+O C Output Cc Cp Cable Insulation Piezoelectric sensor R
An equivalent circuit for a piezoelectric accelerometer, which uses a quartz crystal as the sensing element, is shown in the following figure. The generated charge is denoted by q and the output voltage at the end of the accelerometer cable is vo. The piezoelectric sensor capacitance is modeled by Cp and the overall capacitance experienced at the sensor output, whose primary contribution is due to cable capacitance, is denoted by Cc. The resistance of the electric insulation in the accelerometer is denoted by R. Write a differential equation relating vo to q. What is the corresponding transfer function? Using this result, show that the accuracy of the accelerometer improves when the sensor time constant is large and when the frequency of the measured acceleration is high. For a quartz crystal sensor with R = 1 × 1011 Ω and Cp = 300 pF, and a circuit with Cc = 700 pF, compute the time constant.
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