What is RMS Watts? Understanding AC Signals & DC Conversion

[echoSwe]

Root mean square. The square root of the sum of the squares of a set of quantities divided by the total number of quantities. Used when monitoring ac (alternating current) signals. Many power supplies, for example, issue an ac signal. This needs to be converted to a dc (direct current) signal for the PC interface. The solution is a signal conditioning input that produces a dc signal proportional to the rms of the amplitude of the input signal. The rms operation means the reading will always be positive.

according to google's dictionary.
By my understanding it's a measure of n values squared, added, divided by n, then root-ed. It's some kind of measure of performance peaks over a long period of time. It can be used in physics, statistics and electronics such as audio and loudspeakers.
http://en.wikipedia.org/wiki/Root_mean_square
In the area of audio it's not 'really' called RMS Watts, but 'average sine wave power' according to
http://www.hifi-writer.com/he/misc/rmspower.htm.

Also there is something called 'mean heating power' when referring to DC, when 'mean power in watts' is used when talking about AC.
DC is produced by the computer if I'm not totally mistaken, so does this mean that you have to calculate how the output power in watts (or amps??) from the sound card is used up by the speakers?

Is the AC from the wall socket transformed to DC via the computer's power supply? Is the CPU creating its own Hz - its own ups and down of volt?

Just to get it all right... Watts = Volts * I (Current)
and when the electrical current follows a sine wave (AC) it's the voltage that goes up and down (plus to minus and back)?

So... given the voltage output and amps output at every given instant received from the sound-card in the computer, we can calculate W? Taking all those aggregated/summed (enigma sign...) watts, squaring them, (and adding via the enigma), then multiplying all that by n^-1, given that n is the total amounts of measurements, gives us RMS watts? Or is it, as the hi-fi writer state, the average sine wave power we get then?

However, since power is measured in watts ----? What's the difference?

Thanks for reading all my thoughts and even more thanks for any responses!

 

[Clausius2]

I don't really know where is your doubt. Anyway,

$$P_{rms}=\sqrt{\frac{1}{T}\int_0^T P^2(t)dt}$$

I think that's the RMS value of the power. Yes, is simply a "mean" value, but in fact is different of the real mean value. If the power consumption is senoidal the mean value is 0. If you employ the above formula, you will realize that RMS value is not zero, but something similar to a positive mean value, like the average normalized area under the function.

Sorry If I am being a bit diffuse.

EDIT: all wattmeters give you the RMS value.

 

[echoSwe]

My doubt is within if I'm correct in all of my writing... And also those questions in the end of my first post...

I'm a newbie at integrals, so what exactly does that mean? Is T the time and t the?
Also P^2 - is that the power consumption (or J/s) - i.e. V*I? Or is it the peak power consumption?
How does all this really relate to the real sound - is it because it's a mean that it's interesting?

How is your formula different from this one?
http://en.wikipedia.org/math/f5aa461659eb1abe11c75b9a7e86455a.png

 

[Clausius2]

My doubt is within if I'm correct in all of my writing... And also those questions in the end of my first post...

I'm a newbie at integrals, so what exactly does that mean? Is T the time and t the?
Also P^2 - is that the power consumption (or J/s) - i.e. V*I? Or is it the peak power consumption?
How does all this really relate to the real sound - is it because it's a mean that it's interesting?

How is your formula different from this one?
http://en.wikipedia.org/math/f5aa461659eb1abe11c75b9a7e86455a.png

When you are measuring an oscillating signal (for instance the power P (Watts), it has a period T.

P(t) is the instantaneous power consumption. For example, P(t)=Asin(wt) could be a sinusoidal signal and would be found in some AC circuits. You should realize mean value of P(t) is zero. But RMS value of P(t) is non zero. In fact, P_RMS is the square root of the average value of the area under the square signal over a period T. Check my formula and realize it is the same formula that web says. Substitute T by N and the summatory by the integral sign.

This value is very interesting for electrical engineering. For instance, when measuring the voltage, people would want to know the wave amplitude (it's the most significant figure). Instead of it, all the experimental instruments like voltimeters, amperimeters, wattimeters and so on measure RMS values due to their internal configuration. The RMS value is a bit smaller than the amplitude value, but it gives us an idea about how large is the peak of the wave.

 

[echoSwe]

I actually think I got it now :) Thanks for the help!
It's very interesting indeed. Would it be possible to find some examples to work with just to get some figures into it?
Can RMS watts be used to anything else than giving a good average?
Can RMS output watts be related to dB?
Is there anything more to learn about this?

 

[Dissident Dan]

Also, RMS is exactly half of the peak Wattage.