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HW7 solution - EEL5225 Principles of MEMS Transducers HW7...

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Principles of MEMS Transducers Page 1 of 5 Prepared by D. Arnold November 9, 2010 EEL5225 Principles of MEMS Transducers HW7 Fall 2010 Semester Assigned: Thursday, 11/4 Due: Wednesday, 11/10 1. Some details on general two-port theory… a. Prove that the units of T EM and T ME in the linear transducer model are the same. b. Derive the following relationship between the reciprocal impedance and admittance transduction factors, T and G : G = T Z EB Z MS a. T EM = V U I = 0 So, T EM units = volts m / s Reducing V to base SI units: V = W A = J / s A = J A s = N m A s = kg m 2 A s 3 T EM units = V s m = kg m A s 2 --- 1 And T ME = F I U = 0 So, T EM units = N Amps Reducing N to base SI units: (use Force: F=ma) N = kg m s 2 So, T EM units = N A = kg m A s 2 --- 2 Thus, from equations 1 & 2, the units of T EM and T ME in the linear transducer model are the same. b. From L7, slide 17: --- 1 --- 2 where (reciprocal system) From eq. 2, Substitute in eq. 1,
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Principles of MEMS Transducers Page 2 of 5 Prepared by D. Arnold November 9, 2010 Solve for U, But, from slide 18 So, we get, Now, from slide 21, And, for reciprocal system, G ME = G EM = G G = T Z EB Z MS
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  • Fall '08
  • Arnold
  • Elementary algebra, SI base unit, International System of Units, Metre, Centimetre gram second system of units

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