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I have a load (more specifically a Raspberry Pi 3 B) which requires a voltage of 5.2V and needs around 2-3A current. It should be powered by a LiPo battery with a capacity of 6000 mAh. In addition to that, the battery should be chargeable with a power supply (in less than 6 hours) and at the same time power the load.

As far as I've understood I first need a DC-DC booster to reach 5.2V but also a charger module that is safe. I cannot build such a module from scratch because LiPo powering can be quite dangerous and I'm not a battery expert. But it seems like there is not such a module to buy online, especially when it comes to the 5.2V/2-3A requirements of the load.

Now my question is: Is there actually a way to achieve all this? And if yes, which components do I need to build a charger with an integrated booster?

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You may want to look into LiPo packs that are used in many RC applications, such as the ones available here. These packs consist of multiple cells wired in series, which you could then regulate down instead of boosting. These cells typically have a very high discharge rate, much higher than you'll ever need to power a Pi, and are available in some very high capacities. You can also purchase chargers for your cells here, and since these products are targeted at RC hobbyists, there are many pre-built options for regulation, monitoring, distribution, etc.

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