Jim Kelley wrote:

Roy Lewallen wrote:

In circuits involving purely sinusoidal V and I of the same frequency,
the power waveform is actually a true sinusoidal function, except with a
D.C. offset. It doesn't at all resemble the output from a full wave
rectifier. The D.C. offset is the average value, and the frequency of
the sine portion is twice the frequency of V or I.


Yes, thanks Roy. I've had absolute value circuits on the brain all this
week.

Nevertheless, instantaneous power is simply the instantaneous amplitude
at time t of the (sin^2(wt))/2 function.

73, ac6xg

Only if the voltage and current are in phase. Here's the more general
solution (cosines could be used instead with equal validity):

Given that v = V * sin(wt + phiv)
i = I * sin(wt + phii)

Then p = v * i = VI * sin(wt + phiv) * sin(wt + phii)

The product of the sines can be transformed via a simple trig identity
to give

p = VI * 1/2[cos(phiv - phii) - cos(2wt + phiv + phii)]

The first term in the brackets is D.C. -- it's time-independent. The
second term is a pure sine wave. So the result is a pure sine wave with
a D.C. offset.

I've described the meaning and significance of the power waveform in at
least one earlier posting on this newsgroup. If anyone is interested who
can't find it on Google, I'll look it up and post the subject and date.

Roy Lewallen, W7EL