GATE 2024 IN – Question 52
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched ON at t = 0. Assuming the opamp to be ideal, the frequency of the output voltage Vo is __________ kHz (rounded off to two decimal places).
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Correct answer: 6.00 to 6.30
Explanation
The divider sets threshold fraction $\beta=10/(10+16)=5/13$. Charging from $-\beta V_{sat}$ to $+\beta V_{sat}$ takes $RC\ln[(1+\beta)/(1-\beta)]$.
Hence $T=2(100\ \mu\mathrm s)\ln(2.25)=162.186$ μs and $f=1/T=\boxed{6.17}$ kHz.