Assuming the resultant force acting on the proof mass due

Question

Problem 1:

Consider the silicon piezoresistive accelerometer shown below in Figure. The proof mass dimensions are l_m = 1.2 mm, w_m= 1.2 mm, and h_m = 400 μm. The mass is anchored with a beam oriented in the [110]-direction with dimensions l_c = 250 μm, w_c = 80 μm, and h_c = 5 μm. Two 12.5 kΩ piezoresistors are oriented longitudinally on the cantilever near the anchor and two identical resistors are integrated as a reference at a zero stress location. The four resistors are connected in a Wheatstone bridge configuration. Assuming the resultant force acting on the proof mass due to an acceleration acts at the center of mass of the proof mass, calculate

a) the relative change in resistance due to a 1 G acceleration in the Z-direction,

b) the signal voltage generated by the 1 G acceleration if the sensing circuit is biased with V = 2.5 V, and c) the DC power consumption due to the bias voltage.

Problem 2:

Determine the SNR of the device described in Problem 3 for a 1 mG acceleration in the Z direction. Assume the sensor bandwidth ranges from 0.1 to 100 Hz and that the 1/f-corner frequency is 2 kHz.