GATE 2017 EC (EC2) – Question 51
In the circuit shown, Q1 and Q2 are each biased at collector current 2.6 mA. Assume their current gains are sufficiently large that collector and emitter currents may be equated. With thermal voltage 26 mV, the magnitude of mid-band voltage gain $V_o/V_s$, up to second decimal place, is ________.
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Correct answer: 49.0 to 51.0
Explanation
Each transistor has $g_m=I_C/V_T=2.6\ \mathrm{mA}/26\ \mathrm{mV}=0.1$ S. The capacitor holds Q2's base at AC ground in the mid-band.
Looking into Q2's emitter gives incremental resistance approximately $1/g_m=10\ \Omega$. Q1 therefore sees this emitter degeneration, equal to its own intrinsic emitter resistance. Its base-emitter signal is half the applied source voltage.
The gain is $-g_mR_C/2=-0.1(1000)/2=-50$. The requested magnitude is **50.00**, within the official 49–51 interval.