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TPS2121: Supercap backup power supply - 4A 5V

Part Number: TPS2121
Other Parts Discussed in Thread: LP2998, LMR33640, , TPS61022

Hi,

I'm working on a backup power supply using supercaps.
The supply should be able to deliver 5V at 4A for about 10 seconds to be able to cleanly shut down an embedded pc.

Two supercaps in series seems to be the best approach for this power level when looking at the higher capacity number the 2.5V variants are sold in?
I came across this appnote which uses the LP2998 as a balancer: https://www.ti.com/tool/PMP9766

SD of the LP2998 is tied to AVIN through a divider to make sure AVIN is higher then 2.2V before the device turns on.
Don't know if this is the best approach, a comparator might be better?

An LMR33640 is used to convert 12-24V to 5.1V, a TPS2121 power mux to switch to the supercap power rail when the LMR33640 drops out.
And a TPS61022 to boost the supercap rail to 5V during discharge.
In normal operation the TPS61022 should be getting 5.1V on VIN preventing it from having to regulate and just passing the 5.1V through.

Any remarks or suggestions for this kind of application?
ps: The TPS2121 and TPS61022 scare me a bit package wise, but couldn't seem to find any comparable alternatives with bigger (more reworkable) packages.

Thanks,
Nick