Comparators and Schmitt Triggers

A comparator outputs high when $V_+ > V_-$ and low otherwise. Dedicated comparators (LM393, open-collector) are faster than op-amps used open-loop.

A slowly changing or noisy input causes the output to chatter around the threshold. Hysteresis, from positive feedback, creates two thresholds:

$V_{TH} - V_{TL} \approx \frac{R_1}{R_1 + R_2}(V_{OH} - V_{OL})$

This Schmitt trigger switches cleanly once, then needs the input to move back past the other threshold. Uses: zero-crossing detection, battery-low alarms, cleaning up sensor and button signals.