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[teslaalset]

@teslaalset,

That's very interesting. Think about it, the method from the theoretical writeup also uses in effect the last and the first point, that is, uses a brute force approach. However, when you get into the nitty-gritty the result changes even in the theoretical calculations. How can this be?

I see it like this:
Performing the mathematical integrals one gets two results that needs subtraction (upper time limit results - lower time limit results).
Compare that with using a stopwatch:
press start at the lower time limit, sampling the consumed power; press again at the upper time limit and sample consumed power again, then subtract both results.
The intermediate results are not of any interest.
With the 'slope' function of Excel, the intermediate slope values are also involved.

[Omnibus]

do a google search with :
"Synthesis of Passive RC Networks with Gains Greater than Unity"

there is so much overunity !

What about that Google search?

[Omnibus]

I see it like this:
Performing the mathematical integrals one gets two results that needs subtraction (upper time limit results - lower time limit results).
Compare that with using a stopwatch:
press start at the lower time limit, sampling the consumed power; press again at the upper time limit and sample consumed power again, then subtract both results.
The intermediate results are not of any interest.
With the 'slope' function of Excel, the intermediate slope values are also involved.

I agree but what you gain and lose along the way should be reflected in the final outcome. It appears it isn't in our case.

[Omnibus]

Regarding the experiments -- if we're really sure that what we measure as current and voltage is really the current and voltage (not only in magnitude but also in phase) in the circuit then we're there. Now, current having been taken care of (resistance R too) the only remaining culprit can be the voltage and the influence of the device which measures it. The passive voltage probe I'm using in 1X mode has an input impedance of approx. 1MOhm and less than 50ns rise time but it also has 110pF capacitance. I've checked and determined its presence does not affect the current measured by the current probe. However, when switching from 1X to 10X I saw a slight change in phase shift on the order of 40ns. Also, the peak to peak voltage did undergo slight change -- from 31.4ppV with 1X setting to 31.8ppV at 10X. I did the Pot/Pin measurement with the voltage probe now being at 10X and I got severe underunity -- on the order of 0.1 and less. As you can see in the theoretical model such underunity can be achieved by slightly changing the phase angle, everything else the same. As if we didn't know that from the get go -- correct measurement of I and V is everything in this case. So, how can the 110pF capacitance of the passive probe affect the outcome? Is the voltage we measure different from the real voltage applied to the system and is its lag with respect to current the real lag there is?

[Omnibus]

@teslaalset,

Please take a look at these two spreadsheets. They illustrate the above. Both are taken at 700kHz (the rest is the same as in the latest spreadsheets with experimental data posted), however, one is taken with 1X passive voltage probe while the other one is taken with 10X passive voltage probe. Now, which one is crazier? And, if using the 1X passive probe for measuring voltage isn't the right way to do it then what's the right way? It certainly isn't with the 10X probe. So, another set of theoretical ruminations is needed here to understand the role, if at all, of the 110pF loading exerted by the 1X voltage probe.