Should I need to charge one lithium ion battery with another, what sort of loss would be typical?
If I had a 65wh battery, can I calculate how big a battery I need to charge it taking into account the loss?
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The ESR of each battery determines the fundamental "charge efficiency", e.g. no matter what you do on the outside, some energy will be lost to heat due to this,
Due to this, the lower the charge rate, the less total energy is lost to heating the ESR, this sets your maximum theoretical efficiency,
Next up you need some circuitry in between the 2 to both limit the charge rate, and convert between these 2 voltages with reasonable efficiency, the efficiency of this charge circuit will decrease you below that theoretical value.
You might notice a lot of these values need specifics to solve, e.g. charge rate, each batteries ESR curve, and the charge circuit's efficiency curve in relation to this. so an exact answer will take a bit of work to reach, a ballpark however, choose a charge rate, determine the ESR, and work off an efficiency between 80-90%, most switching charge devices should be able to handle this.