. In that context, it means the average power when reproducing a single tone, but it’s not actually the RMS value of the power.

Summary:

I’ve shown that:

-- The equivalent heating power of a waveform is the average power.

-- The RMS power is different than the average power, and therefore isn’t the equivalent heating power. In fact, the RMS value of the power doesn’t represent anything useful.


--The RMS values of voltage and current are useful because they can be used to calculate the average power.

Imhififan also provided the following reference early in the thread, which again is highly supportive of Kijanki’s position:

http://www.n4lcd.com/RMS.pdf

In any event, I agree with PTSS that Ralph’s (Atmasphere’s) advocacy of a pragmatic outlook on this issue (see his post dated 6-30-2017) is well stated and appropriate. But in going forward on that basis it seems to me that at the very least we should also acknowledge the legitimacy of Kijanki’s point, that based on a strict interpretation "RMS power" does not equal the product of RMS voltage and RMS current, and therefore does not correspond to the heating effect of a given amount of power.

Regards,
-- Al
@kijanki @almarg That author’s conclusions:

It should be noted that the term “RMS power” is (mis)used in the consumer audio industry. In that context, it means the average power when reproducing a single tone, but it’s not actually the RMS value of the power.

Summary:

I’ve shown that:

-- The equivalent heating power of a waveform is the average power.

-- The RMS power is different than the average power, and therefore isn’t the equivalent heating power. In fact, the RMS value of the power doesn’t represent anything useful.


--The RMS values of voltage and current are useful because they can be used to calculate the average power.


Why do you quote a paper that is all about square waves when we are talking about sine waves? This is most unscientific.

http://eznec.com/Amateur/RMS_Power.pdf

I encourage readers, if there are any left over this foolishness, to note all the waves in the picture are square waves. The value of Vp= 1.41 x Vrms applies to sine waves only. Not to square waves where the average is 0.5 and so is the RMS.

In this amateur, by its own name, paper, which is highly flawed. In the first step he aready has the average, is correct and done. However he wants to prove something odd. So he applies 1.414 to the already correct answer and gets a new answer which is incorrect.

If one stops for a moment and looks at a square wave with at flat top the average and the DC value are both 1/2 the peak. Just cut the wave in half and fill in the hole. Then you get a straight DC line. No problem. But with a sine wave as the voltage peaks and current peaks there is a lot of energy at the top. The use of root 2 or 1/ root 2 ONLY APPLIES TO SINE WAVES, not triangular, not square, not you mothers fancy stiching.

TRUE RMS meters actually measure the heating value of nonperodic waves and can even tell you the RMS or heating value of music. That heating value is important to your woofer.

So far the author has supported his position with a flawed page from Wickipedia (flawed in their estimation also) and this paper on square waves. There is no point in going further with this.

Stating there is no such thing as RMS power is a bold statemtent that has uncountable support for the fact that RMS is real, useful and applies to amplifiers.

I did find today a mistake in the authors early math and will present the correct math, I dont know why this author wants to press this most unreasonable theory.

As to the authors commment Al (he wont get it) and( he didnt get it.) Rudely said but true. I dont get what you said and I dont know what engineer would.

http://www.n4lcd.com/RMS.pdf

This is interesting and if all we are actually arguing about is the term "RMS" then we have made a mess of things. Putting the term "RMS" in front of watts is a misnomer. Once you have watts you just have watts. There are no other kind of watts for continuous waves so AVERAGE watts does not apply either. Its just WATTS, AC, DC, any periodic constant value. The RMS I believe is to show that the watts were measured by RMS methods, not peak or peak to peak methods. 

Perhaps we have argued over nothing but 3 letters of the alphabet, however the OP has cited papers that are incorrect and certainly have muddied the water. Heres you out guys:)

We still have to agree on one thing. The heating watts of a 100 watt amplifier is 100 watts. It is measured by V rms sq/R load.

The Peak watts is 200 and there are no other meaningful numbers to be stated. Using RMS to mean  'Hey anything with RMS in front of it gets to be multiplied by 1.4"... is a no no.

Average watts is generally applied to a signal that is non constant and thus an average is needed. Average is not appplicable to measuring sine waves for power. In fact the average squared comes up low. 
@imhififan https://en.wikipedia.org/wiki/Root_mean_square

Thanks, this is most interesting. I note that the coefficient (mulitplier) for peak to peak is 2.8 for the sine, 3.5 for the sawtooth and 1.0 for the square. (divide those numbers in half for the peak, of course) Those are all RMS. So readers might like to know there is not just one RMS in this world. It depends on the waveform. Sines are the best because we have equipment to null out the fundamental and then we can measure and SEE the distortion products on a scope.

Do you have a comment to add to our lovely conversation? 

Recently I have come to the possibiity that the OP decided to apply RMS to power, which I cant imagine anyone doing. There is no RMS of power nor is there average of constant power it is just power. Power determined by RMS voltage. We dont RMS it again. Why go on to use mathmatical arguments to prove or disprove a simple misuse of terms. Thats just grandstanding.

If we want to be perfectly clear we should say:

100 Watts (measured by RMS voltage of an undistorted sinewave into a resistive load) .Then then there is no abiguity. Thats all he had to say!

At first no one was interested, look at 2nd post. They Ralph properly answered how its done. Then the OP objected to Ralphs answer which happend to be exactly how we do it. Though most of us read it off the Sound Tech which has a watts scale. Just Watts, my hands are steady, the meter is steady, the ship is on course, there is nothing to average.

The OP states that the word "average" is appied in ’every textbook". Every is a dangerous word. But im gonna look at a few I have here.
Ramtubes 12-10-2018:
We still have to agree on one thing. The heating watts of a 100 watt amplifier is 100 watts. It is measured by V rms sq/R load.

Yes, of course. As I said earlier:

Almarg 12-10-2018:
I certainly recognize that the heating which occurs in that example corresponds to 100 watts, not to 141 watts.


Ramtubes 12-10-2018:
There is no RMS of power.... Power determined by RMS voltage. We dont RMS it again....

... If we want to be perfectly clear we should say:

100 Watts (measured by RMS voltage of an undistorted sinewave into a resistive load) .Then then there is no abiguity....

Agreed.

Imhififan, thanks for providing the additional link.

Regards,
-- Al
@almarg  Imhififan, thanks for providing the additional link
.

Al,

First please accept my sincere apology for anything I may has said to cause you offence. This has been a muddy thread, made worse by unvetted quotes from poor sources. These I have already cited. 
The OP pulled much of his argument from this self contradictory paper. And the flawed references in the Wickipedia article Audio Power.

http://www.n4lcd.com/RMS.pdf

"The FTC also incorrectly assumed that the measurement of the power in Watts would be RMS Watts. It's not. It's Watts. There's no such thing as RMS Watts. In summary, RMS Voltage is correct, but there's no such thing as RMS Power or RMS Watts. Or stated differently, the Voltage that's measured is RMS Voltage, but the resulting power is Average Power and it's measured in Watts."

Focusing on the wrong of putting RMS in front of Power and then the word Average the horse took off a running.  I dont for a moment believe that the FTC meant to apply any form of root 2 to the aready calculated watts. The were actually trying to get away from Peak watts and Peak to Peak watts which were inflating numbers. 

Perhaps if they has said Watts (RMS) or more correcty Watts measured by the RMS vaue of a sine wave all would well. 

Had the OP simply objected to the language instead of coming back with math (some of which is incorrect) we would have been done with the first post by Atmasphere, thanks Raph. However Ralph was ignored.

I had my Chinese math guy check the integral also. The answer is 3/8 pi not 3/8, working that out the root the answer is 1.08 as I recall. I dont really care whose math is right or wrong, my question is why throw that out at all? Who on this thread is likely to be a math major? The OP fired all his ammo and I think he's out on this.  

As to kijanki we are still in a tussle about emitter resistors and losses in amplifiers. I wish we were sitting around a table drinking and having more fun with this. These topics are interesting to discuss, we all learn from those who can best express their ideas calmly and rationally.    

I would like to have Imhififan at the table. I have enjoyed how he said little but kept coming back a source that cleared it up for me. 

I was doing repairs in a HI FI store when the FTC rule came around. It uas designed to stop the inflation of power into Peak Watts and Peak to Peak watts (which dont exist). I am writing a paper on the history of that which I hope will extend and clairfy what the FTC was trying to do. In my reasearched no one ever RMSed the Watts in any literature. They used RMS to differentiate real Watts from POP (Peak Output Power) and PPOP (Peak to Peak Output Power)

We are all sorry they decided to put RMS in front of watts.I think they has to put something. But I never assumed the meant to RMS the watts. Who would?


Thanks for the gracious post, Roger.

I wish we were sitting around a table drinking and having more fun with this. These topics are interesting to discuss, we all learn from those who can best express their ideas calmly and rationally.  

I would like to have Imhififan at the table. I have enjoyed how he said little but kept coming back a source that cleared it up for me.

 +1. 

And regarding Imhififan's posts, I've participated in quite a few threads to which he has contributed, many involving technical matters, and as far as I can recall every one of his posts has been spot on.

And yes, it would be fun to kick these things around while "hoisting a few," as the saying goes.  And if I weren't on the opposite coast I would certainly be tempted to attend some of your presentations.

Best regards,
-- Al 
Thanks for the nice words, Roger and Al.