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I find this circuit from ON Semiconductor's LM211 datasheet.

enter image description here

There is a 1M resistor from negative power rail to the 'reference' input. ON doesn't describe the circuit's function. I think it's a 'zero-crossing' detector, but why give it a small negative bias (about 1.5mV ?) ?

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That would appear to be part of the hysteresis feedback path. It's part of the voltage divider with the other half being the 510k ohm resistor coming from the output. In that way, it takes a touch more input voltage change to switch between high and low output. Just by adding a few mV of difference to the input side reference, you can drown out noise-caused switching.

For more info:
What is a Schmitt Trigger and its application exactly? http://www.ecircuitcenter.com/Circuits/op_comp/op_comp.htm

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