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LM66100: Auto-switching power mux with similar voltage input levels.

Part Number: LM66100
Other Parts Discussed in Thread: TPS2113A, TPS2110A, TPS2111A, TPS2114A, TPS2115A, TPS2112A, TPS2116

Hi,
I have a related question to this topic.
We know that it's generally not a good idea to put batteries in parallel because one can be more charged and have a higher voltage and this will cause it to drain quickly as it feeds the other battery.
However, in order to increase the battery life time of an application, I was planning to use two sets of batteries in parallel and use a switching device to prevent the event above, selecting the highest voltage level battery.

In the previous post it was mentioned that the LM66100 is not suitable for two identical power supplies and a Power Mux IC should be used instead.
The following options (with some different functionalities) were founded TPS2110A/TPS2111A, TPS2112A/TPS2113A, TPS2114A/TPS2115A. Could it fit the purpose?
Thank you for your attention.