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ME 322: Instrumentation
Lecture 20
March 7, 2014
Professor Miles Greiner
Announcements/Reminders
• I apologize that I didn’t make sure DAQmx was
installed in the ECC
– You may turn in the L7PP on Monday, if necessary.
– It should be fully operational this weekend.
• HW 7 due now
• HW 8 Due next Friday
– Then Spring Break!
• Please fully participate in each lab and complete
the Lab Preparation Problems
– For the final you will repeat one of the last four labs,
solo, including performing the measurements, and
writing Excel, LabVIEW and PowerPoint.
A/D Converter Characteristics
• Full-scale range VRL ≤ V ≤ VRU
– FS = VRU - VRL
– For myDAQ the user can chose between two ranges
• ±10 V, ±2 V (FS = 4 or 20 V)
• Number of Bits N
– Resolves full-scale range into 2N sub-ranges
– Smallest voltage change a conditioner can detect:
• DV = FS/2N
– For myDAQ, N = 16, 216 = 65,536
• ±10 V scale: DV = 0.000,31 V = 0.31 mV = 310 mV
• ±2 V scale: DV = 0.000,076V = 0.076mV = 76 mV
• Sampling Rate fS = 1/TS
– For myDAQ, (fS)MAX = 200,000 Hz, TS = 5 msec
Input Resolution Error
• The reported voltage is the center of the
digitization sub-range in which the measured
voltage is found to reside.
– So the maximum error is half the sub-range size.
• Inside the FS voltage range
– 𝐼𝑅𝐸 =
1 𝐹𝑆
2 2𝑁
=
𝑉𝑅𝑈 −𝑉𝑅𝐿
2𝑁+1
• At edge or outside of FS range
– 𝐼𝑅𝐸 → ∞
– To avoid this, estimate the range of voltage that must be
measured before conducting an experiment, and choose
appropriate A/D converter and/or signal conditioners.
• The IRE is the uncertainty caused by the digitization
process
myDAQ Uncertainties
Scale
±10 Volts
±2 Volts
Absolute Absolute
Accurcacy Accurcacy
23°C
18-28°C
22.8 mV
4.9 mV
38.9 mV
8.6 mV
0.1% FS
0.2% FS
Measurd
Shorted
Voltage Error
Input
Resolution
Error (IRE)
2.4 mV
0.9 mv
0.15 mV
0.03 mV
0.01 -0.02% FS 0.0008% FS
• What are these?
– AA: Maximum error of the voltage measurement reported by the
manufacturer for all voltage levels
• At different temperatures
– MSVE: Maximum error measured at V = 0V for one device
– IRE: Random error due to digitization process
• Which one do you think characterizes voltage uncertainty?
Lab 7 Boiling Water Temperature in Reno
• Water temperature uncertainty
• Standard TC wire uncertainty
– Larger of 2.2°C or 0.75% of measurement
– Note: 0.0075 x 293°C = 2.2°C
– wTC = 2.2°C
• For ±10 Volts, measured shorted voltage uncertainty MSVU = 0.0024V
– For signal conditioner SSC = 0.025 V/°C
– wTsc = MSVU/SSC = 0.0024V/0.025 V/°C = 0.096°C
• 𝑤𝑇 =
𝑊𝑇𝐶 2 + 𝑊𝑆𝐶 2 = 4.84 + .0092 =2.202°C ~ 2.2°C
A/D Converters can be used to measure a
long series of very rapidly changing voltage
• Great for measuring a voltage signal
– Would be very difficult using a regular voltmeter
• Allows determination of Rates of Change and Spectral
(Frequency) Content
• The voltage and time associated with each
measurement has some error
– It is associated with the centers of the voltage sub-range and
sampling time.
– Additional systematic and random errors as well
• What can go wrong?
Example
Ti
TB
T(t)
• A small thermocouple at initial temperature Ti is
placed in boiling water at temperature TB
• Its measured temperature versus time T(t) is
shown
• What caused the temperature to change?
– What do you expect the time-dependent heattransfer rate to the thermocouple 𝑄 [joules/sec =
watts] to look like qualitatively?
– How can we determine it quantitatively?
t [sec]
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0.019
T [oC]
20.599
20.387
20.646
20.316
20.905
20.528
20.716
20.858
20.693
20.905
20.669
20.811
20.811
20.716
20.246
20.646
20.387
20.387
20.693
20.222
1st Law of Thermodynamics
• 𝑄−𝑊 =
𝑑𝑈
𝑑𝑡
=
𝑑
−
𝑑
𝑑𝑇
𝑚𝑐𝑇 = 𝑚𝑐
𝑑𝑡
𝑑𝑇
time-derivative (𝑡)
𝑑𝑡
• How to estimate a
from a table of T versus t data?
– ∆𝑡𝑆 is the sampling time step [sec] (TS)
• First order numerical differentiation
– Centered differencing
–
𝑑𝑉
𝑑𝑡
𝑉 𝑡+∆𝑡𝐷 −𝑉 𝑡−∆𝑡𝐷
𝑡 = lim
∆𝑡𝐷 →0 𝑡+∆𝑡𝐷 − 𝑡−∆𝑡𝐷
𝑉 𝑡+∆𝑡𝐷 −𝑉 𝑡−∆𝑡𝐷
lim
2∆𝑡𝐷
∆𝑡𝐷 →0
=
– ∆𝑡𝐷 is the differentiation time step [sec]
– ∆𝑡𝐷 = 𝑚∆𝑡𝐷 , m = integer (1, 2, or ?)
– What is the best value for m (1, 10, 20, ?)
t [sec]
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0.019
T [oC]
20.599
20.387
20.646
20.316
20.905
20.528
20.716
20.858
20.693
20.905
20.669
20.811
20.811
20.716
20.246
20.646
20.387
20.387
20.693
20.222
Sample Data
• Lab 9 Transient Thermocouple Measurements
– Download sample data
– http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/
Lab%2009%20TransientTCResponse/LabIndex.htm
• Plot T vs t for t < 2 sec
• Show how to evaluate and plot derivatives with
different differentiation time steps
– Plot dT/dt vs t for m = 1, 10, 50
• Slow T vs t for 0.95 s< t < 1.05 s and 20°C < T < 50°C
– How do random errors affect “local” and “time averaged”
slopes?
Effect of Random Noise
• Measured voltage has real and noise components
– VM = VR+VN
–
𝑑𝑉𝑀
𝑑𝑡
=
𝑉𝑅 −𝑉𝑁 + − 𝑉𝑅 −𝑉𝑁 −
2∆𝑡𝐷
𝑑𝑉𝑅
• ∆𝑉𝑅 = 𝑉𝑅+ − 𝑉𝑅− =
∆𝑡𝐷
𝑑𝑡
• ∆𝑉𝑁 = 𝑉𝑁+ − 𝑉𝑁− ≈ 𝑤𝑉
•
•
•
𝑑𝑉𝑀
𝑑𝑡
𝑊𝑉
2∆𝑡𝐷
𝑊𝑉
For small ∆𝑡𝐷 ,
2∆𝑡𝐷
𝑑𝑉𝑅
𝑊𝑉
Want
≫
𝑑𝑡
2∆𝑡𝐷
=
𝑑𝑉𝑅
𝑑𝑡
RF, IRF, other errors
+
is large and random
– wV decreases as FS gets smaller and N increases
– Want ∆𝑡𝐷 to be large enough to avoid random error but small
enough to capture real events
T
TB
Ti
t=0
t
Example
A/D
N= 2
±10V
Interpret: 𝐼𝑜𝑢𝑡 → 𝑉𝑜𝑢𝑡,𝐷 = 𝐼𝑂𝑢𝑡 +
1
2
𝑉𝑟𝑢 −𝑉𝑟𝑙
2𝑁
+ 𝑉𝑐
Input
Range (v)
Iout
Vout,D
Max
Error (V)
-∞ to -5
-5 to 0
0 to 5
5 to ∞
0
1
2
3
-7.5
-2.5
2.5
7.5
∞
± 2.5V
± 2.5 V
∞