improving a cheap wall wart with a "Capacitor Filter Board"

The supercaps being used in that product have rather a high ESR (equivalent series resistance) when compared with normal electrolytics. To get up to 24V volt working, they use 5 in series seeing as individually they're only good for 5.5V. So while you do have in effect 0.6F of capacitance (two parallel strings of 5 * 1.5F in series), that's in series with 25ohm worst case.

If the aim is to reduce noise out of your wallwart, I'd say it won't do much if anything. You'd be better off with a filter using normal 'lytics as their ESR will be orders of magnitudes lower (millohms rather than ohms).
 
Well it certainly increases the reserve capacitance but as the 0.6F you're adding is 'behind' a 25ohm resistor it won't make much difference to the ripple voltage on the 24V rail. That's normally the aim of adding capacitance, to reduce the ripple on the supply rail.
 
Is a simple filter like this not more effective? 2x10uF between plus and minus and one ohm in line in between

IMG_20240107_105643.png



Besides that in the diy audio store is an advanced designed filter offered
 
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I'm trying to increase load capacity, I guess I need one designed specifically for 15v ?

Assuming the wallwart is a traditional EI transformer-based one (i.e. not a switcher) the load capacity is set by the transformer itself. The capacitance on the output is there to smooth the AC but adding more will actually cause the output voltage to drop. More capacitance will not improve the load capacity rather it'll slightly decrease it. If the wallwart's a switcher then things are a bit different but more capacitance won't increase the load capacity in that case either.