GATE 2017 EC (EC2) – Question 52
In the voltage-reference circuit shown, the op-amp is ideal. Transistors Q1,Q2,…,Q32 are identical and have infinite common-emitter current gain. Their collector current obeys $I_C=I_Se^{V_{BE}/V_T}$, where $I_S$ is the saturation current. The indicated voltage $V_p$ is 0.7 V and $V_T=26$ mV. The output $V_{out}$ (in volts) is ________.
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Correct answer: 1.1 to 1.2
Explanation
Let $V_1$ be Q1's base-emitter voltage. The ideal op-amp makes its two input voltages equal. Since both top resistors are 20 kΩ, their currents are equal, say I.
One branch feeds Q1 alone; the other feeds the 31 parallel transistors Q2 through Q32. Each transistor in that bank therefore carries $I/31$, while Q1 carries I. The exponential current law gives $V_1-V_p=V_T\ln31$.
This voltage appears across 5 kΩ, so $I=(V_1-V_p)/5000$. Finally $V_{out}=V_1+20000I=V_p+5V_T\ln31$.
Substitution gives $0.7+5(0.026)\ln31=$ **1.1464 V**, within the official 1.1–1.2 V interval.