[Lowfer] Epson Question

[John Davis]

Dick Cappels writes:
>Seems a little higher than I expected, but agrees with P=(E^2)/R.
>

Remember what Johan noted in his message:
>>> Although it may appear surprising, the Vpp of the fundamental
>>> frequency component is larger than the Vpp of the square wave itself :-)


This may seem a bit odd at first, but think back to drawings you have
probably seen of the phase relationship between the fundamental frequency
and the odd-order harmonics that make up a square wave.  Consider only the
first few harmonics for simplicity--say, the third and the fifth harmonics,
which at the proper amplitudes and phase relationships, add linearly with
the fundamental to produce a pretty good approximation of a square wave.
You can even include the seventh harmonic or higher if the don't clutter
things too much.

The odd order harmonics all cross the zero voltage line at the same time and
in the same direction as the fundamental, both on the positive-going side of
the square wave and the negative-going side.  But because they are odd
numbered multiples, at the very moment the fundamental sine wave is reaching
its maximum value in one direction, the harmonics are at that same moment
reaching their respective peak values in the OPPOSITE direction.  The
arithmetic sum (the peak value of the sine wave, minus the peak values of
the harmonics at that instance) is the peak value of the square wave, and is
thus LOWER than the peak amplitude of the fundamental-frequency sine wave
alone.

That was a very good fact to point out, Johan!  I had not thought of it, nor
the practical consequences, in many years.

John Davis