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Unformatted text preview: HW #4 A. Interdigitated capacitor: Interdigitated capacitors are used in microelectromechanical systems (MEMS). For example, the MEMS accelerometer shown here might be used to deploy an airbag when sudden deceleration is detected. When the car hits something, the proof mass will continue moving causing the fingers on one side to overlap more and on the other side to move apart. The resulting capacitance change (more on one side, less on the other) can be used to determine the deceleration. motion Close up of capacitor Geometry for HW problem: x 2 m Spring suspension Proof mass, free to move Moving part 12 m 1 m gaps Fixed part Suppose a particular comb drive has fingers that are 2 m wide and have a gap of 1 m made of material 20 m thick. The normal interdigitation (overlap) is 12 m and each side has 30 fingers. Estimate the capacitance as a function of displacement x. B. Electrostatic comb drive: The same structure can be used to apply forces and make MEMS devices move in response to a voltage. For the same structure as in Prob. A, determine the force on the free comb if a voltage difference of 5 V is applied between the two combs. Which direction is the force in? What happens if you apply 5 V. Visit http://www.el.utwente.nl/smi/content/education/is/comb_drive.mpg to see a MEMS comb drive in action. C. Electrostatic Speakers This problem is about the design of an electrostatic speaker. (See: http://en.wikipedia.org/wiki/Electrostatic_loudspeaker for an introduction. Consider an electrostatic speaker with a 1.3 m by 1.7 m diaphragm charged to 3,000 volts. The diaphragm is centered between the two metal grids (stators) which are 4 mm apart. The grids are driven with an ac voltage signal (one side positive, the other negative) to produce the sound. What peak voltage needs to be applied to the grids to get a peak sound pressure of 2 x 102 Pa (comfortable listening volume). Assume that the charge on the diaphragm remains constant. D. Capacitive level sensor A capacitive level sensor is used to sense the level of oil in a tank. The sensor consists of a coaxial rod and cylinder immersed in the oil so that the oil can fill the space between the two up to the level of the oil. The rod and cylinder are 2 m long. The rod is 6 mm in diameter and the cylinder has an inner diameter of 9 mm and an outer diameter of 10 mm. The dielectric constant of the oil is 3.2. (a) What is the capacitance as a function of the oil level (in meters) Oil level (b) Suppose a voltage is applied between the inner and outer conductor, will the oil in the intermediate space between the rod and cylinder rise, fall, stay the same or oscillate? (c) If the voltage is 1000 V, by how much will the level in the intermediate space change? D. Capacitor Design Fara Day Inc. in Capa City, OR needs you to design a capacitor to meet the following specs: Capacitance: 1.0 nF Voltage rating: 50 V Tolerance: better than 5% Prepare three designs using the following dielectrics: Mylar, Mica, and Polystyrene. Design for minimum total volume of the capacitor but do not exceed 75% of the breakdown field. In manufacturing of the capacitors, Fara Day can guarantee dimensions to no better than 0.1 m. Which dielectric gives the smallest capacitor? ...
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This note was uploaded on 01/18/2011 for the course ALS 161 taught by Professor Sfuiaf during the Spring '10 term at American InterContinental University Los Angeles.
- Spring '10