..So surely the SMQW322RJT could do the shown ~30W for 20ms?
And as you know, we can always do a test jig which gives it the inrush once every 30 seconds, and leave it on for a week, that should be a good test...but probz not allowable due to fire regs.
about 30 years ago, i had a document from Dale about pulse handling capability of resistors.
it specified the pulse energy handling capability of various resistors
it talked about joule stress - enough joule stress and the resistor would explode, rather than burn up
this is as close to what i had as i have been able to find
TE specs for SMQ: Short time overload 5 times of rated wattage for 5 sec Thus P = 3 W @ 150 'C, E(5s) = 15 J max for so-called "long pulses <=5s."
But for short pulses, e.g. 40 ms Vishay Dale bases analysis and recommendations on the amount of energy required to raise the resistance element to + 350 ºC with no heat loss to the core, coating, or leads.
Integrating your curve ( using triangles) computes to 1.33 J in 0.04 s.
Using a formula for E(t) from Vishay** for a similar non-inductive wirewound (WW);
Vishay Intertechnology's acquisitions include such top companies and businesses as Dale, Sprague, BCcomponents (former passive components businesses of Philips Electronics and Beyschlag), Draloric, Sfernice, Vitramon, Siliconix, the Telefunken semiconductor
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Conclusion
V's specs for 22 ohms 3W implies 5 times rated current =15W in 5s max for DC = 370 mA and thus 5s long pulse spec is 1.846 A max.
You are looking for a solution to withstand a pulse starting at 45W or 1500% of rated spec. This could outgas and explode or fuse open or just tick like a voice coil and be OK once or twice. But there is no guarantee. Thermal shock is much worse than a slow ramp. If you smell anything, I suggest you keep looking.