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HW8 solution

# HW8 solution - EEL5225 Principles of MEMS Transducers HW8...

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Principles of MEMS Transducers Page 1 of 5 Prepared by D. Arnold November 22, 2010 EEL5225 Principles of MEMS Transducers HW8 Fall 2010 Semester Assigned: Friday, 11/12 Due: Friday, 11/19 1. A sensor design calls for a piezoresistor rotated 30° from the <100> direction on a (100) wafer. a.) Sketch the piezoresistor on a wafer, indicating the direction with respect to the wafer flat. b.) Derive the longitudinal and transverse piezoresistive coefficients ( π l and π t ) in terms of the matrix coefficients π l1 , π l2 , and π 44 . c.) Then compute the numeric values for n- and p-doped silicon using the values shown in the table on Lecture 7, Slide 72. (Your answers should match the plots shown on Slide 74) a.) Consider a (100) n-type Si wafer. φ = 30 0 from <100> direction: Note: <100> direction is 45 0 from <110> direction. b.) In this case: and Longitudinal piezoresistive coefficient: But Hence Transverse piezoresistive coefficient: But

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Principles of MEMS Transducers Page 2 of 5 Prepared by D. Arnold November 22, 2010 Note: These answers match the plots shown on slide 74. 2. This problem relates to the Wheatstone bridge shown in Fig. 18.3 (p. 477 Senturia). a.) Derive the output voltage of the circuit, V o , as function of generic resistance values: R 1 = R 0 + Δ R 1 R 2 = R 0 + Δ R 2 R 3 = R 0 + Δ R 3 R 4 = R 0 + Δ R 4 b.) Show the simplified results for the following cases: i. quarter bridge ( Δ R 1 = Δ R; Δ R 2 = Δ R 3 = Δ R 4 =0) ii. half bridge ( Δ R 1 = Δ R; Δ R 2 = - Δ R; Δ R 3 = Δ R 4 =0) iii. full-bridge ( Δ R 1 = Δ R 3 = Δ R; Δ R 2 = Δ R 4 = - Δ R) a.) V s is a constant Voltage source R 1 = R 0 + Δ R 1 R 2 = R 0 + Δ R 2 R 3 = R 0 + Δ R 3 R 4 = R 0 + Δ
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HW8 solution - EEL5225 Principles of MEMS Transducers HW8...

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