Supercap-microcontroller power back up.

Hello,

I was looking for a cap to hold the voltage on a pic16LF1503 for few minutes when the power is disconnected.
I found a nice 0.022F supercap that's more than enough to do the job.
Supercaps act like a short circuit when they're completly discharged so I added a PMOS in between the 2.5 Voltage regulator( SIP21106DT-25-E3 ) and the supercap ( EEC-S0HD224H)
I find it difficult to estimate the supercap charge time since the pmos rds resistance constantly changes as the current through the cap moves along the blue curve shown below. Anyone have a good method? Thank you in advance.

initial cap voltage is =0v. so VDS=-2.5v.
Final Cap volage is ~2.45V so VDS=-0.05v

Worse case scenario RDs0n=9Ω @ 0.175amp
Charge time is about 750ms but I know that's not accurate, maybe close.

can u connect a new trace to charge the capacitor not throw the P mos instead using a diode .. in other words make the charge way different form the discharge way.

and why are u using super capacitor ?? 22000uF is not very high espically at low voltage , check if u want nichicon caps the size for 22000uF 6.3v capacitor measures 18X35.5

if u are concerned about the size you can use a "watch battery" they are used in computer motherboard for keeping time and other settings stored.

If I am going to use a diode that would be 0.3-0.7v drop. The cap will only see a max of 2.1V That's too low since I want to charge the cap to a voltage close to 2.4v.

Supercap have very low leakage current and last for a long time. Batteries aren't reliable for long term application and cost more.

Since this is a very low current draw application ( microcontroller + other elements draw ~ 300-400uA) then super cap would be ideal.

My question remaines un-answered. What do you guys think about my question in the first post?