>...  so why WOULDN'T it work? ...

is very powerful.

But "... why DOESN'T it work .." is often (not always) more powerful.

(Tesla / Shaw / Kennedy versus Edison)

Also often useful is the hybrid.
"Imagine that I tried this and it didn't work. Why might that be?"

In this case you are presenting a device with a falling voltage that
approaches  the maximum charging voltage of  a LiIon cell and then
interposing  some terminals, plugs & socket(s), wiring and known and
somewhat unknown electronics in between source and sink. IF you tried
it and it didn't work as expected it could be because the voltage drop
in the 'stuff' between the two batteries was too high at 1 A to
provide enough voltage for the LiIon cell.

The arithmetic has already been done in prior posts, so this is just
re-noting what has already been  explained. ie it may work well enough
for you, and may not. If it doesn't you should not be at all
surprised.

If you want certain success [tm], then adding a 5th cell and a little
more electronics will make all the difference. Does nasty things to
the battery shape though.

Re LDOs in parallel. As people say - not advisable BUT if they have
thermal and/or over-current graceful linear shutdown they will
probably load share progressively. Not a vastly good idea.


 Russell
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