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- What is The Formula for RMS Wattage?

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- Thread starter lgreen
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W= ( (Vp/sqrt(2)) * (Vp/sqrt(2)) )/ R

Example: Peak volage =42, assume the load is 8 ohms

RMS voltage = 42/ sqrt(2)= 42/1.4=30

W=(30*30)/3 = 112.5

This does not take into account losses the fact that if you are taking impedance rather than resistance, it often varies with frequency.

Yep, but Vp would be Vpp/2 and so 30V.W= ( (Vp/sqrt(2)) * (Vp/sqrt(2)) )/ R

-> P=56.6W

For square waves power would be the same as with DC voltages

and so P=((30V)^2)/8ohm=112.5W.

The "Vpeak/sqrt(2)" is the effective value of the sinusoidal wave. This sqrt(2) comes from a very "dirty" maths.... Some integrals are involved grrr

At square wave the effective valua is simply the duty cycle of the square wave.

which is the RMS value also.excuse me guys, but Vpeak/sqrt(2) is the effective value

The solution to the integral BTW is not that dirty.

For a sine wave, power is peak-to-peak squared divided by eight times resistance (that is, peak squared divided by twice resistance)

Which if you use my starting point of 42Vp comes out to 110.25. Virtually the same result.

I mention this not to be contentious but to keep the original poster from getting confused. We are really just manipulation Ohms Law and the definition of RMS to get the same result by a different sequence.

If you want more precision look at:

http://www.signaltransfer.freeuk.com/powerout.htm

The example I stated with will come out more like 100W in the real world.

60 volts sine peak to peak into 8 ohms is P=56.25Watts.So like 60 volts sine peak to peak into 8 ohms is ____ watts RMS? And 60 volts square peak to peak into 8 ohms is ___ watts?

60 volts square peak to peak into 8 ohms is P=112.5Watts.

Now that would be if you still don´t get it : 60V PEAK-PEAK.

That is not 60V rails and neither 60V peak.

I mention this not to be contentious but to keep the original poster from getting confused

Ok, this is getting confusing.

As for RMS, are not amplifiers rated to deliver so many watts per channel RMS???

When I say peak-to-peak, I mean it! 60 v peak-to-peak is the same as plus AND minus 30 volts, so on a scope at 10V/div, the wave would go up 3 div and down 3 div, for a total of 6 div. being occupied vertically by the wave on the screen.

lgreen said:.....As for RMS, are not amplifiers rated to deliver so many watts per channel RMS???...

"A serious and reliable measure of the power output of a loudspeaker or audio amplifier is average power, commonly called watts RMS. RMS stands for root mean square and is actually a

a squarewave puts out exactly twice as much power as a sinusoidal voltage if the squarewave bandwidth extends to infinity.

For reference the extra power of the square wave is all above the second harmonic which is why tweeters burn out in a clipping amp. So a 100w single frequency 1kHz signal into a two way passive speaker should put almost zero power into the tweeter but a similar drive voltage square wave will put 100w out at 1kHz and another 100w out at 3kHz and above (if perfect squarewave).

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- What is The Formula for RMS Wattage?