Lithium 5V stabilization

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v4000ds

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2-3 battery input
1) 2bt: min: 2*3.2=6.4V, mid 2*3.6=7.2V
2) If the chips for the first option are too expensive
3bt: min: 3*3.2=9.6V, mid 3*3.6=10.8V, max 3*4.2=12.6V

Out stable 4...5V, lower limit 4V. Current <=3A
 
The MC7805 is really only good for 1A maybe 1.5A. You need 3A. It needs 3 to 4 volts higher input than the output. That is a serious problem here.

There are "LDO" regulators where the input to output voltage can get down to less than 1 volt. Low Drop Out

Because you are running from batteries a "switching power supply" will make the batteries last much longer.

5A Here is a link to a DC-DC 5A buck power supply. It will work with the 3 battery option better. There are smaller 3A versions.
1.8A (3A short time) This one is maybe too small.
The good point about switching power supplies:
Using a MC7805, 3A load it will draw 3A from any battery voltage.
With a switcher 5V 3A out will pull only 1.5A from a 10V battery and only 1A from a 15V battery.
 
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