Capacitor Selection for TPS56221
You're making something like a desktop PC CPU VRM, except your output current is lower, but the input power is the same. So, let's use PC mobo 105°C polymer caps.

Input caps: we have 20A 500kHz ripple. This will be handled mostly by  MLCCs, but since you mention 14A load step, if we have a load step in the 10-100kHz range, then the 12V supply may or may not respond quickly enough. So we need local bulk caps.


4-5 R7 or the more expensive but smaller OSCONs
0805/0603 MLCCs, try to stagger the values like 10x10µF - 10x1µF. The 10µF can be 1206's. The 1µF should be small and as close as possible to the DC-DC.


Use a wide copper pour for VIN...

The MLCC's job is to close the HF current loop right at the source so the nasty fast edges don't turn into EMI. The polymer cap's job is to help the main 12V power supply.

Mind the ripple current rating of your MLCCs too! If they heat too much they will crack. I would't use less than 10 caps, that's 2 amps pumped in a tiny 0805 or 1206...

Output caps:

The load will decide how many close decoupling ceramics it needs. Here, I'm just talking about the caps at the output of the DC-DC, which again close the HF current loop and absorb the inductor ripple current. The datasheet goes for 6A ripple, so let's use that.

So, 2-3 S8 or R7 or OSCON or flat caps... plus a few 1-10µF in 0805 or 0603, say 4 of each.

If the caps use too much space, you're gonna need a higher switching frequency. If you wanted to use MLCCs only due to height restrictions, check the flat Panasonic polymer caps I posted. Also, big MLCCs tend to crack if the board is flexed.

Also, even at 95% efficiency, you'll still burn 4W in a tiny area, so keep thermal management in mind...