Using a capacitor to buffer power to eMMC
Well,

\$ \frac{dv}{dt} = \frac{i}{C} \$

You'll have to measure i while it is writing.

Then you'll need to know for how long you want it to last.

The problem with capacitors as backup power is that the voltage will decrease quickly as the capacitor discharges. So if the nominal voltage is 3.3V, and the minimum allowed voltage is 3.1V, only a small fraction of the charge inside the cap can actually be used.

However, you want to protect against sudden power loss, which means your circuit is not running from batteries, and thus there isa good chance  your 3.3V is derived from a higher voltage (say, 5V or more).

In this case you can place the capacitor on this higher voltage, then use a regulator to power the eMMC. For example, using 10mA current, and a 100µF cap:

di/dt = 100V/s = 0.1V/ms

Time for cap to go from 3.3V to 3.1V: 2ms

Time for cap to go from 5V to 3.3V: 17ms

In the latter case, having more voltage margin means we can use more of the charge stored inside the cap (but an extra LDO is required, and also a schottky diode to make sure the cap doesn't discharge back into the power supply). Something like that:







simulate this circuit &ndash; Schematic created using CircuitLab

U2 could also be a switching converter, but at this point the added complexity would be a bother. One could also use a coin cell battery.