Consider Op-Amp biasing voltage as ±15V. The threshold voltages for Schmitt trigger is :

Concept:

A Schmitt trigger is a comparator circuit with hysteresis, meaning it has two distinct threshold voltages: one for the rising input (upper threshold) and one for the falling input (lower threshold).

The threshold voltages are determined by the positive feedback network. For a non-inverting Schmitt trigger configuration using an op-amp, the threshold voltage is given by:

\( V_T = V_{out} \cdot \frac{R_2}{R_1 + R_2} + V_{ref} \cdot \frac{R_1}{R_1 + R_2} \)

Given:

R₁ = 2 kΩ, R₂ = 1 kΩ

V_out = ±15V (op-amp saturation levels)

V_ref = 3V (battery at non-inverting terminal)

Calculation:

Feedback fraction = R₂ / (R₁ + R₂) = 1 / (2 + 1) = 1/3

Battery contribution = V_ref · (R₁ / (R₁ + R₂)) = 3 · (2 / 3) = 2V

Case 1: When V_out = +15V:

\( V_{UTP} = \frac{15}{3} + 2 = 5 + 2 = 7V \)

Case 2: When V_out = -15V:

\( V_{LTP} = \frac{-15}{3} + 2 = -5 + 2 = -3V \)

Final Answer:

Threshold voltages are: 7V (upper), −3V (lower)

Correct Option: 3) 7V, −3V