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I'm looking to use a solar + lithium ion battery combination in order to be able to continuously power a Raspberry Pi.

I have found an MPPT solar battery charger, which will output a fixed voltage. From my understanding, however, a fixed voltage output isn't the best way to charge l-ion batteries. So my thought is to feed this fixed voltage into a l-ion battery charger like this one, which will then charge the battery.

Once the battery is charged, it should provide current to the RPi and some other motors via a step-down regulator or two.

The thing I can't wrap my head around is how to make a circuit that will always give the RPi/load the power it needs, but charge the battery if there is any juice left over. If the panels are only getting a little bit of power, the battery should also augment them in order to power the load.

What is the most energy-efficient and reliable way to do this?

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You just need to design an UPS (uninterruptible power supply). You need to select proper solar block, which will give you interruptible source. All you need then is to study PMIC (power management IC) offerings by companies like TI. Look at something like BQ24296, which will provide the rest of functions: Li-ion charger, +5V system voltage boost, and balanced power bypass.

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