What is a portable headphone amplifier?

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I could estimate it. I'm really just trying to determine the maximum required supply voltage, erring on the high side if necessary. Let's just say your design approach is different than mine. Moving on:
You've stated a 5V supply would be sufficient, but by far the simplest rechargeable battery system would be a 3.6V Li-Ion cell (which at end of charge is likely less than 3V) and a USB charger IC. This is where I got to when I decided I needed a boost converter and it became a matter of what voltage to boost it to.
If you plan to use primary cells, just use a 9V battery and build a Cmoy.
 
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