Mobile Phone Battery + Teensy 3.6?

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haiku

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Hi, I'm planning on making a small hand-held device out of a teensy 3.6 but I've been struggling to find a good power solution. The tricky part isn't really the battery capacity but rather the dimensions. The case I'm using means I can't really go thicker than 5mm, also height and length need to be less than 9cm & 5cm respectively but its the thickness that's the hard part.

Normally with projects like these I go with some standard li-poly cells like these from pimoroni and combine them with a power booster like this to get the 5V I need. But even these cells are slightly too thick unless I go with the lowest capacity ones.

I am wondering if I could use a mobile phone battery like one of these. Duracell seems to do quite a few different versions for different phones some 3.7V and some 3.85V. They also seem to have pretty decent capacities.

I was thinking that by combining one of these with a power booster I'd be able to run the teensy off the battery and have the usb data lines skip the booster and go right to the teensy. That way I could could charge the battery and program the teensy using just the power booster.

Ideally I would like the device to last at least 3 - 4 hours. I've already got the teensy working with a small 64 x 128 GLCD display from jeeLabs (see here). I haven't measured the power draw yet but it says it draws '6 mA on 3.3V and 19 mA on 5V' and I think that's with the backlight on (Which I'm not using).

So if the teensy draws 80mA (going by here) and the GCLD takes a further 6mA and if we say the power booster is 90% efficient would I expect the time the device lasts to be ((battery capacity mAh) / (80 + 6)) * 0.9 ?
I'm guessing its not going to be that simple since I know you cant fully discharge some of these batteries.
 
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