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.
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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 :)
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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.