Schmitt Trigger

A Schmitt trigger is a comparator with built-in hysteresis. It ignores slow drifts and noise near the threshold, making it the standard input stage for noisy signals in industrial sensors and the NE555 timer.

Core Concept

The Schmitt trigger adds positive feedback to a comparator. A fraction of the output is fed back to the non-inverting input. This shifts the threshold in the same direction as the output, creating two distinct trip points: an upper threshold VUT and a lower threshold VLT.

The gap between VUT and VLT is the hysteresis width. Any noise smaller than this gap cannot cause the output to chatter. The output can only change state when the input crosses the appropriate threshold, and once it crosses, the threshold shifts away to prevent re-triggering.

The NE555 timer uses internal Schmitt trigger comparators at 2/3 VCC (upper threshold) and 1/3 VCC (lower threshold). This is the source of the 555 timer's stable switching behaviour in monostable and astable modes.

Key Equations

For an inverting Schmitt trigger with op-amp supply rails +Vsat and -Vsat:

VUT = +Vsat * R1 / (R1 + R2)

VLT = -Vsat * R1 / (R1 + R2)

Where R1 is the resistor to ground and R2 is the resistor from output to non-inverting input. Hysteresis width:

Vh = VUT - VLT = 2 * Vsat * R1 / (R1 + R2)

For a non-inverting Schmitt trigger with reference voltage Vref:

VUT = Vref * (1 + R2/R1) - Vout_low * R2/R1

VLT = Vref * (1 + R2/R1) - Vout_high * R2/R1

Given:
  Op-amp supply = ±12V (so Vsat = 12V)
  R1 = 10 kΩ (to ground from V+ node)
  R2 = 10 kΩ (from Vout to V+ node)

Why this formula:
  VUT and VLT depend on the output voltage and the
  resistor divider ratio R1/(R1+R2)

Formula:
  VUT = +Vsat * R1 / (R1 + R2)
  VLT = -Vsat * R1 / (R1 + R2)

Substitution:
  VUT = +12 * 10,000 / (10,000 + 10,000)
  VLT = -12 * 10,000 / (10,000 + 10,000)

Calculation:
  VUT = 12 * 0.5 = +6V
  VLT = -12 * 0.5 = -6V
  Vh = VUT - VLT = 6 - (-6) = 12V

Final Answer:
  Upper threshold VUT = +6V
  Lower threshold VLT = -6V
  Hysteresis width Vh = 12V

Exam Tip: GATE frequently tests the direction of feedback. Schmitt trigger uses POSITIVE feedback (from output to non-inverting input). Op-amp amplifiers use negative feedback. Confusing the two is the main error. Also, the hysteresis width formula Vh = 2VsatR1/(R1+R2) applies only to the symmetric inverting topology. If the question changes R1 or R2, recalculate from first principles using the voltage divider.

Key Properties

• Positive feedback from output to non-inverting input creates two stable states (bistable operation).
• VUT and VLT are determined by the resistor ratio R1/(R1+R2) and the output saturation voltage.
• Hysteresis width Vh = VUT - VLT. Larger R2 relative to R1 gives narrower hysteresis.
• Noise immunity equals half the hysteresis width on each side of the average threshold.
• The NE555 timer's internal comparators form a Schmitt trigger with thresholds at 1/3 VCC and 2/3 VCC.
• Transfer curve is non-linear: it forms a rectangular hysteresis loop, not a straight line.
• Schmitt triggers are used in TTL logic gates, zero-crossing detectors, and switch debouncing circuits.

Quick Revision

• Feedback goes from output to non-inverting input (positive feedback).
• Two thresholds: VUT (upper) and VLT (lower).
• VUT = +Vsat * R1/(R1+R2), VLT = -Vsat * R1/(R1+R2).
• Vh = 2VsatR1/(R1+R2) is the hysteresis width.
• NE555 uses 1/3 VCC and 2/3 VCC as its internal Schmitt thresholds.
• Larger R1 or smaller R2 increases hysteresis width.
• Used to clean up noisy signals before feeding into digital logic.
• Exam trap: Students write the threshold formula as VsatR2/(R1+R2) instead of VsatR1/(R1+R2). Always check which resistor connects to ground (R1) and which connects from output to V+ (R2), then write the divider correctly.