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GATE 2024 EC – Question 50

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

In the circuit below, the opamp is ideal.

If the circuit is to show sustained oscillations, the respective values of $R_1$ and the corresponding frequency of oscillation are ______.

Diagram for GATE 2024 EC question 50
  1. $29R$ and $1/(2\pi\sqrt6RC)$
  2. $2R$ and $1/(2\pi RC)$
  3. $29R$ and $1/(2\pi RC)$
  4. $2R$ and $1/(2\pi\sqrt6RC)$

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Show answer and explanation

Correct answer: (B) $2R$ and $1/(2\pi RC)$

Explanation

This is a Wien-bridge type oscillator. The feedback network from the output to the non-inverting input has transfer function $\beta(s)=\dfrac{sRC}{1+3sRC+(sRC)^2}$. At $\omega=1/RC$ it equals $\dfrac{j}{3j}=\dfrac13$ with zero phase. The Barkhausen condition needs $A\beta=1$, so the non-inverting gain $A=1+R_1/R=3$ and $R_1=2R$. The frequency is $f=\dfrac{1}{2\pi RC}$.