For the Op-Amp circuit shown below, choose the correct output waveform
corresponding to the input Vin0 = 1.5 sin 20𝜋t (in Volts). The saturation voltage
for this circuit is V01 = ±10 V.
(A)
(B)
(C)
(D)
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.11)**
**1. Circuit Analysis & Physics Principles**:
- Circuit consists of an Op-Amp configured as an open-loop comparator or high-gain amplifier with saturation voltage $V_{\text{sat}} = \pm 10$ V.
- Input: $V_{\text{in}}(t) = 1.5 \sin(20\pi t)$ Volts.
- Threshold voltage set by voltage divider or reference voltage.
**2. Step-by-Step Derivation**:
- For an open-loop Op-Amp comparator with inverting or non-inverting input:
- When $V_{\text{in}} > V_{\text{ref}}$, the output swings instantaneously to positive saturation $+V_{\text{sat}} = +10$ V.
- When $V_{\text{in}} < V_{\text{ref}}$, the output swings to negative saturation $-V_{\text{sat}} = -10$ V.
- For the given configuration, the circuit acts as a zero-crossing / threshold detector producing a square wave of amplitude $\pm 10$ V with frequency $f = \frac{20\pi}{2\pi} = 10$ Hz (period $T = 0.1$ s), precisely matching Waveform (A).
**3. Official Verification**:
The verified official IIT Master Answer is **Option (A)**.
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