Hysteresis Comparator Calculator

Design inverting Schmitt triggers with precision. Compute upper threshold VUT (switching high→low), lower threshold VLT (low→high), hysteresis width, and midpoint. Visualize the transfer characteristic on an interactive graph. Essential for noise‑immune comparator design, signal conditioning, and debouncing.

Voltage at the non‑inverting input (threshold center reference).
Comparator output high voltage (e.g., VCC).
Comparator output low voltage (e.g., GND).
Resistor from output to non‑inverting input.
Resistor from non‑inverting input to VREF.
Enter all voltages in volts, resistances in kΩ. Inverting hysteresis topology: input signal is applied to the inverting terminal. R1 and R2 form a positive feedback network around the non‑inverting input.
? 5V logic, VREF=2.5V (R1=R2=10k)
⚡ 3.3V logic, VREF=1.65V
? Wide hysteresis (R1=47k, R2=10k, Vref=2.5V)
? Narrow hysteresis (R1=2.2k, R2=100k, Vref=1.8V)
±5V comparator (Voh=5V, Vol=-5V, Vref=0V)
Local computation: All calculations run in your browser – no data uploaded. Circuit theory based on TI Application Report SNVA997 and Sedra/Smith.

What is Hysteresis in Comparators?

A hysteresis comparator (Schmitt trigger) uses positive feedback to create two distinct threshold voltages: an upper threshold VUT and a lower threshold VLT. In the inverting topology (input at the inverting terminal), when the input voltage rises above VUT, the output switches from high to low. When the input falls below VLT, the output returns from low to high. This eliminates oscillations and provides noise immunity – critical for real‑world environments with noisy signals or slowly varying inputs.

For an inverting Schmitt trigger (input at inverting terminal):

VUT = VREF · \frac{R_2}{R_1+R_2} + VOH · \frac{R_1}{R_1+R_2}

VLT = VREF · \frac{R_2}{R_1+R_2} + VOL · \frac{R_1}{R_1+R_2}

Hysteresis width ΔV = (VOH – VOL) · \frac{R_1}{R_1+R_2}

Midpoint Vcenter = (VUT + VLT)/2

Design Principles & Derivation

The equations are derived by applying superposition at the non‑inverting input. The voltage at the non‑inverting pin is set by VREF and the output through the resistive divider R1–R2: V+ = VREF·R2/(R1+R2) + Vout·R1/(R1+R2). The comparator switches when the input voltage at the inverting terminal equals V+. Solving for the input voltage that causes switching yields the formulas above. The resistor divider factor for VREF is β = R2/(R1+R2). The hysteresis width increases with larger R1/R2 ratio, providing excellent noise rejection.

Otto H. Schmitt invented the circuit in 1934, and today hysteresis comparators are essential in sensor interfaces, zero‑crossing detectors, battery management systems, and switch debouncing.

Why Use This Interactive Calculator?

  • Noise Rejection: Determine exact thresholds to avoid false toggling in industrial controls or automotive electronics.
  • Educational Clarity: Visualize how R1/R2 ratio shifts the hysteresis window. Experiment instantly.
  • Rapid Prototyping: Obtain resistor values to match desired voltage margins for ADC input protection or signal conditioning.
  • Bidirectional Analysis: See both rising and falling transfer curves on the same graph – understand the loop.

Step‑by‑Step Calculation Procedure

  1. Enter VREF, VOH, VOL, R1, R2.
  2. The calculator computes the voltage divider factor R1/(R1+R2) and R2/(R1+R2).
  3. VUT = VREF·R2/(R1+R2) + VOH·R1/(R1+R2).
  4. VLT = VREF·R2/(R1+R2) + VOL·R1/(R1+R2).
  5. Hysteresis width ΔV = (VOH – VOL)·R1/(R1+R2).
  6. The interactive graph draws the transfer characteristic for the inverting Schmitt trigger with vertical transitions at the thresholds.

Reference Table: Common Hysteresis Scenarios

Application VOH/VOL VREF R1, R2 VUT / VLT Hysteresis Width
5V logic noise filter 5V / 0V 2.5V 10k, 10k 3.750V / 1.250V 2.500V
3.3V sensor interface 3.3V / 0V 1.65V 10k, 10k 2.475V / 0.825V 1.650V
Narrow hysteresis (precision) 5V / 0V 1.8V 2.2k, 100k 1.869V / 1.761V 0.108V
Wide hysteresis (large noise) 5V / 0V 2.5V 47k, 10k 4.561V / 0.439V 4.122V
Bipolar comparator +5V / -5V 0V 10k, 10k 2.5V / -2.5V 5.0V
Case Study: Audio Signal Peak Detector

An audio peak detector requires clean switching without chatter. Using a comparator with hysteresis (VREF=1.5V, VOH=5V, VOL=0V, R1=22k, R2=10k): VUT = 1.5·(10/32) + 5·(22/32) ≈ 0.469 + 3.437 = 3.906V, VLT = 0.469 + 0 = 0.469V, ΔV = 5·(22/32) ≈ 3.437V. The calculator quickly optimizes thresholds; the interactive graph helps engineers verify the safety margin before PCB layout.

The Role of the Feedback Network

The ratio R1/(R1+R2) directly controls the hysteresis width: ΔV = (VOH – VOL)·(R1/(R1+R2)). For proper operation, VREF should be chosen between VOH and VOL (or the thresholds will be inverted). Typical resistor values range from 1kΩ to 1MΩ. The calculator assumes ideal comparator with infinite input impedance.

Common Misconceptions Clarified

  • Hysteresis always increases noise immunity: Yes, but excessive hysteresis reduces resolution – trade‑off must be balanced.
  • VREF is the midpoint of the thresholds: Only when VOH = –VOL (symmetric supplies). Otherwise the midpoint shifts.
  • Only non‑inverting topologies exist: Inverting Schmitt triggers are equally common; this calculator covers the inverting case with correct formulas.
  • Output swing exactly equals supply rails: Real comparators have saturation voltages, but you may enter effective VOH/VOL from datasheet.

Applications Across Engineering Fields

  • Power Electronics: Hysteresis controllers for buck/boost converters.
  • Automotive: Window comparators for battery over‑voltage/under‑voltage protection.
  • IoT Sensors: Clean digital output from analog temperature or light sensors.
  • Test Equipment: Zero‑crossing detectors with robust switching.

Based on rigorous circuit theory – This tool implements classical feedback analysis from “Microelectronic Circuits” by Sedra & Smith, and “The Art of Electronics” by Horowitz & Hill. Formulas validated against Texas Instruments application notes (SNOA997). Reviewed by GetZenQuery tech team, updated May 2026.

Frequently Asked Questions

VUT is the input voltage at which the output transitions from high to low. VLT is the input voltage where the output returns from low to high. The difference is the hysteresis width.

Real comparators have finite output resistance, input bias currents, and propagation delays. The calculator assumes ideal behavior; always consult your device datasheet and add small safety margins.

Double‑precision floating point is used, yielding 15+ decimal digits. For practical resistor tolerances (±1% or ±5%), rounding to 3‑4 decimals is sufficient.

The calculator will detect invalid resistance and show a warning. Positive resistances are required for proper feedback.
References: TI Application Report: Comparator Hysteresis; Sedra/Smith "Microelectronic Circuits", 8th Ed.; Wikipedia: Schmitt Trigger.