What is the formula for Hysteresis Comparator (Schmitt Trigger)?

Core formula: ΔV = (Voh − Vol)·R1/(R1+R2) (inverting) | ΔV = (Voh − Vol)·R1/R2 (non-inverting). The tool returns results instantly using this formula and the selected parameters.

Hysteresis Comparator (Schmitt Trigger)

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Comparator positive-feedback hysteresis network: for the inverting / non-inverting topologies, derive the upper and lower trip points and hysteresis width from R1/R2 and the output swing, bound the width / trip-point error with the resistor tolerance, or pick standard resistors and a reference voltage from target trip points.

Key points

Hysteresis Comparator (Schmitt Trigger): Comparator positive-feedback hysteresis network: for the inverting / non-inverting topologies, derive the upper and lower trip points and hysteresis width from R1/R2 and the output swing, bound the width / trip-point error with the resistor tolerance, or pick standard resistors and a reference voltage from target trip points. Formula: ΔV = (Voh − Vol)·R1/(R1+R2) (inverting) | ΔV = (Voh − Vol)·R1/R2 (non-inverting). Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. The comparator positive / negative supply rails must cover the reference, the trip points and the output swing: a single supply (V− = 0) only handles 0–V+, so any negative trip point, negative reference or negative output swing requires a negative supply — otherwise the comparator cannot toggle (a common cause of “hysteresis not working”). Hysteresis width = output swing × positive-feedback factor: increase R1 (inverting) or R1/R2 (non-inverting) for more noise immunity, but too wide costs sensitivity and pushes the trip points toward the output rails.

Inputs

ΔV = (Voh − Vol)·R1/(R1+R2) (inverting) | ΔV = (Voh − Vol)·R1/R2 (non-inverting)

TopologyDirectionPositive supply rail V+VComparator positive supply (Vcc); used to verify that the output / reference / trip points are reachableNegative supply rail V−VEnter 0 for single supply / ground; must be negative when a negative output swing or negative reference is needed (e.g. −5 in a ±5 V system)Output high level VohVUse the actual output high level (including saturation drop / pull-up voltage), not the supply railOutput low level VolVAn open-drain / OC output is about 0 V without a pull-up; a push-pull output uses its saturation drop; may be negative in ± swing systemsReference voltage VrefVResistor R1kΩInverting: Vref→non-inverting input; non-inverting: Vin→non-inverting inputResistor R2kΩPositive-feedback resistor: output→non-inverting inputSource resistance RskΩIn the non-inverting topology Rs adds to R1 and makes the trip points drift with source resistance; negligible in the inverting topologyInput bias current IbnAAbout 25 nA for the LM393; CMOS comparators go down to the pA rangeResistor tolerance%Used to bound the trip-point and hysteresis-width error from R1/R2 tolerance

Calculation model (updates with parameters)

Upper trip point VT+ (switches on rising input)	2.727 V	Vref + (Voh−Vref)·R1/(R1+R2)
Lower trip point VT− (switches on falling input)	2.273 V	Vref + (Vol−Vref)·R1/(R1+R2)
Hysteresis width ΔV	454.5 mV	(Voh−Vol) × factor = 5 V × 0.0909
Hysteresis width range (resistor tolerance)	446.3 mV ~ 462.9 mV	±1.00% resistor worst case: nominal 454.5 mV
Trip-point range (resistor tolerance)	VT+ 2.723 V~2.731 V ｜ VT− 2.269 V~2.277 V	±1.00% resistor worst case
Maximum resistor-mismatch error	±4.166 mV	maximum trip-point shift; hysteresis width error -1.80% ~ +1.83%
Trip-point center voltage	2.5 V
Positive-feedback factor	0.0909	k = R1/(R1+R2)
Threshold network Thevenin resistance R_eq	9.091 kΩ	R1∥R2 (Thevenin impedance at the + input)
Bias-current trip-point offset Ib·R_eq	227.3 µV	of hysteresis width 0.05%; should be << ΔV

Engineering notes

The comparator positive / negative supply rails must cover the reference, the trip points and the output swing: a single supply (V− = 0) only handles 0–V+, so any negative trip point, negative reference or negative output swing requires a negative supply — otherwise the comparator cannot toggle (a common cause of “hysteresis not working”).
Hysteresis width = output swing × positive-feedback factor: increase R1 (inverting) or R1/R2 (non-inverting) for more noise immunity, but too wide costs sensitivity and pushes the trip points toward the output rails.
Voh / Vol must be the actual output levels (including saturation drop or pull-up voltage), not the supply rails, otherwise the calculated hysteresis width comes out too large.
The larger the threshold network resistance R_eq = R1∥R2, the larger the trip-point offset Ib·R_eq from input bias current; for LM393-class parts with Ib around 25 nA, keep R_eq within 1 MΩ.
The reference source impedance must be small compared with R1, otherwise positive-feedback current pulls it and the actual trip points deviate; use a low-impedance divider with a buffer, or a dedicated reference.
In the non-inverting topology R1 sits between the source and the + input, so source resistance adds to R1; if the source impedance is unstable the trip points drift — add a buffer or use the inverting topology.

FAQ

What is Hysteresis Comparator (Schmitt Trigger) for?: Comparator positive-feedback hysteresis network: for the inverting / non-inverting topologies, derive the upper and lower trip points and hysteresis width from R1/R2 and the output swing, bound the width / trip-point error with the resistor tolerance, or pick standard resistors and a reference voltage from target trip points.
What is the formula for Hysteresis Comparator (Schmitt Trigger)?: Core formula: ΔV = (Voh − Vol)·R1/(R1+R2) (inverting) | ΔV = (Voh − Vol)·R1/R2 (non-inverting). The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using Hysteresis Comparator (Schmitt Trigger)?: The comparator positive / negative supply rails must cover the reference, the trip points and the output swing: a single supply (V− = 0) only handles 0–V+, so any negative trip point, negative reference or negative output swing requires a negative supply — otherwise the comparator cannot toggle (a common cause of “hysteresis not working”). Hysteresis width = output swing × positive-feedback factor: increase R1 (inverting) or R1/R2 (non-inverting) for more noise immunity, but…