Electronic comparator

An electronic comparator is an electrical circuit that converts the ordering of two input electric potential differences into an output state. For the usual non-inverting convention, the output is high when $V_{+}>V_{-}$ and low when $V_{+}<V_{-}$. Unlike a linear amplifier, an electronic comparator deliberately makes a threshold decision; its output does not report how large the input difference is. A sensor signal can therefore become a pulse marking the instant it crosses a reference.

Real threshold decisions have an input offset voltage and a finite propagation delay. The permitted input range and the output drive also matter: an open-drain output needs a pull-up resistor, whereas a push-pull output drives both states. The manufacturer’s inverting example explicitly includes the pull-up resistor and explains how input offset voltage, resistor tolerances and internal hysteresis affect the thresholds.^[ref]

With a single threshold, a slowly varying input plus electrical noise can cause repeated transitions. A Schmitt trigger adds hysteresis: the threshold depends on the existing output state. For an illustrative non-inverting design, suppose the output switches high on a rise through $2.55\mathrm{V}$ and low on a fall through $2.45\mathrm{V}$. At $2.50\mathrm{V}$, either output is possible, depending on the preceding input. The $0.10\mathrm{V}$ interval is deliberate memory of the last state, rather than an ambiguous instantaneous comparison. Positive feedback can produce this behavior; the cited design derives the two thresholds from the feedback resistor network.^[ref]

A useful bench demonstration applies a slow triangular input with a small superposed ripple and displays both input and output on an oscilloscope. Record the rising and falling switching levels separately. Repeated transitions near one level demonstrate noise sensitivity; distinct rising and falling levels demonstrate hysteresis. The time between an input crossing and the output transition measures propagation delay, a different quantity from the separation between the two thresholds.

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]