how to calculate in rush current limit circuit

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Hi,
find the PSUD11 design software. It's free and really helpful.

You can select all the PSU components and simulate a resistive load over any timescale you want to investigate.

It will show peak and average currents and the gradual charging (with big peak currents) of PSU smoothing caps.

The slow start circuit seems to be a special case using some kind of current limiting circuit and may not simulate a solid state slow start accurately, it was designed by a valve (tube) fanatic.

I have seen a reference stating 3 to 5 cycles (60ms to 100mS) may be enough to achieve close to steady state conditions but I generally look at the first 500mS using this software or 1500ms to 2000mS for steady state.
 
First: The soft start is mainly to avoid blowing your mains fuses (in the wall) and also not be forced to have unnecessary big fuses in the amp.

You don't need a softstart for charging the caps, only for "charging" the magnetic field in the transformer.

The time is 0.3-0.6 seconds only. EDIT as Andrew says only a few mains periods is enough.
 
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