Hi PhysicsProf,
That is an interesting thing, but what is missing is the average phase angle which could be determined in post by the following:
Mean Power / (Vrms * Irms) = Cos(θ) or θ = InvCos(Mean Power / (Vrms * Irms).
Pavg = Vrms * Irms * Cos (θ) (the formula in my prior post is for purely resistive circuits only where θ = 0)
So for POUTmean = 61.62 mVV (or mW) we get θ = InvCos(0.06162 / (2.92 * 0.0315)) = 47.69° And for PINmean = 106.2 mVV (or mW) we get θ = InvCos(0.1062 / (1.43 * .110)) = 47.53°
So there is some phase differential between the input and the output by about 0.16°. If the scope were able to give you this average phase angle, then you would have arrived at the same values as the mean. I would like to point out that these are 'effective' phase angles that allow us to treat the signal as a sinusoid in these calculations. The more complex the waveform, the more difficult it is to process in this way.
But looking at the actual factors involved, we see that Cos(47.69) is 0.673 and Cos(47.53) is 0.675 so the differential of 0.675 / 0.673 is .0029 away from 1 and this falls below your 2 digit rounding. So essentially excluding your phase angle in this case was the same as having a factor of 1.
I think that is why it came so close to being the same thing.
Something I wanted to try, and did not get a chance yet, was to compare Lawrence's index differences to actual average power differences. In other words, if Lawrence was doing the math wrong, he was doing it wrong for both the input and the output so both were inflated or deflated by the same algorithm and that may mean that the ratios held. Just a thought. Also, do you know if his scopes output any data? If he has the raw data then we could have a look at that and see what it shows.
Harvey
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