Is joule thief circuit gets overunity?

[TinselKoala]

A 1 meter copper coil was wound around the toroid on Board 135.  A load of 50 ohm + 1 ohm was used.  The Secondary Coil Voltage was taken across the 51 ohms and the Secondary Coil Current was taken across the 1 ohm resistor.

Congratulations! You've invented the transformer!

(sorry, I couldn't resist.     )

[Void]

Well, that's good, but of course you realize that your power supply already has a lot of filter capacitance in parallel with its output, probably, and chokes in series; it's just that the caps in the power supply have their charge constantly replenished from the voltage regulator.
Certainly there will be differences in things like impedance of the three power sources (bat, cap, psu) so why shouldn't waveforms and measured efficiencies differ a bit?

Yes, there is no doubt that the joule thief circuit operation will be affected by what is connected to its power input terminals, but rather than having a higher efficiency with the regulated power supply connected, the measured efficiency is higher with the super cap connected, although the waveforms appear to be fairly similar overall. Although the input voltage is about the same, the circuit seems to draw less current with the super cap connected, and that might account for the higher efficiency, although I don't know exactly why that is. Perhaps the joule thief can draw more current with the power supply connected because of the better regulation. This just may indicate that a joule thief type circuit runs more efficiently as the input current draw is reduced, but again, I am not certain exactly why that would be.

[Void]

Power and Efficiency of my Joule thief circuit powered with regulated DC power supply:
Input Voltage: 504mV
Input Power: 2.995mW
Output Power: 2.002mW
Efficiency: 66.84%

Scope shots are attached below.
Yellow traces are voltage, and blue traces are current.

[Void]

Power and Efficiency of my Joule thief circuit powered with my 3000 Farad Super cap:
Input Voltage: 500mV
Input Power: 2.501mW
Output Power: 1.947mW
Efficiency: 77.85%

That's an increase in circuit efficiency of about 11%. This is the exact same JT circuit as in the previous test I posted, with the only difference being that the input power is now being supplied by a super cap, charged to very close to the same voltage that the regulated power supply was set to in the previous test. Notice that the output power consumption of the LED is very close in both circuit arrangements, but the input current draw drops when using the super cap, thus reducing the input power a fair bit.

@Lawrence, this is just preliminary, but the tests I have run comparing JT circuit efficiency between using a regulated DC supply and using a super cap as the input power source would seem to lend support to your own tests where I think you were using a battery and a timer to intermittently charge a super cap, (or what was your exact setup?), and you noticed that it took longer for the battery to run down.

Scope shots are attached below.
Yellow traces are voltage, and blue traces are current.

[TinselKoala]

It would be interesting if you could equate the output impedances of the psu and the cap somehow, but I have no idea how to do this. It hardly seems fair to have to put a resistor in series with the supercap. It certainly looks like you are getting more ringing with the PSU, and this is a loss mechanism.