The supercap idea is quite charming, but always make a reference measurement without any load before and after the real measurement. Check that cap leakiness is stable and subtract it from the measured discharge.
Lot´s of supercaps are super leaky when they were idling for a long time. The electrodes reform after a few hours of use and so the leakiness get´s better again.
It's actually a bit simpler than that, in my opinion; or, arguably I guess, but it seems simpler to me.
The terminal current of a supercap can be described as the sum of two currents: "normal" capacitor current, and leakage.
Leakage increases exponentially around rated voltage. The mechanism is simply solvent electrolysis, much as the self-discharge or failure mechanism(s) are for battery over/under dis/charge. The self-discharge time constant can be some days near ratings (maybe even hours when hot), weeks or months at a modest fraction.
There is no "reforming" mechanism -- there's no oxide barrier at all, unlike aluminum electrolytics for example. The barrier is the solvent itself (or the salt dissolved in it: forming an ionic double layer), so leakage doesn't go down the longer you hold it there, it's purely a voltage thing.
I've had one sit on my shelf at ~2.1V for whole months; I'd have to write down what the actual changes are to see for real, but it was quite slow at room temp and this modestly derated voltage.
"Normal" capacitor current, for a supercap, is highly diffusion mediated. That is, instead of X = 1/(2*pi*F*C), you get R = X ~ sqrt(Ro / (2*pi*F*C)). This F^(-0.5) asymptote extends over a wide frequency range: perhaps 10s µHz to 10Hz+. (It may not be consistently 0.5 exponent, but varying; or alternately, it might be well described by a modest-size lumped equivalent model, give or take the diffusion element still; I haven't seen data on specific parts, unfortunately -- this is mostly a hand-wave.) Whatever the exact function, the important part is to think about capacitance and ESR as variables, even moreso than for regular capacitor types -- and exactly as much as battery impedance models do, and for similar reasons (ionic diffusion).
The biggest take-aways are: capacitance varies with frequency, so it depends on how long you let it dis/charge, what efficiency (both charge and energy) you measure, what value, and say if setting a constant voltage to measure leakage, how long you need to let it settle for before you're finally measuring the steady-state leakage per se.
And, because the tail on this response is
just so long (days, weeks), you might think the current has stabilized to leakage, and measure it then, but actually it's still creeping down, little by little. Datasheets themselves fall victim to this -- I would say more as a matter of convenience, as, who can wait full days
or weeks to test otherwise-normal components before shipping them? So, you see somewhat pessimistic leakage values in datasheets, and you can expect better leakage if you're patient.
This long tail can look like reforming, but it's actually a linear effect, and everything that applies for charge, applies for discharge as well! It's just a very slow to reach steady state, depending on how close you need it to approach "steady".
Another way to put it: it might look like dielectric absorption, but, it's kind of... the whole damn thing is absorption?! The "droop rate" for a step charge can be quite massive, like 20, 30% (i.e., charge the capacitor from 0V to 2.5V in some seconds or minutes, then disconnect and wait).
So, if you're testing something like an IoT gadget that sits around for weeks or months at a time (or years?), and just wakes up and beeps once in a while or whatever it's doing, expect to "soak" the capacitor(s) for a good week or two before starting the test, and take "mid stream" sample data -- measure it periodically, note the initial droop rate and discard if it's still settling, then calculate from there.
Of course, if energy consumption varies with data, or configuration, or activity or whatever, make sure to set that to a reasonably-worst-case condition so you're getting a representative upper bound here.
For shorter durations like single wake events, coulometry can be done with a much smaller capacitor, and, say, measuring the delta V on the oscilloscope. Then extrapolate average power based on average wake rate.
Dielectric absorption of other capacitor types is much lower -- AFAIK, a similar diffusion effect underlies those, too (perhaps not ionic diffusion, but relaxation of polarization sites in the dielectric, and electrolyte where applicable, stuff like that), it's just a smaller fraction of the total (electrolytics might be a few percent, etc.).
Tim
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