Powering ON is a simple, yet tough thing to do well.
We simulate ramps, and ramps with dips, and other things, and we test with ramps, but we can't and don't simulate for every possible power supply made.
Thus, the typical power ON specification wants to see a "monotonic" rise.
In the strictest sense, this means that the slope is always the same sign (never stops rising).
Will it work if there is a plateau? Will it work with a slight dip?
Generally, yes. But if you call, and say it does not work with your ABC power supply, and that supply is not monotonic, we can say "sorry, but we warned you that it doesn't work with every possible power supply in the universe."
If you use a power supply that does not comply (for example, all of our listed power partners DO comply), then it is up to you to characterize your board, and be sure it will work with all possible variations of your powering solution.
Now it is clear that Xilinx devices do not tolerate dips. I would also have liked to understand why it is the case. Altera's devices have a similar level of complexity but I have not seen such constrains on their power-on specs.
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