Op-Amp Schmitt Trigger Hysteresis

Vhyst = Vref × R1 / (R1 + R2)

Quick answer

This calculator solves V_hyst = V_sat × R₁ / (R₁ + R₂) for Hysteresis Voltage. With Saturation Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, the result is 8.25 V. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Hysteresis Voltage (V)
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Formula

V_hyst = V_sat × R₁ / (R₁ + R₂)

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.

Symbols and units

Symbol Meaning Default unit Accepted units
Vhyst Hysteresis Voltage V pV, nV, µV, mV, V, kV
Vref Saturation Voltage V pV, nV, µV, mV, V, kV
R1 Feedback Resistor kΩ mΩ, Ω, kΩ, MΩ
R2 Input Resistor kΩ mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Saturation Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
  2. 2. The relation: V_hyst = V_sat × R₁ / (R₁ + R₂)
  3. 3. Substitute: Vref = 26.4 V, R1 = 10 kΩ, R2 = 22 kΩ
  4. 4. Result: Hysteresis Voltage = 8.25 V

Related quantities from the same inputs

  • P = V² / R = 69.7 mW
  • I = V / R = 2.64 mA

Worked examples

Minimum range

Given: Saturation Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ

Result: Hysteresis Voltage = 0.2269 V

Low range

Given: Saturation Voltage 7.26 V, Feedback Resistor 1 kΩ, Input Resistor 2.2 kΩ

Result: Hysteresis Voltage = 2.269 V

Typical

Given: Saturation Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ

Result: Hysteresis Voltage = 8.25 V

High range

Given: Saturation Voltage 0.506 kV, Feedback Resistor 100 kΩ, Input Resistor 0.22 MΩ

Result: Hysteresis Voltage = 158.1 V

Maximum range

Given: Saturation Voltage 5.06 kV, Feedback Resistor 1 MΩ, Input Resistor 2.2 MΩ

Result: Hysteresis Voltage = 1.581 kV

Solving for each variable

Solve for Hysteresis Voltage

Saturation Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → 0.2269 V

Solve for Saturation Voltage

Hysteresis Voltage 0.33 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → 1.056 V

Solve for Feedback Resistor

Hysteresis Voltage 0.33 V, Saturation Voltage 0.726 V, Input Resistor 0.22 kΩ → 0.1833 kΩ

Solve for Input Resistor

Hysteresis Voltage 0.33 V, Saturation Voltage 0.726 V, Feedback Resistor 100 Ω → 120 Ω

How Hysteresis Voltage changes with Saturation Voltage

Saturation Voltage (input) Hysteresis Voltage (result)
2.64 V 0.825 V
6.6 V 2.063 V
13.2 V 4.125 V
19.8 V 6.187 V
26.4 V 8.25 V
39.6 V 12.37 V
52.8 V 16.5 V
105.6 V 33 V
0.1848 kV 57.75 V
0.264 kV 82.5 V

The same result in other units

Unit Value
µV 8250000
mV 8250
V 8.25
kV 0.00825

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Frequently asked questions

How do you calculate Op-Amp Schmitt Trigger Hysteresis?

Use V_hyst = V_sat × R₁ / (R₁ + R₂). With Saturation Voltage 26.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, Hysteresis Voltage works out to 8.25 V.

What is the formula for Op-Amp Schmitt Trigger Hysteresis?

The formula is V_hyst = V_sat × R₁ / (R₁ + R₂). A Schmitt trigger uses positive feedback to create two distinct switching thresholds, separated by the hysteresis voltage.

How do you find Saturation Voltage when you know the other values?

Rearrange for Saturation Voltage: with Hysteresis Voltage 0.33 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ, Saturation Voltage is 1.056 V.

How do you find Feedback Resistor when you know the other values?

Rearrange for Feedback Resistor: with Hysteresis Voltage 0.33 V, Saturation Voltage 0.726 V, Input Resistor 0.22 kΩ, Feedback Resistor is 0.1833 kΩ.

What units does Op-Amp Schmitt Trigger Hysteresis use?

Hysteresis Voltage is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Op-Amps formulas →
Non-Inverting Amplifier Inverting Amplifier Summing Amplifier Difference Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain Op-Amp Schmitt Trigger Hysteresis

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