Schmitt Trigger Calculator Formula

Understand the math behind the schmitt trigger calculator. Each variable explained with a worked example.

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Formulas Used

Upper Threshold (V_TH)

v_upper = v_sat_pos * r1_kohm / (r1_kohm + r2_kohm)

Lower Threshold (V_TL)

v_lower = v_sat_neg * r1_kohm / (r1_kohm + r2_kohm)

Hysteresis Width

hysteresis = (v_sat_pos - v_sat_neg) * r1_kohm / (r1_kohm + r2_kohm)

Variables

VariableDescriptionDefault
v_sat_posPositive Saturation(V)12
v_sat_negNegative Saturation(V)-12
r1_kohmR1 (input to inv.)(kΩ)10
r2_kohmR2 (feedback to non-inv.)(kΩ)100

How It Works

Inverting Schmitt Trigger

Formulas

V_TH = V_sat+ x R1 / (R1 + R2)

V_TL = V_sat- x R1 / (R1 + R2)

Hysteresis = (V_sat+ - V_sat-) x R1 / (R1 + R2)

The ratio R1/(R1+R2) sets the threshold as a fraction of the saturation voltages.

Worked Example

Op-amp saturates at +/-12 V, R1 = 10k, R2 = 100k.

v_sat_pos = 12v_sat_neg = -12r1_kohm = 10r2_kohm = 100
  1. 01V_TH = 12 x 10/110 = 1.091 V
  2. 02V_TL = -12 x 10/110 = -1.091 V
  3. 03Hysteresis = 24 x 10/110 = 2.182 V

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