GATE 2015 EE (EE2) – Question 21

Analog and Digital Electronics · Active filters: single stage, Sallen Key, Butterworth · 1 mark · Numerical answer

The shown op-amp is ideal. Input is $V_i=2\sin(2\pi\cdot2000t)$ V. The output-voltage amplitude in volts is ________.

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Correct answer: 1.1 to 1.4

Explanation

The feedback network is 1 kΩ in parallel with 0.1 μF, so gain is $-(R_f/R_{in})/(1+j\omega R_fC)$. Both resistors are 1 kΩ, giving a DC magnitude of one.

At 2 kHz, ωRfC=2π2000(1000)(0.1 μF)=1.256637. Output amplitude is $2/\sqrt{1+1.256637^2}=$ **1.24535 V**, within 1.1–1.4.

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