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I have a circuit that is off almost all the time, when a button is pressed an MCU will be brought outside of sleep mode perform a log and go back to sleep. This device should run on 3 1.5V AAA batteries giving more than 3.3V.
How can I regulate the voltage when I wake up from sleep and have the regulator not waste energy when device is not used?
If you use a CMOS flip/flop, the 'button press' can SET the flip/flop, which can enable a low-dropout regulator like TPS706 . The regulator turns on, your MCU goes through power-on operations, does its thing, and turns the power off by issuing a RESET to the flip/flop. When in 'shutdown', that TPS706 takes under 150 nA.
This is usually needless, though: many MCU chips have a variety of on-chip functions to go into sleep mode. A trio of alkaline AAA cells has roughly 1200 mAh of capacity, so a modest drain (like, 30 uA) might be supportable. 30 uA will drain the cells in a bit over 4 years, and 150 nA will take longer (so long that battery shelf-life dominates).
