Problem 2: Butterworth Van Dyke (BVD) Equivalent Circuit (25 points) The circuit in figure below is...

 

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Problem 2: Butterworth Van Dyke (BVD) Equivalent Circuit (25 points) The circuit in figure below is used to represent a MEMS resonator in the electrical domain. Let's do some circuit analysis. V I HE Cm Lm Co H Rm m a) Replace circuit elements with complex impedances and find the equivalent admittance, Y=I/V, (Z=1/Y) of the circuit in figure. b) Replace the "s" variable with "jo" where j is the imaginary unit and @=2.7.f is the angular frequency of the electrical signal applied to the circuit (f is the frequency). Plot magnitude (dB) and phase () of the circuit admittance versus frequency, f, assuming: Co-629 fF (fF=10-¹5F), Rm=66.6 , Cm=7.3 fF, Lm=113 µH, and 160 MHz<f<190 MHz. c) For which frequency is the admittance of the circuit equal to 1/Rm? Please justify your answer. Problem 2: Butterworth Van Dyke (BVD) Equivalent Circuit (25 points) The circuit in figure below is used to represent a MEMS resonator in the electrical domain. Let's do some circuit analysis. V I HE Cm Lm Co H Rm m a) Replace circuit elements with complex impedances and find the equivalent admittance, Y=I/V, (Z=1/Y) of the circuit in figure. b) Replace the "s" variable with "jo" where j is the imaginary unit and @=2.7.f is the angular frequency of the electrical signal applied to the circuit (f is the frequency). Plot magnitude (dB) and phase () of the circuit admittance versus frequency, f, assuming: Co-629 fF (fF=10-¹5F), Rm=66.6 , Cm=7.3 fF, Lm=113 µH, and 160 MHz<f<190 MHz. c) For which frequency is the admittance of the circuit equal to 1/Rm? Please justify your answer.

Answer rating: 100% (QA)

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