power of a sine wave (electronics engineering)

priscared

This is obviously an electronics question.
In communication systems, to calculate the power of a sine wave, the formula below is used
Power (Sine Wave) = 1/2 * (peak amplitude)^2

This formula is apparently a standard electronics formula.
I'm trying to understand where it comes from. How is it possible to get a power figure from a voltage only? There is no information on period, current, or resistance. Can some one please help explain the logic behind this formula for me?

Maybe its a simple trick, to me they've probably simply integrated the sign wave, but the limits must cancel out... i Don't know.... help please..

Cheers
(

daviddoria

priscared, I'm pretty sure the definition makes the assumption of "1" unit of resistance - where the unit is whatever makes sense to produce the power units you choose. I've asked this question several times, and that is the only answer I've seen.

Freddy_Turnip

yeah... normalised with a 1 Ohm resistor.

gnurf

>> I'm trying to understand where it comes from.

It is derived from the Poynting vector.

>> How is it possible to get a power figure from a voltage only?

P = UI = U*(U/R) = U²/R

trambolin

Have you ever tried Fourier Transform of a pure sine?

daviddoria

what does that have to do with anything trambolin? I mean I know rayleighs equality... but we are wondering about the units here, right?

trambolin

I meant power of a infinite signal in terms of 2-norm, Plancherel, parseval etc. If everthing is normalized as you did for 1 ohm resistance... but anyway, nevermind, maybe you are right.

priscared

hmmm... indeed the poynting vector may have some relevance. But if some1 could point me to a meaningful explanation i would be impressed. I am assuming the assumptions is resistance = 1. And thats how the formula exists.

The rule almost seems like an anomaly, every1 uses it without thinking about its origin...

trambolin

Maybe you should use google wisely? I mentioned the Fourier Transform already... Does not tickle something at least?

http://cnx.org/content/m0062/latest/

priscared

" A signal's instantaneous power is
defined to be its square, as if it were a voltage or current passing through a 1 Ω resistor. "

THanks for the link

This rule is obviously just an arbitrary convention. It's obviously the definition of "instantaneous power".

BTw i can't see how this has anything to do with Fourier transforms.