RMS Power?

@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?