While my supercaps are ordered, but still not delivered, I made a few experiments with charging "classic" 4,7mF capacitor.
I added 10Ohm resistor in series with my laboratory power supply set to 3V to roughly "emulate" CR2032 cell, but my primary goal was to get current sense resistor to obtain somehow more accurate power measurements. I started with discharged capacitor, turned the supply on, and waited for scope to trigger. This is how the measurement looks like.
The pink trace is voltage on transistor gate, yellow is voltage on sense resistor (here -60mV means 6mA of current) and blue is voltage on capacitor. Notice how the comparator turned off the charging at preset 2,2V, with occasional charge impulses to cover self-discharge.
The capacitor charges in 1,35s, with average current of 6,6mA, that is approximately 26mJ of energy, while there is approximately 10mJ of energy in the capacitor, yielding 40% efficiency. Not exactly totally bad, but not brilliant either. The first suspect was BAT43 diode - I assumed it's OK for this purpose (low current, low leakage), but it seems to be not the case, with high current spikes charging the capacitor. Higher power diodes do have lower voltage drop, but also higher leakage current, specified up to 1mA or so - usually at maximal voltage and elevated temperature, both being rough conditions for leakage. I measured dozen of randomly chosen SB130 diodes and all of them were in region of 1-2uA of leakage at 3V, so with fingers crossed I can be happy with its leakage properties. Interesting enough, the SB130 diode improved efficiency of the converter to approximately 54%, so I'm more OK-ish with that. The protoboard isn't particularly great for impulse circuits, so moving the project to proper PCB can increase the efficiency a bit too.
Now I'm really curious about the supercapacitors.