Question

A piezoelectric transducer with a sensitivity of $2.0pC/N$ having a capacitance of $1200pF$ and leakage resistance of ${10}^{12}\Omega$ is connected to a charge amplifier as shown in the figure. If a force of $0.5sin10tN$ is applied to the transducer, the output amplitude of the charge amplifier is ____.

• A. $70.7mV$
• B. $0.707mV$
• C. $0.707V$
• D. $77.0V$

Answer 1

The correct option is B $0.707mV$

Redraw the circuit


Where,
$Z_F=\frac{{10}^8\times \frac{1}{{10}^{-9}s}}{{10}^8+\frac{1}{{10}^{-9}s}}=\frac{{10}^8}{1+0.1s}$

$i=\frac{dQ}{dt}$

Where,

$Q=KF=2pC/N\times 0.5sin10tN=sin10tpC$

$i=\frac{d}{dt}\left(sin10t\right)pC=10cos10t\times {10}^{-12}A$

Since output of charge amplifier is given by,

$V_0=-i|Z_F{|}_{\omega =10}=10\times cos10t\times {10}^{-12}{\left|\frac{{10}^8}{\sqrt{1+(0.1\omega {)}^2}}\right|}_{\omega =10}$

$=\frac{10cos10t\times {10}^{-12}\times {10}^8}{\sqrt{1+(0.1\times 10{)}^2}}=0.707cos10tmV$

$\text{Amplitude of}{V}_0=0.707mV$