Schmitt trigger

A Schmitt trigger is a threshold circuit with hysteresis: its switching level depends on its current output state. An input rising through an upper threshold causes one transition, whereas an input falling through a lower threshold causes the reverse transition. Between the thresholds, the circuit retains the state reached previously. This makes a Schmitt trigger useful for turning a slowly varying or noisy signal into clean transitions, rather than repeatedly switching whenever noise crosses a single reference level.^[ref]

A simple inverting implementation puts the signal on the negative input of an electronic comparator. Connect its positive input to output $V_o$ through a resistor $R_o$ and to a reference $V_r$ through a resistor $R_r$. Neglecting comparator input current, Kirchhoff's current law givesFor ideal high and low output levels $V_H,V_L$, the input switches on a rise at $V_{\uparrow }=\alpha V_H+(1-\alpha )V_r$ and on a fall at $V_{\downarrow }=\alpha V_L+(1-\alpha )V_r$. Thus the separation of the switching thresholds isThe output feeds back so as to reinforce its new state: after a rising input makes the output low, the positive-input threshold falls too.

For illustrative values $R_o=90\mathrm{k\Omega }$, $R_r=10\mathrm{k\Omega }$, $V_r=2.5\mathrm{V}$, $V_H=5\mathrm{V}$ and $V_L=0$, the thresholds are $2.75\mathrm{V}$ and $2.25\mathrm{V}$. At an input of $2.50\mathrm{V}$, the output can be either high or low, depending on the preceding trajectory. These chosen numbers describe the ideal circuit above, not a particular device specification.

An oscilloscope demonstration applies a slow triangular input with a small ripple and records input and output together. Compare the rising and falling transition levels, and then reduce the threshold separation to see when the ripple produces additional transitions. In a real circuit, input offset voltage, resistor tolerances, output loading and any internal hysteresis change the thresholds. An open-drain output also requires a pull-up resistor; its load must be included in the feedback calculation.^[ref]