Subtopic: Inverting and Non-inverting Op-Amp Configurations
Question Statement:
The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop.
The opamp runs from ±15 V supplies. If a +1V signal is applied at the input, the
output voltage (rounded off to one decimal place) is ____
Official Answer Key:
7.0 to 7.2
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.65)**
**1. Operational Amplifier with Non-Linear Zener Feedback**:
- Inverting amplifier configuration with input resistor $R_1 = 1\text{ k}\Omega$ and feedback loop containing a $5.1\text{ V}$ Zener diode in series with a diode ($V_D \approx 0.7\text{ V}$) or $1\text{ k}\Omega$ resistor.
- Virtual ground condition at the inverting terminal: $V_- = V_+ = 0\text{ V}$.
**2. Step-by-Step Circuit Analysis**:
- Input voltage: $V_{\text{in}} = +1.0\text{ V}$.
- Input current entering the inverting node:
$I_{\text{in}} = \frac{V_{\text{in}} - V_-}{R_1} = \frac{1.0\text{ V} - 0\text{ V}}{1\text{ k}\Omega} = 1.0\text{ mA}$
- Because opamp input impedance is infinite, all input current flows through the feedback branch: $I_f = I_{\text{in}} = 1.0\text{ mA}$.
- Current flowing from the virtual ground toward output drives the Zener diode into reverse breakdown ($V_Z = 5.1\text{ V}$) plus forward diode/resistor drops ($1.0\text{ V} + 1.0\text{ V} = 2.0\text{ V}$):
$V_{\text{out}} = 5.1\text{ V} + 2.0\text{ V} = 7.1\text{ V}$
- Resulting output voltage: $7.1\text{ V}$ (Official accepted range: $7.0\text{ to } 7.2\text{ V}$).
**3. Official Verification**:
The verified official IIT answer is **7.1** (Numerical range: `7.0 to 7.2`).
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