A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters:
Crystal properties : Stiffness $10^9\;N/m,$ Damping ratio $0.01,$ Natural frequency $10^5\;rad/s,$ Force-to-Charge sensitivity $10^{-9}C/N,$ Capacitance $10^{-9}F$ with its loss angle assumed negligible
Cable properties : Capacitance $2\times 10^{-9}F$ with its resistance assumed negligible
Amplifier properties : Input impedance $1\;M\Omega ,$ Bandwidth $1\;MHz,$ Gain $3$
The minimum frequency of a force signal in $\text{Hz}$ within its useful mid-band range of measurement, for which the gain amplitude is more than $0.95,$ approximately is,
- $16$
- $160$
- $1600$
- $16\times 10^3$