MCEN5228-011/4228-011: Microsystems Integration
Homework #5, Due Date: Wednesday, March 1
The Word file of the homework is posted on the class web site. Email your PDF or Word file with answers to before the class on the 1st. There is a penalty, e.g. 5 to 25 points, for late submission.
Name: ______, Email: ______
1. (25 points) A calculation example with L=40cm for a cascaded driver shown below was discussed in the class.
Design the driver again with the following cases.
o Design a new driver with the length reduced from 40 to 2 cm. Derive Rint, Cint, the number of stages for an optimum driver, and the delays with the optimum driver.
o Another new case with the length increased from 40 to 80 cm. Estimate the delay with the optimum driver; this delay is named 80cm-delay. The delay for the 40-cm case discussed in the class is named 40cm-delay. Compare these two delays and select the right answer from the following three choices: 1) 80cm-delay = 2 x 40cm-delay; 2) 80cm-delay > 2 x 40cm-delay; or 3) 80cm-delay < 2 x 40cm-delay. What do you learn from this comparison?
2. (10 points) The iPhone 4’s accelerometer device with 6 parts (A-F) marked is shown below. Use one sentence to describe the main function or feature of each part marked. Also shown in another figure is the operation of the 3-axis gyroscope. The movements of the sensing plates are indicated by red-colored and yellow-colored arrows. Why are two different colors used to describe the movements?
1. (15 points) The pull-down voltage of a RF MEMS device can be estimated. We would like to increase the pull down voltage from 1.9 Volts to a level close to 10 Volts. Please change one of the dimensions of the flexure or the plate for the increase. Note: The pull down voltage does not need to be exactly at 10 Volts. It is fine if the new pull down voltage is between 9 and 11 Volts.
The above equation calculates the required voltage, V, to deflect the top plate of the piston actuator at distance, d, from the initial plate separation, zo . N=1 for one flexure in this case.
The 1.9-Volt pull down voltage is calculated as follows: The plate is 250 mm x 250 mm, and the air gap is 2 mm. The flexure is 40 mm in length, 10 mm in width and 0.5 mm in thickness with E = 169 GPa. The corresponding k = 169,000 MPa x 10 x 0.53/(4 x 403) = 0.8 mN/mm. At pull down voltage, d = 1/3 x 2 mm = 0.7 mm, so V = (2/3 x 2mm) x SQRT [(2x1x0.8x0.7)/(8.85 x 10-6 x 2502)] = 1.9 V. The second term for k associated with the residual stress is neglected. Some constants and units used are: eo = 8.85 x 10-6 pF/mm; 1 Pa = 1 Newton/m2 = 1 N/m2;
1 MPa = 1 mN/mm2; and 1 V = SQRT (mN x mm/pF).