A plain comparator has one threshold: its output flips the instant the input crosses zero. That is fine for a clean signal, but a real signal always carries noise — and near the crossing, the noise pushes the input back and forth across the threshold dozens of times, so the output chatters. The Schmitt trigger fixes this with positive feedback: instead of one threshold it has two, separated by a gap called hysteresis. Noise smaller than the gap cannot flip the output at all.

Figure 1: The Schmitt trigger (a) and its transfer loop (b). The output feeds a fraction of itself back to the + input, so the threshold follows the output — +1.18 V while the output is high, −1.18 V while it is low. (Schematic, not to scale.)

Two thresholds from one divider

The circuit is an op-amp with its output fed back to the + input through a divider, R₁ to ground and R₂ from the output. The + input therefore sits at a fraction of the output voltage:

V₊ = V_out × R₁ / (R₁ + R₂)

With a 741 on ±15 V supplies the output saturates at about ±13 V. Using R₁ = 10 kΩ and R₂ = 100 kΩ, the fraction is 10 / 110 = 0.0909, so:

Upper trip point U_TP = +13 × 0.0909 = +1.18 V  ·  Lower trip point L_TP = −13 × 0.0909 = −1.18 V

Hysteresis = U_TP − L_TP = 2.36 V

When the output is high, the + input sits at +1.18 V, so the input must rise above +1.18 V to flip the output low. Once it is low, the + input sits at −1.18 V, so the input must fall below −1.18 V to flip it back. The output remembers which way the input came from — that is the loop in Figure 1(b).

Worked example — cleaning a 3 V sine with 0.5 V of noise

Feed in a 3 V peak sine at 1 kHz with 0.5 V peak of noise riding on it, near the zero crossings. A plain comparator with a 0 V threshold would flip every time the noise crossed zero — many extra edges per cycle. The Schmitt trigger flips only twice per cycle:

Rising input crosses +1.18 V at arcsin(1.18 / 3) = 23.2° of the cycle → output flips high to low

Falling input crosses −1.18 V at 180° + 23.2° = 203.2° → output flips low to high

The output is low for exactly half the cycle (203.2° − 23.2° = 180°), so it is a clean ±13 V square wave at 1 kHz with 50% duty cycle. The noise cannot cause a single extra flip, because its 1 V peak-to-peak swing is far smaller than the 2.36 V hysteresis gap: once the output has flipped, the threshold has moved 2.36 V away, and the noise cannot reach it.

Design — thresholds of ±2 V

Suppose you need wider thresholds, ±2 V, with the same ±13 V saturation. The divider fraction must be 2 / 13 = 0.154:

R₂ = R₁ × (1 − 0.154) / 0.154 = 5.5 × R₁

Keeping R₁ = 10 kΩ, R₂ = 55 kΩ — the nearest standard value is 56 kΩ, giving U_TP = 13 × 10 / 66 = 1.97 V, essentially the 2 V wanted, with a hysteresis of 3.94 V. The same recipe works for any threshold: pick the fraction from the saturation voltage, then pick the resistors. Note that this circuit is the inverting Schmitt trigger (the input goes to the − input, so the output is high while the input is low); feeding the input to the + input instead makes the non-inverting version.

Key points to remember

• A plain comparator chatters on noise because it has one threshold; the Schmitt trigger has two, separated by hysteresis, so noise smaller than the gap cannot flip the output.
• Worked example: 741 on ±15 V supplies, R₁ = 10 kΩ, R₂ = 100 kΩ give U_TP = +1.18 V, L_TP = −1.18 V, hysteresis 2.36 V.
• A 3 V peak sine with 0.5 V peak noise flips the output only at +1.18 V (23.2° of the cycle) and −1.18 V (203.2°), producing a clean ±13 V square wave at 1 kHz with 50% duty cycle.
• Design example: for ±2 V thresholds, R₂ = 5.5 × R₁; with R₁ = 10 kΩ, the standard 56 kΩ gives U_TP = 1.97 V.
• The + input follows the output — +1.18 V while the output is high, −1.18 V while it is low — which is why the transfer curve is a loop, not a single line.
• Always make the hysteresis wider than the peak-to-peak noise; here 2.36 V against 1 V of noise leaves a comfortable margin.