# Hysteresis calculation for "open-collector output comparator" with a pull-up resistor

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?

## 1 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.

• If lets say the feedback resistor is (R4) is 220K, what would you choose the pull-up resistor (R3) to ignore its effect on hysteresis? Is there a practical ratio? Commented Mar 7, 2016 at 13:46
• Like I said in my answer already....1K maybe 2.2K. The ratio of 100 or more leads to the pullup contribution being quite small. On the other hand you could simply throw it in as a feedback of 221K or 222.2K into the calculations. That would really only be applicable to the most exacting calculations in a precision circuit with very accurate temperature stable resistors and a comparator with a very very low differential offset voltage range. Commented Mar 7, 2016 at 13:53
• i used to set R3 equal to R4. Commented Mar 7, 2016 at 13:55
• This output will be connected to a load by the way. Would that be also 100 times greater than R3 not to effect hysteresis? Commented Mar 7, 2016 at 13:57
• by load I mean to a voltage divider which will be fed to a Daq Commented Mar 7, 2016 at 14:00