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GATE 2020 EC – Question 45

Analog Circuits · BJT and MOSFET Amplifiers · 2 marks · Multiple choice

For the BJT in the amplifier shown below, $V_{BE}=0.7$ V, $kT/q=26$ mV. Assume that BJT output resistance ($r_o$) is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input $V_i$ is direct coupled. The low frequency voltage gain $v_o/v_i$ of the amplifier is

Diagram for GATE 2020 EC question 45
  1. $-89.42$
  2. $-128.21$
  3. $-178.85$
  4. $-256.42$

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Show answer and explanation

Correct answer: (A) $-89.42$

Explanation

DC bias: the base is at 0 V, so $I_E=\frac{0-0.7-(-10)}{20\text{ k}\Omega}=0.465$ mA and $I_C\approx0.465$ mA. Then $g_m=\frac{I_C}{V_T}=\frac{0.465\text{ mA}}{26\text{ mV}}=17.9$ mS. The emitter is bypassed by $C_E$, so the gain is $-g_m(R_C\|R_L)=-17.9\text{ mS}\times5\text{ k}\Omega=-89.4$.