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For ground sense comparators, there is a period where Low level is output regardless of input while the power is turned ON, but will it fluctuate during the power up time?
The area where the comparator output becomes low is determined by the value of the supply voltage and not the power-up time. While the power supply voltage VCC is in the vicinity of 0V to 0.7V the internal circuit is turned completely OFF and the High pull-up point is output, regardless of input. While VCC is between 0.7V and 1.4V the input transistor does not operate and the output transistor turns ON and outputs Low. Ultimately, when it exceeds 1.4V normal comparator operation will be performed. The guaranteed operating voltage listed in the datasheet is greater than 2V.