A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters : Crystal properties : Stiffness 109 N/m, Damping ratio 0.01, Natural frequency 105 rad/s, Force-to-Charge sensitivity 10-9 C/N, Capacitance 10-9 F with its loss angle assumed negligible Cable properties : Capacitance 2 × 10-9 F with its resistance assumed negligible Amplifier properties : Input impedance 1 MΩ
, Bandwidth 1MHz , Gain 3 The minimum frequency of a force signal in Hz within its useful mid-band range of measurement,
for which the gain amplitude is more than 0.95, approximately is,