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).
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe963568a-e3d0-49c4-a9c2-d7bf6836177a%2F7ea5d7d6-0273-41d0-a580-cf31effc5e49%2Fau9po3u_processed.jpeg&w=3840&q=75)
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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