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Consider the device shown in the following figure 1: pressure p(t) Solid frame Piezoresistive element Diaphragm Battery (V) + R₁ The diaphragm displacement r(t) is related to pressure p(t) as 1 d²r 20 dr w² dt² wn dt R₂ + x(t) = k₁p(t), R₂ R₂+k₂a(t), = R₂ where ( = 0.4, n = 100m rad/s, and k₁ = 10-5 m/mmHg. The diaphragm changes the resistor of a piezoresistive element R₂. The r(t) is related to piezoresistive element Re by the following equation where R₂10002, and k₂ 200 /m. This element is connected to a wheatstone bridge and the resistors of the bridge are selected as R₁ = R₂ = R3 = 1000. Suppose the battery voltage is 10V, calculate the output voltage Vab for a step change of the amplitude 100 mmHg in the pressure p(t).

Consider the device shown in the following figure 1: pressure p(t) Solid frame Piezoresistive element Diaphragm Battery (V) + R₁ The diaphragm displacement r(t) is related to pressure p(t) as 1 d²r 20 dr w² dt² wn dt R₂ + x(t) = k₁p(t), R₂ R₂+k₂a(t), = R₂ where ( = 0.4, n = 100m rad/s, and k₁ = 10-5 m/mmHg. The diaphragm changes the resistor of a piezoresistive element R₂. The r(t) is related to piezoresistive element Re by the following equation where R₂10002, and k₂ 200 /m. This element is connected to a wheatstone bridge and the resistors of the bridge are selected as R₁ = R₂ = R3 = 1000. Suppose the battery voltage is 10V, calculate the output voltage Vab for a step change of the amplitude 100 mmHg in the pressure p(t).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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MEN/BioE642 HW#4 Problem 1: Consider the device shown in the following figure 1:1 pressure p(t) Solid frame Piezoresistive element Diaphragm R₁ R The diaphragm displacement r(t) is related to pressure p(t) as 1 d²x, 20 dx + Wn dt w² dt² + x(t) = k₁p(t), R₂ where ( = 0.4, n = 100 rad/s, and k₁ = 10-5 m/mmHg. The diaphragm changes the resistor of a piezoresistive element R₂. The r(t) is related to piezoresistive element Re by the following equation R₂=R₂+k₂x(t), where R = 100, and k₂ = 200 /m. This element is connected to a wheatstone bridge and the resistors of the bridge are selected as R₁ = R₂ = R3 = 1000. Suppose the battery voltage is 10V, calculate the output voltage Vab for a step change of the amplitude 100 mmHg in the pressure p(t). (hint: calculate the steady-state response of x with the transfer function, which is A*H(0). A is the amplitude of the step function input 100mmHg. Then, calculate Rx and output voltage.) Problem 2: A differential capacitive sensor interfaced using the two circuits shown in the figure 2(b) and (d) below. The parallel plate approxima 10um. Th CF = 30fF. (1) For the circuit in figure 2(b), find the voltage ratio of Vo/Vs with the lateral displacement x = 6.78e-008m. (2) For the circuit in figure 2(d), find the voltage ratio of Uo/U with the lateral displacement x = 6.78e-008m. (hint: the
Transcribed Image Text:MEN/BioE642 HW#4 Problem 1: Consider the device shown in the following figure 1:1 pressure p(t) Solid frame Piezoresistive element Diaphragm R₁ R The diaphragm displacement r(t) is related to pressure p(t) as 1 d²x, 20 dx + Wn dt w² dt² + x(t) = k₁p(t), R₂ where ( = 0.4, n = 100 rad/s, and k₁ = 10-5 m/mmHg. The diaphragm changes the resistor of a piezoresistive element R₂. The r(t) is related to piezoresistive element Re by the following equation R₂=R₂+k₂x(t), where R = 100, and k₂ = 200 /m. This element is connected to a wheatstone bridge and the resistors of the bridge are selected as R₁ = R₂ = R3 = 1000. Suppose the battery voltage is 10V, calculate the output voltage Vab for a step change of the amplitude 100 mmHg in the pressure p(t). (hint: calculate the steady-state response of x with the transfer function, which is A*H(0). A is the amplitude of the step function input 100mmHg. Then, calculate Rx and output voltage.) Problem 2: A differential capacitive sensor interfaced using the two circuits shown in the figure 2(b) and (d) below. The parallel plate approxima 10um. Th CF = 30fF. (1) For the circuit in figure 2(b), find the voltage ratio of Vo/Vs with the lateral displacement x = 6.78e-008m. (2) For the circuit in figure 2(d), find the voltage ratio of Uo/U with the lateral displacement x = 6.78e-008m. (hint: the
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