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I tried to select the fuse based on this selection guide, but found my calculation for fuse I2t is not practical. Can someone point out the error in my calculation?

The application scenario is a 240V AC power supply system, rated current 1A, filter capacitor before DC/DC is 220uF, ESR 1ohm.

  • calculate the peak pulse current

enter image description here

  • calculate the pulse I2t, here I select the waveshape E

enter image description here

  • calculate the nominal I2t for 100,000 occurrences of the pulse I2t.

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  • I went to Digikey to look for a fuse with 250V1A rating and I2t > 420 but found none. I assume there is some mistake in my calculation but cannot find it. Can someone show me where my error is?

Edit: Thanks to @Neil_UK @Spehro Pefhany answer.I 've simulate this scenario to get the accurate time.

The circuit is like this. I assume the ESR of rectifier/wire is 1ohm.

enter image description here

The following is the waveform

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enter image description here

From this waveform, I got the pulse current 160A and time 1ms, therefore the pulse I2t is

enter image description here

This is more practical I2t value and there are a lot alternatives to choose from on Digikey.

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  • \$\begingroup\$ ESR of the entire circuit includes that of the recitifier bridge and the fuse and wiring, as well as the 220uF, so will be > 1 ohm. Where did the 100k occurences factor of 1/0.22 come from, that's not helping, it sounds a statistical thing that should not be relevant. Note that many DC-DC converters and 'capacitive dropper' LED lamps use a small series resistor (at the cost of a bit of heating and inefficiency) to reduce inrush current to manageable levels. \$\endgroup\$
    – Neil_UK
    Commented Jun 1, 2022 at 7:40
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    \$\begingroup\$ Where did the 4ms come from? At 340A that’s enough to charge 220uF to more than 6kV. In other words the pulse will be much shorter. \$\endgroup\$
    – Spehro 'speff' Pefhany
    Commented Jun 1, 2022 at 7:43
  • \$\begingroup\$ Waveshape 'F' is more appropriate to capacitor charging, with a t=220 us, given by your 1 ohm and 220 uF. \$\endgroup\$
    – Neil_UK
    Commented Jun 1, 2022 at 7:55
  • \$\begingroup\$ P.S. if your DC output current is 1A then a fuse on the AC side will see a considerably higher steady-state RMS current than 1A, aside from the start-up surge, likely in the range 1.5A to 1.7A. Fuses respond to RMS current, not average. \$\endgroup\$
    – Spehro 'speff' Pefhany
    Commented Jun 1, 2022 at 7:55
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    \$\begingroup\$ @Ross I don't trust your simulations - I think LTSpice is hiding extra parasitic components in the C and R, or doing something weird with its default choice of integration algorithm and control parameters (you can choose others, you know!). Things don't happen on a ns timescale with those components, it just doesn't smell right! I think Ipeak = 340 A, t=220 us, just by doing simple sums on the voltages and components involved, using waveform F, is more appropriate. That's why they provide waveform F, specifically for the exponential capacitor charging case! \$\endgroup\$
    – Neil_UK
    Commented Jun 2, 2022 at 11:14

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