RMS Power?

@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