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GATE 2020 PH – Question 39

Electronics · Oscillators, operational amplifiers and their applications, active filters · 2 marks · Multiple choice

The input to the shown circuit is $V_{in}=2\cos(100t)$ V and its output is $V_{out}=2\cos(100t-\pi/2)$ V. Given R = 1 kΩ, find C in μF.

Diagram for GATE 2020 PH question 39
  1. 0.1
  2. 1
  3. 10
  4. 100

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Show answer and explanation

Correct answer: (C) 10

Explanation

The noninverting input is the low-pass node, $V_+=V_{in}/(1+sRC)$. Equal input and feedback resistors give $V_{out}=2V_+-V_{in}$, hence transfer function $(1-sRC)/(1+sRC)$. Its phase is $-2\tan^{-1}(\omega RC)$. A −π/2 shift requires $\omega RC=1$. With $\omega=100$ rad/s and R = 1000 Ω, C = $10^{-5}$ F = 10 μF, option C.

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