Question E6C01:
What is the function of hysteresis in a comparator?  

Choices:  
A: To prevent input noise from causing unstable output signals  
B: To allow the comparator to be used with AC input signals  
C: To cause the output to continually change states  
D: To increase the sensitivity    

Correct Answer is  A: To prevent input noise from causing unstable output signals  

Correct answer: A — To prevent input noise from causing unstable output signals

1) Why A is correct
- Adding hysteresis (positive feedback) to a comparator creates two distinct switching thresholds: one for rising input and one for falling input.  
- This prevents “chatter” when the input hovers near the threshold, because small noise spikes cannot flip the output back and forth.

Common Schmitt-trigger behavior:
- If input is rising, the output switches high only after $V_{IN} > V_{TH+}$.
- If input is falling, the output switches low only after $V_{IN} < V_{TH-}$.
- The separation $\Delta V_H$ between $V_{TH+}$ and $V_{TH-}$ sets the noise immunity.

2) Why the other choices are incorrect
- B: “To allow the comparator to be used with AC input signals” — Comparators can already compare time-varying (AC) signals without hysteresis. Hysteresis is for noise immunity, not AC compatibility.
- C: “To cause the output to continually change states” — The opposite is true; hysteresis prevents rapid, repeated switching near the threshold.
- D: “To increase the sensitivity” — Hysteresis reduces sensitivity to small variations near the threshold to avoid false triggering.

3) Useful formulas and rules of thumb
For an inverting Schmitt trigger with positive feedback to the non-inverting input via a divider $R_1$ (from output) and $R_2$ (to ground), let $V_{OH}$ and $V_{OL}$ be the comparator output levels and $\beta = \dfrac{R_2}{R_1 + R_2}$.

Thresholds:
$$V_{TH+} = \beta V_{OH}, \quad V_{TH-} = \beta V_{OL}$$

Hysteresis width:
$$\Delta V_H = V_{TH+} - V_{TH-} = \beta \left( V_{OH} - V_{OL} \right)$$

With symmetric rails $V_{OH} \approx +V_{SAT}$ and $V_{OL} \approx -V_{SAT}$:
$$V_{TH\pm} = \pm \beta V_{SAT}, \quad \Delta V_H = 2 \beta V_{SAT}$$

Rule of thumb:
- Choose $\Delta V_H$ greater than the expected peak noise on the input (often set to at least 2× the peak noise, or several times the noise RMS) to avoid false toggling.