Mid-Term Take-home assignment: 

NOTE: This assignment counts for a DOUBLE HOMEWORK.  It MUST be completed in order to receive a grade for the class.

NO LATE SUBMISSIONS WILL BE ACCEPTED

Individual Assignment:

Consider an electrostatic pressure transducer, described in class, and illustrated here:

1. Write down the linearized equivalent circuit model for this system.  Make sure that the circuit is sensible, by changing various parameters and making sure that the system behaves as expected.
2. Derive and clearly show the linearized transfer function  - the ratio of the output voltage to the applied pressure, plotted as a function of frequency.   You need not simplify the expression  - you can use the computer for that.
3. For each of the following special cases, plot the transfer function.

1. The baseline sensor, with zero bias voltage
2. The baseline sensor with a non-zero bias voltage (your choice)
3. The baseline sensor with zero bias voltage and with NO vent hole
4. The baseline sensor with zero bias voltage, and a 4 micron cavity

Based on these results, modify the baseline design to generate an improved device which shows greater sensitivity to pressure fluctuations, optimized to operate between 50 Hz to 10 kHz.  Discuss the changes you make and the reasons for making them

Your solution should be clearly presented, with supporting equations, references (if necessary). State clearly your assumptions, and any approximations you make.