Taken to be that by who (whom?)? I'm not being snide, I've just never seen (that I recall) the claim that the average voltage of a pure sine wave is anything other than zero (before the graphic that JoeJester posted, anyway). If I pass a signal through a low pass filter (of appropriately low cutoff frequency) I will see the average value of the waveform. If I pass a pure sine wave through such a filter I will see zero (or very nearly zero) at the output. I will NOT see 2/pi times the peak. A sine wave and a full-wave rectified sine wave are two fundamentally different waveforms.
My 'alerts' dont seem to work right for some reason so i am just now seeing this. Maybe they only show the most recent reply?
Not everything in science can be calculated using a straight forward calculation that works for everything. Many times the context of the calculation has to be taken into consideration so we know how to apply the formulas correctly. The average value of a sine wave is one of those times because there are at least two interpretations of what the average value is, and the correct interpretation depends on what we are actually using that calculation for (the context).
If we are standing in an empty parking lot and take two steps to the right, then two steps to the left, we are back to the same spot we started from. We can say we didnt accomplish anything, if the context is how far we got geographically. If the context is how far we actually walked, we might say that we walked a total of four steps. So the result is either 0 or 4 depending on what we wanted to know.
The more important thing is that when we walked, we did not do 'nothing', we did 'something', something that made a difference in SOME way. So it may be hard to say that we averaged zero of 'everything possible'. There must be something that we did do. If we say the average was zero then it looks like we did not do anything at all when clearly we did something like burn energy.
In the calculation of the average value of a sine wave, we can either average over one cycle or a half cycle.
If we wanted to know if there was any offset, we would average over an integer number of cycles and if there was any non zero result we know we have an offset, which may greatly affect the circuit that relies on a zero offset. But if we wanted to know how an average reading AC meter would respond, we would average over one half cycle, and we would get 2/pi times the peak value every time. This second interpretation could come from noting that area is really always positive, and we calculate the average from the positive area. This means when we take the average we get it from the area under the curve which even if it goes negative could be considered positive, but it's easier to just integrate over the positive half cycle.
So it's really the average of a perfectly rectified sine wave and comes out to 2/pi times the peak value.
The other interpretation is still valid however, that it is zero, but that is limited to applications that require that kind of averaging just as the second interpretation is limited to knowing the average value that WOULD result from a full wave rectified sine like what an AC average reading meter would read.
AC averaging meters would take the average as the absolute value of the sine, then use a built in constant to convert that average to the RMS value and display that on the face of the meter. That constant is the ratio of the RMS value to the average value that was actually measured and is approximately 1.11 and the reciprocal of that is the more familiar 0.9 (also approximate).
Another application would involve finding the average DC of a transformer and rectifier. We calculate the average of the absolute value of the sine, but then apply that knowledge directly as one of the properties of the sine itself rather than have to go through an explanation every time we do this kind of thing.
Interesting, i found a link on this site: