I need to limit the Inrush Current to this to avoid fuses tripping,.
..you ask an excellent question. But you cannot select a fuse which will avoid nuisance tripping from inrush pulses......because eventually, after so many inrush current pulses, your poor fuse will die. Its just a matter of how many inrush pulses you want to withstand before it dies...and you select the fuse on that basis. But yes, inrush kills fuses...eventually...its just a matter of how long it holds out.
Pages 6 and 7 show you how to select a fuse for this...based on the inrush current pulse shape etc
https://www.littelfuse.com/~/media/electronics/product_catalogs/littelfuse_fuseology_selection_guide.pdf.pdfWhat you usually do is calculate the "pulse I^2.t". (using the chart shown in the littelfuse link.)
Then, for example, to survive 100000 inrush pulses, you would need a fuse with an I^2.t" value of (100/22) * "pulse I^2.t".
Might as well take the worst case pulse at "on at mains peak".
And yes, their are piles upon piles of scrapped electronics products , all over the world, which have been scrapped for no other reason than the fuse died after so many inrush pulses......and all because the nice manufacturer (or rather the millionaire middle man who used the manufacturer) didnt want the added cost of an inrush limiter....which could have been as cheap and simple as an "on at zero cross" circuit.
In truth, to be kind to the environment, all offline power supplies should start up through a massive inrush resistor, which allows through just enough current to power a mains zero crossing detector". Then, a little micro should switch on a relay or back-to-back fet etc which shorts out the big inrush resistor....and this being done at the zero cross.
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So from the inrush pulse example, (LTspice sim attached, LTspice is free) the I^2.t = 0.5 * 284^2 * 241us = 9.72
(as per the littelfuse fuseology example)
So, to get a fuse that can withstand 100000 of these pulses, it must have a melting i^2.t of (100/22) * 9.72 = 44.2 A^2.s
…So as you can see, the 3.15A version of this (0034.3122) is good for 100000 pulses of inrush at mains peak, at high mains of 265VAC.
https://us.schurter.com/bundles/snceschurter/epim/_ProdPool_/newDS/en/typ_FST_5x20.pdf