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GATE 2023 EC – Question 39

Analog Circuits · Op-amp Circuits · 2 marks · Multiple choice

The $\dfrac{V_{OUT}}{V_{IN}}$ of the circuit shown below is

Diagram for GATE 2023 EC question 39
  1. $-\dfrac{R_4}{R_3}$
  2. $\dfrac{R_4}{R_3}$
  3. $1+\dfrac{R_4}{R_3}$
  4. $1-\dfrac{R_4}{R_3}$

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Show answer and explanation

Correct answer: (A) $-\dfrac{R_4}{R_3}$

Explanation

The top op-amp is an inverting amplifier: $V_1=-\dfrac{R_2}{R_1}V_{IN}$. The lower op-amp is non-inverting: $V_2=\left(1+\dfrac{R_2}{R_1}\right)V_{IN}$. The last stage is an inverting summer with equal input resistors $R_3$: $V_{OUT}=-\dfrac{R_4}{R_3}(V_1+V_2)=-\dfrac{R_4}{R_3}\left(-\dfrac{R_2}{R_1}+1+\dfrac{R_2}{R_1}\right)V_{IN}=-\dfrac{R_4}{R_3}V_{IN}$.