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LMR36503: Power management for battery and power supply

Part Number: LMR36503
Other Parts Discussed in Thread: LMR38010, TPS62826, TPS62840, TPS62177, TPS62175

Tool/software:

We are currently using the product LMR36503RFRPER in the series. We used as Buck converter for an output voltage of 3,3V and wide range input voltage nominal 4,5 – 28V. In Error case, for safety integrated max. input voltage 60V.
Now for a new product we need an input range from 2V – 3,8V in battery mode and wide range input from 4,2 – 60V in power supply mode. Both input range relate to the same wire on the board. Is there a converter how pass through the voltage of battery since 3,8V directly to sw pin, until 3,8V the converter should be switch off and should have a small quiescent current. Over 4,2V the converter switch on.