GATE 2018 IN Q.23: solution and answer

Official answer: ASource: Official answer key, GATE 2018 IN (IIT Guwahati)

1. A piezoelectric sensor produces charge only when the applied force changes. The charge leaks away through the finite insulation resistance and the amplifier input resistance. So the sensor behaves as a high-pass element at low frequency.

2. The sensor has a bandpass characteristic with a lower cut-off of $0.1\text{Hz}$ and an upper cut-off of $1\text{MHz}$. The gain therefore falls to zero as $f\to 0$.

3. A static constant pressure has frequency $f=0\text{Hz}$. This is far below the lower cut-off, so the transfer function gives $H(0)=0$.

4. The sensitivity applies only inside the passband. For a dynamic pressure of $100\text{kPa}$ the output would be $100\text{mV/kPa}\times 100\text{kPa}=10\text{V}$.

5. For the static input the steady-state output is $V_{ss}=H(0)\times 10\text{V}=0\text{V}$. The charge produced when the pressure is first applied decays to zero. The answer is option (A).