Comparator Hysteresis Calculator

Design or analyse inverting and non-inverting comparator thresholds, with standard resistor values, reference voltage and worst-case resistor, offset and reference bounds.

Method, formulas and references

Threshold equations

The circuit uses a stiff reference Vref, an effective resistor R and a feedback resistor RF from Vout to IN+. Input bias current and intrinsic hysteresis are zero in this model. The entered VOH and VOL are constant loaded output voltages.

Inverting: Vin connects to IN−; R connects Vref to IN+. With k = R/RF, VH = (Vref + k·VOH)/(1 + k) and VL = (Vref + k·VOL)/(1 + k). A reference divider can be replaced by its Thevenin voltage and resistance; include that resistance in R.

Non-inverting: R connects Vin to IN+ and Vref connects to IN−. VH = Vref(1 + k) − k·VOL and VL = Vref(1 + k) − k·VOH. Include any source resistance in R. The reference is assumed unloaded at IN−.

Design and bounds

Let b = (VH − VL)/(VOH − VOL). Inverting design requires 0 < b < 1: RF = R(1 − b)/b and Vref = (VL − b·VOL)/(1 − b). Non-inverting: RF = R/b and Vref = (VH + b·VOL)/(1 + b). The standard resistors are independently rounded to the nearest selected E-series value; their calculated thresholds use the exact reference voltage.

Independent resistor corners, ±reference uncertainty and ±constant input offset are evaluated. Switching is defined by IN+ = IN− + Vos. Each threshold band is an independent bound across devices. Hysteresis width is evaluated with the same offset/reference for both transitions, so those constant terms cancel. Output-voltage uncertainty, intrinsic hysteresis, bias-current error, reference-divider component correlations, propagation delay and dynamic output loading are excluded. Use worst-case loaded output levels and check the comparator’s common-mode and supply limits. Open-drain circuits need a pull-up/loading model beyond this calculation.

References

TI TLV3201/TLV3202, SBOS561C, §8.1.2: inverting and non-inverting external hysteresis networks; Figure 8-5 provides the 330 kΩ / 1 MΩ, 2.5 V reference example.
TI SBOA219B, Comparator With and Without Hysteresis Circuit: positive feedback, threshold accuracy and noise at a switching point.
IEC 60063, preferred number series. Series selection does not specify resistor tolerance.

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