I am designing the power input circuit for a microcontroller. The controller operates between 2.1v - 3.6v. For power purposes, I am using a Lipo battery with a range from 2.5v to 4.2v. I am looking to regulate the Lipo battery when in the range 3.6v-4.2v to a fixed 3.6v output. Once the battery starts draining below 3.6v I want the regulator to ideally just pass on the voltage from Lipo since it is now in the supply range of the controller. If someone has worked on something similar and can recommend a chip for regulation. I am currently looking at synchronous dc/dc buck converters. But their datasheets don't usually talk about the operation once the input voltage drops below the fixed output voltage, whether they just pass the voltage or not. The current draw from the battery will be max 50mA.