Filter Homework

-Design a MEMS filter using a polysilicon MEMS process and analyze it using linearized electrostatic actuatiors in PSpice (see Senturia, 7.3.2-7.3.4).

-Assume that the resonating mass is 50 microns long, 100 microns wide, and 10 microns thick.

-Assume that the actuators are implemented on the 10x100 micron faces of the mass.

-Use a 5V DC bias on the actuator (the operating point is then 5V and the gap you have chosen).

-Use 10x5 micron (10 thick, 5 wide) beams to suspend the mass. Make the beams at least 40 microns long.

-A small gap between two polysilicon electrodes can be fabricated using sacrificial layers. Gaps 50 nm or larger are reasonable.

-Calculate the squeeze-film damping/spring force for your gap to get the damping for the filter. Assume air at standard temperature and pressure. Note that the final spring constant will consisto of the beam spring constant and the "spring" part of the squeeze film effect. (Refer to the recently modified slide 19 on fluids.)

-There are no required specifications, so you can just choose what you think would be good dimensions and do the analysis, but we encourage you to examine the effect of different dimensions on the performance of the filter.

-Simulate the filter using a 300 Ohm source resistance and a 300 Ohm load resistance. Or for the electrical engineers, you are hoping to use this filter in a system with a characteristic impedance of 300 Ohms. In practice, this just means that you should use the 300 Ohm source and load resistors as drawn in the PSpice filter homework schematic. Note that the other values do not correspond to this problem, but are just present to give you a working circuit so that you can use it as a model for your design. You can look at the properties of the dependent sources by double clicking on them. By doing this you can see how the two sources model a transformer.

Notes: The linearized transducer model is given in Fig. 7.7. There are 3 parameters. They are all given near the end of 7.3.4. The turns ratio is given in eq. 7.7.6. ZEB and ZMS are given is somewhat disguised form in equations 7.73 and 7.78 as impedances. For spice, you want capacitances, the circuit element associated with the impedances in 7.73 and 7.78. Since the complex impedance of a capacitor is 1/sC, the capacitance representing ZEB is C=eA/go, and the capacitance representing ZMS is C=1/k(1-Qo^2/eAkgo). Qo is given in eq. 7.65, and the other parameters come from the device geometry.

Filter Properties to be determined:

1. Center frequency.

2. Bandwidth at the half-power (or 3 dB) points. (0.707 times the peak amplitude of output voltage or current)

3. Insertion loss (again a term for electrical engineers). The idea is to find out how much of the signal is lost by passing it through the filter. So the appropriate comparison to make is between a system consiting of the source, the 300 Ohm source resistor, and the 300 Ohm load resistor, where the power in the load resistor would be (Vs)^2/1200; and the actual power in the load resistor with the filter that you simulate in PSpice. You sould get a number smaller than 1, possibly very much smaller than 1. The insertion loss in dB (decibels) is then 10 log (P/Pideal), where log is a base 10 logarithm and Pideal is the power given by the equation for the directly connected resistors. So, if the filter is perfect, the insertion loss is 0 dB, and otherwise the insertion loss will be negative (-30 dB, for example).