Op-Amp Schmitt Trigger Hysteresis

Formula

Description

A Schmitt trigger uses positive feedback to create two distinct switching thresholds, separated by the hysteresis voltage. The non-inverting Schmitt trigger feeds back a fraction of the output saturation voltage to the non-inverting input through R₁, creating an upper threshold (V_ref + Vhyst) and a lower threshold (V_ref − Vhyst). Hysteresis prevents oscillation when the input signal is noisy or slowly changing, making Schmitt triggers essential for clean digital signal generation from analog inputs. Applications include zero-crossing detectors with noise immunity, level detectors, and oscillator circuits.

Variables

• V_hyst — Half the hysteresis window (V)
• V_ref — Output saturation voltage (V, typically V+ or V+ − 1.5 V for rail-to-rail)
• R₁ — Positive feedback resistor (Ω)
• R₂ — Series input resistor (Ω)

Practical Notes

The total hysteresis window is 2 × Vhyst. For a CMOS op-amp with rail-to-rail output (Vsat ≈ Vcc = 5 V) and R1 = 10 kΩ, R2 = 100 kΩ: Vhyst = 5 × 10k/110k ≈ 0.45 V, giving a total window of 0.9 V. Too little hysteresis fails to reject noise; too much makes the circuit less sensitive. For power supply supervisors, typical hysteresis is 1-5% of the threshold voltage.