The SOA of the Bypass FET is very poor
this is because many MOSFETs (generally: transistors) are considered for switching applications. Look for a MOSFET for linear operation, often they have a big package with heatsink tab.
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SOA:
the main job of the NTC (or other inrush limiter) is to limit the current into the bulk capacitor at power on situations.
Ignoring other currents .. the energy stored in the capacitor is 0.5 x C x V x V.
The same energy has to be dissipated by a linearely operating limiter. Independent of type, resistance, voltage, current, time....
This is what your limiter device (SOA) needs to handle.
But the problem is the extra current.
It might be a faulty short circuit ... or it might be the expectable current to drive the load.
* to limit the "current by the load", I recommend to include a delayed soft start of the SMPS circuit. Maybe the delay is controlled by the limiter circuit (In a way the SMPS starts only after the limiter has become fully ON)
* to care about faulty currents .. is a bit more tricky. Here the NTC has it´s advantage, because due to it´s thermal behaviour it is rugged and thus a simple fuse may be used.
Other current limiting circuits dissipate a lot of heat ... and in one applicartion I used the temperature of the limiting element to decide a "fault condition". (Either too high current or too long time...). Still needs careful design of: power dissipation, timing, heat capacity...
Klaus