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School
New Jersey Institute Of Technology *
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Course
215
Subject
Mechanical Engineering
Date
Feb 20, 2024
Type
docx
Pages
33
Uploaded by GeneralOxideLeopard44
Department Of Mechanical And Industrial Engineering
Signal Conditioning By RC
Filter
By
Kisei Mano
Team 1
1.
Clair Wagner
2.
Courage Lahban
3.
Elijah Smith
Date of Experiment: 5-24-2023 & 5-25-2023
Instructor: B. S. Mani
ME343-011, MECHANICAL LAB-1
Summer 2023
1
Table of Contents
Cover Page………………………………………………………………………………………………………………………… Page 1
Table of Contents………………………………………………………………………………………………………………. Page 2
Grading Citaria………………………………………………………………………………………………………………….. Page 3
Table of Tables…………………………………………………………………………………………………………………… Page 5
Table of Figures…………………………………………………………………………………………………………………. Page 5
Abstract…………………………………………………………………………………………………………………………….. Page 6
Introduction………………………………………………………………………………………………………………………. Page 7
Experimental systems……………………………………………………………………………………………………….. Page 8
o
Equipment……………………………………………………………………………………………………………. Page 8
o
Experimental description…………………………………………………………………………………... Page 12
Data and Result………………………………………………………………………………………………………………. Page 15
Discussion……..………………………………………………………………………………………………………………… Page 23
Conclusion………………………………………………………………………………………………………………………. Page 25
Bibliography……………………………………………………………………………………………………………………. Page 26
Appendix………………………………………………………………………………………………………………………… Page 27
Bonus Points…………………………………………………………………………………………………………………… Page 35
2
SIGNAL CONDITIONING BY RC FILTER AND
CHARACTERISTICS ANALYSIS
Grading Criteria for Lab Report 2
(Maximum Possible 50 points + Bonus 15 points
)
1.
General Format
(
20 points = 2.5+7.5+2.5+2.5+5.0
)
Cover page (
2.5 points
)
Grading Criteria
Table of Contents(
Include Responses for Bonus points, if any, after Conclusion
Table of Figures
Abstract
Theoretical principles
(MUST include derivation - include at appendix)
(7.5 points)
Fourier series representation of a general signal
Filtration characteristics of R-C filters:
Low-pass: Gain Vo/Vi, Gain Vo/Vi in dB, Φ in degrees, cut-off frequency
High-pass: Gain Vo/Vi, Gain Vo/Vi in dB, Φ in degrees, cut-off frequency
Experimental system
(
2.5 points
)
Schematic diagram of experimental system
Photograph of the experimental setup and label its key components
Results and discussions
(See details below given separately)
Conclusion
(
2.5 points
)
Appendices
(
5 points
)
Lab manual organization
Photocopy of original data
Detailed sample calculation
Nomenclature used in report
2.
Results and Discussions
(
30 points = 10.0 + 10.0 + 10.0
)
Sample calculation
(
10 points
)
3
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Include the sample calculations in Appendix
From original data obtain Vo/Vi (in dB) & Φ (high pass and
low pass filter)
Calculate cut-off frequency of the actual RC filter;
Calculate theoretical Vo/Vi (in dB) and Φ (high pass and
low pass filter)
Graphically compare experimental Vo/Vi (in dB) with theory
(high & low pass filter) Both High pass and Low pass filter gain characteristics should be plotted on the same graph
like the poster in the lab. (
10 points
)
Graphically compare experimental Φ against theory
(high and low filter) Both High pass and Low pass filter phase lag/lead characteristics should be plotted on the same graph
the poster in the
lab. (
10 points
)
3. Bonus: (15 points)
Based on the derivations shown for the low pass filters (which was presented in class), derive the gain and phase shift relationships for a band pass filter.
Table of Figures
4
Figure #
Description
Page #
1
Signals and noise Combined making Distorted Results
7
2
Distorted result corrected with the use of RC Filter
8
3
General Setup of low pass filter
8
4
General Setup of high pass filter
9
5
General Setup of base pass filter
9
6
Graphical Representation of All three Types of Filters
9
7
General understanding of how RC Filters Work
10
8
General Graph of Phase Lag vs Frequency of Both low pass and High pass
10
9
Overall setup of the experiment
12
10
Schematic Diagram of experimental systems
12
11
RC Filter
12
12
Frequency Counter
12
13
Frequency Generator
13
14
Oscilloscope
13
15
Gain Characteristics of Both High and Low Filter with Theoretical Plot
18
16
Phase lag Characteristics of Both High and Low Filter with Theoretical Plot
18
17
Phase lag Characteristics Plot Logarithmic Value of Frequency Ratio
19
Table of Tables
Table #
Page #
1
14
2
15
3
15
4
16
5
17
6
17
Abstract
The abstract of this lab was to observe several frequencies the oscillator set to 8 pre-determined frequencies, 200, 500, 1000, 2000, 4000, 8000, 20000, and 40000. With these frequencies, that 5
were passing through a Low or High filter, we were able to obtain the amplitude and N values in the provided table. In the low pass filter, the received signals have lower frequencies compared to the
cutoff frequency while attenuating or blocking signals. However, a high-pass filter is an electronic circuit that allows signals with frequencies above a certain cutoff frequency to pass through while
attenuating or blocking signals. The next thing we did was observe
the phase shift between the two frequencies to acknowledge how the filter works in this experiment. Theoretical Principles
The Fourier series representation is a mathematical tool used to express a general periodic signal as a sum of sine and cosine functions of 6
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different frequencies. This Fourier series could decompose the general signal into a series of harmonically related sinusoidal components.
Fourier series Reduction of General Signals:
f
(
x
)
=
d
+
∑
n
=
1
∞
¿¿
Where the coefficients a
n
, b
n
, d
shown below:
a
n
=
(
2
L
)
∫
0
L
f
(
x
)
∗
cos
(
2
πnx
L
)
dx
b
n
=
(
2
L
)
∫
0
L
f
(
x
)
∗
sin
(
2
πnx
L
)
dx
d
=
1
L
∫
0
L
f
(
x
)
dx
In the figure below shows how the combinations provided signal and the noise frequency results to a distorted frequency which is useless in collecting data.
Figure 1: Signals And Noise Combined Making Distorted Result
To correct this disturbed frequency to a proper frequency we use an RC filtering to extract the noise from the “Distorted Result” which leads to a cleaner and better frequency. (Shown in Figure 2) 7
Figure 2: Distorted Result Corrected With The Use Of RC Filter
In today's science and technology, there are three types of RC Filters:
Low-pass Filter
The Low Pass Filter takes in
disrupting high frequency and reduces the signals at lower frequency.
|
V
out
|
=
|
V
¿
|
1
√
1
+
ω
2
R
2
C
2
Figure 3: General Setup Of Low Pass Filter
High-pass Filter
The High Pass Filter takes in
disrupting low frequency and
reduces the signals at higher
frequency.
|
V
out
|
=
|
V
¿
|
ωRC
√
1
+
ω
2
R
2
C
2
8
Figure 4: General Setup Of High Pass Filter
Band-pass Filter
The bandpass filter is the combination of the lower cutoff frequency and the upper cutoff frequency. These frequencies define the range of frequencies that the filter allows to pass
through.
Figure 5: General Setup Of Band Pass Filter
When the three RC Filters are collecting data, the graphs looks like this:
Figure 6: Graphical Representation Of All Three Types Of Filters
The figure below briefly shows how the RC filter works:
9
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Figure 7: General Understanding Of How RC Filters Work
In this lab we need to compare the Theoretical frequency and Experimental
frequency. The easiest way to compare the frequencies is to make graphs and acquire the important data sets.
With the obtained values of R and C we were able to calculate the cut-off frequency (
f
c
), and the f
stands for the planned frequency for theoretical calculations shown below.
Theoretical Gain Low Pass:
(
V
0
V
i
)
th
dB
=−
10 log
[
1
+
(
f
f
c
)
2
]
Theoretical Gain High Pass:
(
V
0
V
i
)
th
dB
=
20log
(
f
f
c
√
1
+
(
f
f
c
)
2
)
Figure 8: General Graph of Phase Lag vs Frequency
Of Both Low Pass and High Pass
Theoretical Phase Lag Low Pass:
φ
TH
=−
tan
−
1
(
f
f
c
)
Theoretical Phase Lag High Pass:
φ
TH
=
π
2
−
tan
−
1
(
f
f
c
)
10
For the Experimental values we need the values of the output voltage (
V
0
), input voltage (
V
i
), Phase shift (N), and Wavelength (M). These values can be acquired from the oscilloscope measurement and the equations shown below are used at the graph for comparison.
Experimental Gain Low Pass: 20log
(
V
0
V
i
)
Experimental Gain High Pass: 20log
(
V
0
V
i
)
Experimental Phase Lag Low Pass:
φ
=
(
N
M
)
∗
360
Experimental Phase Lag High Pass:
φ
=
(
N
M
)
∗
360
11
Experimental System
F
i
g
u
r
e
9: Overall Setup of The Experiment Figure
10:
Schematic
Diagram
Of
Experimental Systems
The two figures shown above are the way this experiment is set up. First the frequency generator generates specific frequency transporting to the RC Filter. Next the RC filter sends frequency data to the oscilloscope, showing the clear graph image. With this graph we were able to measure the wavelength, amplitude and phase lag. After that the oscilloscope is connected to the frequency
counter, showing how much frequency is applied.
Figure 11: RC Filter Box, With R = 1000Ω C = 6.6*
10
−
8
F
12
Figure 12: Frequency Counter
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Figure 13: Frequency Generator
Figure 14: Oscilloscope
g
In this experiment, we only set up to the provided frequency from the RC filter. Basically the RC filter has an Low Pass side and High Pass Side, to get frequency signal the wire management needs to be set to Low in to Low Out and High in to High Out. Next we keep changing the frequencies to see what happens, and how the input filters across to the output.
13
Results And Discussion
1.
Low Pass Filter
Theoretical:
#
Frequency
(plan)
Cut-off
frequency
X-axis
y-axis
(
ϕ
)
f
f
c
log
(
f
f
c
)
(
V
0
V
i
)
th
dB
=−
10 log
[
1
+
(
f
f
c
)
2
]
φ
TH
=−
tan
−
1
(
f
f
c
)
Hz
Hz
1
200
2411.4
-1.0812462
-0.029771621
-0.08275
2
500
2411.4
-0.6833062
-0.18280976
-0.20445
3
1000
2411.4
-0.3822762
-0.689157489
-0.39311
4
2000
2411.4
-0.0812462
-2.273394955
-0.6924
5
4000
2411.4
0.2197838
-5.742035377
-1.02828
6
8000
2411.4
0.52081379
-10.79396573
-1.27803
7
20000
2411.4
0.9187538
-18.43775742
-1.4508
8
40000
2411.4
1.2197838
-24.41143128
-1.51058
Table 1: Calculations of Theoretical Gain values for Low Pass Filter
14
Experimental:
Table 2: Calculations of Experimental Gain values for Low Pass
Filter
15
#
Cut-off
frequency
Frequency
(set)
Initial
voltage
Twice
Amplitude
multiplied
Factor
Initial
voltage
Twice
Amplitude
multiplied
Factor
X-axis
y-axis
f
c
f
2*Vi*
(volts/cm)
2*V
o
*(Volts/cm)
log
(
f
f
c
)
20log
(
V
0
V
i
)
Hz
Hz
Volts
cm
1
2411.4
199
22.5
22.5
-1.0812462
0
2
2411.4
500
22.5
22.5
-0.6833062
0
3
2411.4
1000
22.5
21
-0.3822762
-0.59926
4
2411.4
2000
22.5
17
-0.0812462
-2.43467
5
2411.4
3981
21.5
10.6
0.2197838
-6.14265
6
2411.4
8010
21.5
6
0.5208137
9
-11.0857
7
2411.4
20020
21.5
2.5
0.9187538
-18.69
8
2411.4
40398
22
1.22
1.2197838
-25.1213
Phase shift
(lead '+', lag
'-')
Wav length
φ
Φ*(
π
180
)
N
M
N/M
seconds
seconds
-0.00008
0.0049
-0.01633
-5.87755
-0.10258
-0.00008
0.00188
-0.04255
-15.3191
-0.26737
-0.00007
0.00094
-0.07447
-26.8085
-0.4679
-0.000055
0.000475
-0.11579
-41.6842
-0.72753
-0.000042
0.00024
-0.175
-63
-1.09956
-0.000026
0.000122
-0.21311
-76.7213
-1.33904
-0.000011
0.000048
-0.22917
-82.5
-1.4399
-0.0000055
0.000024
-0.22917
-82.5
-1.4399
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Table 3: Calculations of Experimental Phase Lag for Low Pass Filter
2.
High Pass Filter
#
Frequency
(plan)
Cut-off
frequency
X-axis
y-axis
y-axis
(
ϕ
)
f
f
c
log
(
f
f
c
)
(
V
0
V
i
)
th
dB
=
20log
(
f
f
c
√
1
+
(
f
f
c
)
2
)
φ
TH
=
π
2
−
tan
−
1
(
f
f
c
)
Hz
Hz
1
200
2411.4
-1.0812462
-21.6547
1.488048
2
500
2411.4
-0.6833062
-13.8489
1.366348
3
1000
2411.4
-0.3822762
-8.33468
1.17769
4
2000
2411.4
-0.0812462
-3.89832
0.878395
5
4000
2411.4
0.2197838
-1.34636
0.54252
6
8000
2411.4
0.52081379
-0.37769
0.292768
7
20000
2411.4
0.9187538
-0.06268
0.119993
8
40000
2411.4
1.2197838
-0.01576
0.060213
Theoretical:
Table 4: Calculations of Theoretical Gain values for High Pass
Filter
16
Experimental:
Table 5: Calculations of Experimental Gain values for High Pass
Filter
Table 6: Calculations of Experimental Phase Lag for High Pass Filter
17
#
Cut-off
frequency
Frequency
(set)
Initial
voltage
Twice
Amplitude
multiplied
Factor
Output
voltage
Twice
Amplitude
multiplied
Factor
X-axis
y-axis
f
c
f
2*Vi*
(volts/cm)
2*V
o
*(Volts/cm)
log
(
f
f
c
)
20log
(
V
0
V
i
)
Hz
Hz
Volts
cm
1
2411.4
199
22.5
2.5
-1.08342
-19.0849
2
2411.4
500
22.5
5
-0.68331
-13.0643
3
2411.4
1000
22.5
9.5
-0.38228
-7.48918
4
2411.4
2000
22.5
15.5
-0.08125
-3.23702
5
2411.4
3981
21.5
19.5
0.217716
-0.84808
6
2411.4
8010
21.5
21.5
0.521356
0
7
2411.4
20020
21.5
21.5
0.919188
0
8
2411.4
40398
22
22
1.224084
0
Phase shift
(lead '+', lag
'-')
Wavelength
φ
Φ*(
π
180
)
N
M
N/M
(N/M)*360
seconds
seconds
0.00115
0.0049
0.234694
84.4898
1.474625
0.0004
0.00188
0.212766
76.59574
1.336848
0.00016
0.00094
0.170213
61.2766
1.069478
0.00007
0.000475
0.147368
53.05263
0.925943
0.00002
0.00024
0.083333
30
0.523599
0.000003
0.000122
0.02459
8.852459
0.154505
0.000001
0.000048
0.020833
7.5
0.1309
0.0000003
0.000024
0.0125
4.5
0.07854
-1.5
-1
-0.5
0
0.5
1
1.5
-30
-25
-20
-15
-10
-5
0
f(x) = 0
R² = 0
Gain VS Frequency
Low Pass Gain (Theoretical)
Polynomial (Low Pass Gain (Theoretical))
Low Pass Gain (Experimental)
High Pass Gain (Theoretical)
Frequency: log(f/fc)
Gain (V0/Vi)
Figure 15: Gain Characteristics Of Both High and Low Pass Filter With Theoretical Plot
0
2
4
6
8
10
12
14
16
18
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Phase Lag vs Frequency
Low Pass Phase Lag (Theoretical)
High Pass Phase Lag (theoretical)
High Pass Phase Lag (Experimental)
Low Pass Phase Lag (Experimental)
Frequency (f/fc)
Phase Lag
18
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Figure 15: Phase lag Characteristics Of Both High and Low Pass Filter With Theoretical Plot
-1.5
-1
-0.5
0
0.5
1
1.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Chart Title
High Pass Theoretical Phase
Low Pass (theoretical Phase)
Series6
Low Pass (Experimental Phase)
log(f/fc) φ Figure 16: Phase Lag Characteristics Plot With Logarithmic Value Of Frequency Ratio
Conclusion
In conclusion, we were able to see that the experimental value is very close to the theoretical value on the graphs. For example, in the Phase Lag vs Frequency (f/fc), it’s obvious that the experimental points and theoretical points don’t exactly match. The main reason the two types of values were close and not exact because the set frequency and predicted frequency were closely different. Also, there’s a possibility of a measurement error from the oscilloscope and other stuff that were used to collect data. In 19
the end we understand that frequencies change and there is a low chance of obtaining the perfect frequency. Bibliography
Holman, J. Experimental Methods for Engineers 8
th
edition
. Mc Graw Hill. Zhu, C. (2009). Me 343 Laboratory Introduction
.
Wolfram Research, Inc. (2023, June). Fourier Series -- from Wolfram MathWorld
. Wolfram MathWorld. Retrieved June 7, 2023, from https://mathworld.wolfram.com/FourierSeries.html
.
Storr, W. (2022a, August 6). Passive High Pass Filter
. Basic Electronics Tutorials. Retrieved June 5, 2023, from https://electronics-tutorials.ws/filter/filter_3.html
Storr, W. (2022b, August 6). Passive Low Pass Filter
. Basic Electronics Tutorials. Retrieved June 5, 2023, from https://www.electronics-tutorials.ws/filter/filter_2.html
20
Appendix
Original Data:
R = 1000
Ω
C = 6.6*
10
−
8
LOW PASS FILTER
#
Frequency
Input Voltage Twice
amplitude
Multiplication factor
Output Voltage
Twice amplitude
Multiplication factor
Phase shift
(lead '+', lag '-')
Multiplication factor
Wav length
Multiplication factor
plan
set
2*V
i
2*V
o
N
M
UNIT
S
Hz
Hz
cm
volts/
cm
cm
volts/
cm
cm
seconds/
div
Cm
seconds/
div
1
200
199
4.5
5
4.5
5
-0.4
0.2EE-3
9.8
0.5EE-3
2
500
500
4.5
5
4.5
5
-0.8
0.1EE-3
9.4
0.2EE-3
3
1000
1000
4.5
5
4.2
5
-1.4
50EE-6
9.4
0.1EE-3
4
2000
2000
4.5
5
3.4
5
-1.1
50EE-6
9.5
50EE-6
5
4000
3981
4.3
5
5.3
2
-2.1
20EE-6
4.8
50EE-6
6
8000
8010
4.3
5
6
1
-2.6
10EE-6
6.1
20EE-6
7
2000
0
2002
0
4.3
5
5
0.5
-1.1
10EE-6
4.8
10EE-6
8
4000
0
4039
8
4.4
5
6.1
0.2
-1.1
5EE-6
4.8
5EE-6
Table 7: Original Data of Low Pass Filter part of Experiment
21
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HIGH PASS FILTER
#
Frequency
In put Voltage
Twice amplitude
Multiplication factor
Output Voltage
Twice amplitude
Multiplication factor
Phase shift
(lead '+', lag '-')
Multiplication factor
plan
f' set
2*V
i
2*V
o
N
UNIT
S
Hz
Hz
cm
volts/cm
cm
volts/cm
Cm
seconds/div
1
200
199
4.5
5
22.5
0.5
5
2.5
2.3
0.0005
2
500
500
4.5
5
22.5
1
5
5
2
0.0002
3
1000
1000
4.5
5
22.5
1.9
5
9.5
0.8
0.0002
4
2000
2000
4.5
5
22.5
3.1
5
15.5
1.4
0.00005
5
4000
3981
4.3
5
21.5
3.9
5
19.5
2
0.00001
6
8000
8010
4.3
5
21.5
4.3
5
21.5
0.3
0.00001
7
20000
20020
4.3
5
21.5
4.3
5
21.5
0.5
0.000002
8
40000
40398
4.4
5
22
4.4
5
22
0.3
0.000001
Table 7: Original Data of High Pass Filter part of Experiment
Detailed Sample Calculation
:
f
c
=
1
2
∗
π
∗
R
∗
C
=
1
2
∗
1000
∗
6.6
∗
10
−
8
=
2411.438532
Theoretical Gain Low Pass: 22
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(
V
0
V
i
)
th
dB
=−
10 log
[
1
+
(
f
f
c
)
2
]
=−
10log
[
1
+
(
200
2411.438532
)
2
]
=−
10log
[
1
+
(
0.082938046
)
2
]
=−
10log
[
1.00687871
Theoretical Gain High Pass:
(
V
0
V
i
)
th
dB
=
20 log
(
f
f
c
√
1
+
(
f
f
c
)
2
)
=
20 log
(
200
2411.438532
√
1
+
(
200
2411.438532
)
2
)
=
20log
(
0.082938046
√
1
+
(
0.082938046
)
2
)
=
20log
(
0.08293804
√
1.0068787
Theoretical Phase Lag Low Pass:
φ
TH
=−
tan
−
1
(
f
f
c
)
=−
tan
−
1
(
200
2411.438532
)
=
¿
−
tan
−
1
(
¿
0.082938046
)=−
0.082748658
¿¿
Theoretical Phase Lag High Pass:
φ
TH
=
π
2
−
tan
−
1
(
f
f
c
)
=
π
2
−
tan
−
1
(
200
2411.438532
)
=
π
2
−
tan
−
1
(
0.082938046
)
=
1.488047669
Experimental Gain Low and High Pass:
20log
(
V
0
V
i
)=
20log
(
4.5
4.5
)
=
20log
(
1
)
=
0
Experimental Phase Lag Low Pass:
φ
=
(
N
M
)
∗
360
∗
(
π
180
)
=
(
−
0.00008
0.0049
)
∗
2
π
=−
0.102582617
Nomenclature:
Symbol
Description
f
F
requency motor
f
c
Cut-off F
requency
C
Capacitance
dB
Decibels
23
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Hz
Hertz
M
Period
N
Phase Shift
R
Resistance
V
i
Input Volt
V
o
Output Volt
ϕ
∨
φ
Phase Change
π
3.141592
ME 343 Laboratory Instructions
Safety Hazards
Instrumentation Laboratory Room 214
HAZARD: Rotating Equipment / Machine Tools
Personal Protective Equipment
: Safety Goggles;
24
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Standing Shields, Sturdy Shoes.
Personal Care
1.
Do not wear loose clothing, Neck Ties/Scarves;
Jewelry (remove).
2.
Tie back long hair.
HAZARD: Heating – Burns
Personal Protective Equipment
: High temperature
gloves; High temperature apron.
HAZARD: Electrical - Burns / Shock
Personal Care:
Take Care while doing electrical
connections, particularly with grounding; do not use
frayed electrical cords.
HAZARD: Water / Slip Hazard
Personal Care:
Clean any spills immediately.
HAZARD: Noise
Personal Protective Equipment:
Ear Plugs
Rotation Speed Measurement and General Data Analysis
Objectives:
1.
Least square method application (Linearity)
2.
Random Data Analysis (Gaussian Distribution): Rotation speed
measurement by Digital Tachometer
3.
Noise Filtration: Characteristics of High and Low pass RC Filter
4.
Additional methods of rotational speed measurement
a. Stroboscope
25
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b.
Oscilloscope Direct Measurement
c.
Lissajou Figures
Major Equipments
:
D.C. Generator with Magnetic Pickup Output and D.C. Motor; Electronic
Frequency Counter; Digital Multimeter; Electronic Tachometer; Stroboscope;
Oscilloscope; Function Generator; Hi/Lo RC Filter
Procedure
:
A. Least Square Method Application (Linearity)
a.
Connect magnetic pickup to electronic frequency counter. The counter
measures rotation speed in revolution per minute (rpm), as the gear on the motor shaft has 60 teeth, which produces 60 counts per revolution.
b.
Connect D.C. generator to digital voltmeter. Set motor speed to 1500
rpm on the electronic frequency counter with the motor speed control
knob.
c.
Turn the D.C. amplifier knob to 15.0 Volts and lock the knob on Test
Rig.
d.
Adjust the motor speed from 1500 to 0 rpm in interval of 300-rpm, at
each point, record the electronic frequency counter reading and
voltage.
B.
Random Data Analysis: Rotating Speed by Digital Tachometer
Caution
: Use minimum pressure
needed to record the actual shaft speed, in order to minimize the loading error and to avoid damage to the
equipment.
1.
Set the motor speed to 1000 ± 10 rpm (as read on the electronic
frequency counter).
2.
Repeat the first step at least for 60 measurement data with each
member of the team should record at least 15 readings with the digital tachometer.
C.
Additional Methods for Rotational Speed Measurement
a.
Stroboscope
i.
Set motor speed to 1000 rpm and record the electronic frequency
counter reading.
ii.
Set the stroboscope frequency to approximately the electronic
frequency counter reading by fine-adjust the stroboscope frequency,
until the timing mark appears stationary. Record the stroboscope
reading, and sketch the mark on the gear face (or take a picture for
record).
26
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iii.
Without changing the motor speed, increase the stroboscope
frequency until it is doubled. Record the stroboscope frequency.
Sketch the timing mark pattern (or take a picture for record).
iv.
Repeat step “c” for a stroboscope frequency of 3 and ½ times true
shaft speed
.
b.
Lissajou Figures
i.
Connect the output of the electronic frequency counter to the vertical
amplifier of the oscilloscope.
ii.
Set the motor speed to 1500 rpm, adjust the vertical amplifier gain until a 4 or 5 cm peak-to-peak sine wave appears on the screen.
The time sweep setting can be set at any convenient value.
iii.
Leave the motor speed and all the setting which you just made
unchanged; but temporarily disconnect the input to the vertical
amplifier of the oscilloscope. Turn your attention now to the horizontal amplifier of the oscilloscope as explained below.
iv.
Connect the output of the audio-oscillator to the horizontal amplifier
of the oscilloscope.
v.
Adjust the oscillator frequency to equal approximately the frequency
of the electronic frequency counter output. Turn the trigger control to
the x-y position.
vi.
Adjust either the amplitude setting of the oscillator or the gain setting
of the horizontal amplifier of the oscilloscope, or
both, until the resulting display on the oscilloscope screen will be a “line” of approximately 5 cm length.
vii.
Re-connect the output of the electronic frequency counter to
the vertical amplifier of the oscilloscope. The resulting Lissajous figure should remain essentially stationary, although it will be subject to
some fluctuation.
viii.
Sketch the Lissajous figure (or take a picture for record) and
record both oscillator frequency and motor speed from the electronic frequency counter.
ix.
Increase the oscillator frequency until a double loop figure appears
(leaving the motor speed unchanged). Sketch the Lissajou figure (or
take a picture for record) and record both
oscillator frequency and motor speed from the electronic frequency counter.
27
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x.
Decrease the oscillator frequency until another double loop figure
appears. Sketch the Lissajou figure and record both oscillator frequency and motor speed from the electronic frequency counter.
xi.
Leave the oscillator frequency unchanged, and change the motor
speed until a single loop appears. Sketch the figure and record oscillator frequency and the motor speed from the electronic frequency counter.
D.
Signal to Noise Ratio Improvement by RC Filter
a.
Set oscillator (frequency generator) to 1000 Hz.
b.
Connect the output to the electronic counter and to the input
terminals A & B of the low pass RC filter and also to CH 1 of the
oscilloscope.
c.
Adjust the vertical gain to produce a suitable (say 4.0 com peak-
to-valley) display.
d.
Connect the output of the low-pass filter to CH 2 vertical input of the
oscilloscope. Record:
i.
Vertical peak-to-valley CH 1 display (cm) and gain setting
(volts/cm).
ii.
Vertical peak-to-valley CH 2 display (cm) and gain setting
(volts/cm).
iii.
Phase lag of the filter output signal with respect to the filter
input signal, i.e. record “M” and “N” (see Fig.4).
Note: φ = (N)(360)/M, where φ = phase angle in degrees.
(In Fig.4, there is a phase lag φ is negative)
Note: Gain Controls must be in “detent position!!
Repeat the above for the following oscillator frequency settings: (making sure
that the input signal amplitude remains unchanged).
200; 500; 1,000; 2,000; 4,000; 8,000; 20,000; 40,000 Hz
Repeat the above measurements for the high pass filter. Clearly note what lags
(or leads) what.
28
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Bonus Question
Based on the derivations shown for the low pass filters (which was presented in class), derive the gain and phase shift relationships for a band pass filter.
Figure : Bonus question Bandpass RC Filter Schematic Diagram
For Low pass:
i
(
t
)
=
v
i
(
t
)
−
v
0
(
t
)
R
1
=
C
2
d v
0
(
t
)
dt
v
i
(
t
)
−
v
0
(
t
)
=
R
1
C
2
d v
0
(
t
)
dt
v
i
(
t
)
=
v
0
(
t
)
+
R
1
C
2
d v
0
(
t
)
dt
……………………………...equati
on 1
For High pass:
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i
(
t
)
=
v
0
(
t
)
R
2
=
C
1
d v
i
(
t
)
−
d v
0
(
t
)
dt
v
0
(
t
)
=
R
2
C
1
d v
i
(
t
)
−
d v
0
(
t
)
dt
R
2
C
1
(
d v
i
(
t
)
)
dt
=
R
2
C
1
d v
0
(
t
)
dt
+
v
0
(
t
)
……………………………...equa
tion 2
Form equation 1 and 2
d
dt
(
v
i
(
t
)
)
=
d
dt
(
v
0
(
t
)
+
R
1
C
2
d v
0
(
t
)
dt
)
d
dt
(
v
i
(
t
)
)
=
d
dt
(
v
0
(
t
)
)
+
R
1
C
2
d
2
v
0
(
t
)
d t
2
d
dt
(
v
i
(
t
)
)
−
R
1
C
2
d
2
v
0
(
t
)
d t
2
=
d
dt
(
v
¿¿
0
(
t
)
)
¿
……………………………...
equation 3
d
dt
(
R
2
C
1
(
d v
i
(
t
)
)
dt
)=
d
dt
¿¿
R
2
C
1
d
2
d t
2
(
v
i
(
t
)
)=
R
2
C
1
d
2
d t
2
(
v
¿¿
0
(
t
))+
d
dt
(
v
¿¿
0
(
t
)
)
¿¿
R
2
C
1
d
2
d t
2
(
v
oL
(
t
)
)
−
R
2
C
1
d
2
d t
2
(
v
¿¿
0
(
t
))=
d
dt
(
v
¿¿
0
(
t
)
)
¿¿
……………………………...equation 4
Plugging in equation 3 and 4:
R
2
C
1
(
d v
i
(
t
)
)
dt
=
(
R
2
C
1
+
R
1
C
2
)
d v
0
(
t
)
dt
+
v
0
(
t
)
+
(
R
2
C
1
∗
R
1
C
2
)
d
2
dt
2
(
v
0
(
t
)
)
With the use of inverse Laplace, we were able to get:
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V
0
V
i
=
1
√
(
1
+
R
1
R
2
+
C
1
C
2
)
2
+
(
2
πf R
2
C
1
−
1
2
πf R
2
C
1
)
2
33
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Τρ
סוי
D2L Notes de cours 2 - MA...
D2L Solutions d'examen -...
B https://uottawa.brights...
ChatGPT
← Homework 4 - Fall 2024
Question 1 of 6
View Policies
>
education.wiley.com
ELG 3736 - Google Docs
On mesure la traînée s...
WP Homework 4 - Fall 2024
X W Question 1 of 6 - Hom...
- / 20
0
Current Attempt in Progress
The spring of modulus k = 203 N/m is compressed a distance of 300 mm and suddenly released with the system at rest. Determine the
absolute velocities of both masses (positive if to the right, negative if to the left) when the spring is unstretched. Neglect friction.
k
2 kg
= 203 N/m
wwwwww
5.6 kg
Answers:
2kg mass,
v=
5.6kg mass,
v =
Hi
eTextbook and Media
Save for Later
m/s
m/s
Attempts: 0 of 1 used Submit Answer
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A car part manufacturing company currently produces a suspension assembly for Toyota Motor Corporation. Figure 1 shows the breakdown structure of the suspension assembly and Figure 2 shows the final assembly and how to fit into a car. Table 1 shows the name of components, part numbers, and the number of components in each suspension assembly.
Table 1. Part lists for Suspension Assembly
Number in Figure 1
Part number
Part name
Amount per assembly
1
PA-T15-001
Shock absorber unit
1
2
PA-T15-002
Lower insulator
1
3
PA-T15-003
Spring bumper
1
4
PA-T15-004
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5
PA-T15-005
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6
PA-T15-006
Spring upper seat
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7
PA-T15-007
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8
PA-T15-008
Suspension Support
1
9
PA-T15-009
Washer
1
10
PA-T15-010
Stop nut
1
11
GE-001
Bolt
2
12
GE-002
Nut
5
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