Figure 1 shows a potentiometer used to measure the displacement and velocity of an elevator. The elevator shall travel at a speed up to 10m/s and the total travel distance / = 100m. In the design, R$ 99MM and the total resistance of the potentiometer Rp = 1MQ. x is the displacement of the elevator. A voltage follower is used to isolate the sensor from the remaining circuit and a differentiating amplifier circuit is used to obtain the velocity, in which Rf = 1MΩ and C 1μF. The sensor circuit then is connected to a filter circuit as shown in Figure 2 to remove the noise due to the vibration from the actuator. In the filter, R₁ = R₂ = 10000 and C₁ = C₂ = 100µF. Please 1. Find the sensitivity of the sensor circuit in terms of the velocity Sv = = Vi

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Hi, I received a solution for parts 1-3 for this question. Now, I need help with parts 4-6 please, thanks.
Question 2
Figure 1 shows a potentiometer used to measure the displacement and velocity of an elevator. The
elevator shall travel at a speed up to 10m/s and the total travel distance 1 = 100m. In the design,
Rs = 99MN and the total resistance of the potentiometer Rp = 1MN. x is the displacement of the
elevator. A voltage follower is used to isolate the sensor from the remaining circuit and a
differentiating amplifier circuit is used to obtain the velocity, in which Rf = 1MN and C= 1μF.
The sensor circuit then is connected to a filter circuit as shown in Figure 2 to remove the noise due
to the vibration from the actuator. In the filter, R₁ = R₂ = 10000 and C₁ = C₂ = 100µF. Please
1. Find the sensitivity of the sensor circuit in terms of the velocity S₁ =
Vi
x
2. Determine the transfer function of the filter circuit: H₁ (s) =
vo(s)
vi(s)*
3. Determine the type of filter (include its order), the bandpass gain, cut-off frequency and
quality factor of H₁ (s).
4. Please determine the minimum frequency required for the A/D converter so that a computer
can recover the frequency information of the elevator's velocity.
Determine the transfer function between the displacement x and v: H₂(s)
5.
6.
+
Determine the type of filter (include its order), the bandpass gain, cut-off frequency and
quality factor of H₂(s).
10V
Rs
ww
v₁ (1)
R₂
R₁
Figure 1.
C₁
R₂
Figure 2.
C₂
vo(1)
=
Rr
vo(s)
x(s)*
vi(t)
Transcribed Image Text:Question 2 Figure 1 shows a potentiometer used to measure the displacement and velocity of an elevator. The elevator shall travel at a speed up to 10m/s and the total travel distance 1 = 100m. In the design, Rs = 99MN and the total resistance of the potentiometer Rp = 1MN. x is the displacement of the elevator. A voltage follower is used to isolate the sensor from the remaining circuit and a differentiating amplifier circuit is used to obtain the velocity, in which Rf = 1MN and C= 1μF. The sensor circuit then is connected to a filter circuit as shown in Figure 2 to remove the noise due to the vibration from the actuator. In the filter, R₁ = R₂ = 10000 and C₁ = C₂ = 100µF. Please 1. Find the sensitivity of the sensor circuit in terms of the velocity S₁ = Vi x 2. Determine the transfer function of the filter circuit: H₁ (s) = vo(s) vi(s)* 3. Determine the type of filter (include its order), the bandpass gain, cut-off frequency and quality factor of H₁ (s). 4. Please determine the minimum frequency required for the A/D converter so that a computer can recover the frequency information of the elevator's velocity. Determine the transfer function between the displacement x and v: H₂(s) 5. 6. + Determine the type of filter (include its order), the bandpass gain, cut-off frequency and quality factor of H₂(s). 10V Rs ww v₁ (1) R₂ R₁ Figure 1. C₁ R₂ Figure 2. C₂ vo(1) = Rr vo(s) x(s)* vi(t)
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