rudy wrote:One point worth considering. From what I understand, the most current demanding operation is when the ESP8266 does an analog calibration on startup. And I think this is where it is most likely to fail. So maybe, once it is up and running, it can tolerate a lower supply voltage, like the spec sheet lists.
This is true, but you can minimise the power spike at the start by changing the RF calibration settings using system_phy_set_rfoption() with the value 2 (No RF calibration after Deep-sleep wakeup) and system_phy_set_powerup_option() with the value 1 or 2 (1 = RF initialization only calibrate VDD33 and Tx power which will take about 18 ms, 2 = RF initialization only calibrate VDD33 which will take about 2 ms).
I've found that for fixed installations of a sensor unit you can perform RF calibration once when the unit is first set up, and then after the unit is calibrated for the installation site, you can turn it off or only do it periodically (by using system_phy_set_powerup_option() with 0 or 3), reducing the initial current spike by a lot. Since installation is when a battery is most likely to be at its highest charge, this works quite well. After that, a decent sized capacitor will manage the start up spike quite nicely.
Note that these calls should be protected with a corresponding check on existing values as they write to the flash so you only want to call them if the value needs to be changed.
Having said that, you will still need to find a good 2.8V LDO that does at least 400mA peak - but I am going to go through the list in this post and see what I can find. While I am happy with the one I have now, the list has a few that have an even smaller drop out voltage.
PS: @rudy I also really like your idea of using a pair in parallel! I know it was a hack, but it was a brilliant one