My latest project uses an ESP8266 (ESP-01) to transfer data when a button is pressed. The ESP is always connected to the AP. No deep sleep. Right now I am powering it with an USB-charger which is directly connected to an AMS1117 LDO to regulate the voltage to 3,3V. This works fine so far.
Now I need to power the ESP with AA Nimh rechargeable batteries. I thought of putting 4 AA in a battery tray which should result in nearly ~5V. Because of the high quiescent current (>1mA) of the AMS1117 I am searching for a 'better' LDO. I see a lot of projects using the MCP1700 LDO in combination with the ESP. This LDO has a very low quiescent current (<2 µA), but the datasheet says the max output current is 200mA, from what I've read the ESP can have peaks up to 250+ mA. Isn't this a problem? I also found the MCP1825s which has an output current up to 500mA, but a higher quietscent current of <120µA.
1) Which LDO should I use to have a stable but power saving setup?
2) How can I calculate the time this setup will work until the batteries voltage drops below their minimum? Using 4 AA (each 1900 mAh) starting at about 5V until 3,6V. 3,6V because the dropout of the LDO is about 0,3V and the ESP needs 3,3V. Assuming an average current draw of about 100mA. Is it just simple 1900mAh/(100mA+LDO current) = ~19h ? How fast will the voltage drop from 5V to 3,6V?
3) Which caps should I use for decoupling the LDO? Just the ones suggested in the datasheet? Is it important if the capacitors are ceramic or electrolytic?