High sensitivity accelerometer design An accelerometer is being selected for seismic applications. The ENS designer wishes to estimate the minimum mass and size that this device can attain while meeting the goal of acceleration values of 10
9 g=

ffiffiffiffiffiffiffi Hz p

:

(a) This accelerometer includes an electronic displacement sensor having a position sensitivity of 1pm=

ffiffiffiffiffiffiffi Hz p

. For a target acceleration sensitivity of 10
5ðm=s2Þ=

ffiffiffiffiffiffiffi Hz p

in the bandwidth from 0.001 to 1 Hz, find the largest sensor resonance frequency that meets this objective while ignoring the effect of thermal noise.

(b) Include the effect of thermal noise for operation at 300K and compute the required proof mass value for this accelerometer for Q values of 1, 100, and 104 such that the thermal noise contribution does not exceed the sensitivity target.

(c) What would be the spring constant value required to achieve the specified resonance frequency above and with masses corresponding to each Q value?

(d) Compute the static deflection of this spring mass system when exposed to the Earth’s gravity (acceleration) field.