This is a work in progress, and I am only a hobbyist!
This is a 3.3V max. 1A power supply for microcontroller circuits, based on a Texas Instruments Webench Power Designer design report using a TPS82084SIL step-down converter with an integrated inductor.
The single-cell Li-Poly charger circuit is straight off MCP73871 datasheet. MCP73871 is an USB/AC battery charger with power path management; it passes the power through even when no battery is connected. Only use single-cell (3.7V nominal) Li-Po batteries with protection circuit built in!
According to the design report and TPS82084 datasheet, the converter should be 90%+ efficient at 1mA (3.4V to 5.5V input), 92%+ efficient at 10mA and higher currents, and 94%+ efficient at 200mA to 1000mA. Technically, the converter can do up to 2A, but this particular design is intended for smaller currents. (A linear regulator dropping 5V to 3.3V is only 66% efficient. This means that a 3W load would generate 1.5W of waste heat in the regulator only. TPS82084 providing a 3W load from either 5V USB or a LiPo cell will only generate 0.2W of waste heat.)
(For use with USB-WWAN adapters, TPS82084 might need some additional filtering to not interfere with the radio circuits, as it uses 2.4 MHz (typ.) switching frequency; I have a separate project for that kind of use here.)