Standard comparators such as LM2903 and LM311 have open collector outputs. I see many times the output of these comparators are tied to Vcc by a pull-up resistor (e.g. in a Schmitt trigger case). Eventhough there is a question about why it is tied to Vcc here: Why do they usually make comparators open collector? I still don't understand the reason.
Anyway my question is not that. It is about calculation of hysteresis. Many times for Schmitt trigger hysteresis calculation I was given the following link: http://www.random-science-tools.com/electronics/inverting-schmitt-trigger-calculator.htm
But this calculator I suppose does not take into account the pull-up resistor.
Imagine using a pull-up resistor to Vcc for a Schmitt trigger in an open-collector output comparator such as: 
Would the hysteresis calculation include this pull-up resistor (R3)? Does it have effect on the hysteresis?
Answer
The output pullup resistor does play a role in the calculation for the case of setting the high threshold. R3's value is essentially in series with the R4 feedback resistor. In similar manner when computing the low threshold the output impedance of the comparator is added to R4.
In both cases the output impedance and the R3 pullup value are typically much smaller values as compared to the value of the feedback resistor. You may have a pullup of 1K ohm and and an output impedance of 20 ohms and yet a feedback resistor on the order of 100K ohms or more. This makes the net contribution of their value to the threshold values rather small so that it is often simply ignored.
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