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Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
@allObjects
Power consumption is usually measured 'integrated' with di/dt over some t... for example for blue tooth - which is just another type of RF communication - see this Measuring Bluetooth Low Energy Power Consumption pdf document from TI.
Figure 26 thru 28 on pages 21 thru 23 show the great fluctuation in power consumption: 'high' power over very 'brief' periods and 'very very low' power of 'long' periods. Such behavior is not knew... and you may have wondered why for each IC on a board there is/are very closely capacitor/s to 'catch' - smoothen out - these power demand spikes so they do not 'back-fire' and jeopardize the power on the rest of the circuitry...
ESP8266 has similar behavior. Especially at the beginning spikes of up to 300mA have been measured (caused by RF calibration of the circuitry). Some details you can find here: esp8266_power_usage.
To find the proper battery configuration - capacity of the battery - depends on two things: what is the peak draw, how often over how long, and what are the low draws and for how long... To not wear down a battery too quickly, the peak draw should not go above 10% of the capacity/hour - for example - a cell may have a nominal capacity of 225mAH (22.5mA over 10 hours) - and therefore, peak should not be higher than 22.5mA in order to nominally guarantee a capacity of 225mAH. Drawing much less than the 22.5mA will 'let you live longer', but there is also a limit to that because each battery has an inherent self discharge. These battery parameters you can find in the respective data sheets.