ME 322: Instrumentation
Lecture 19
March 4, 2015
Professor Miles Greiner
LabVIEW program, A/D converter characteristics, actual
measured grounded output, Input resolution error
Announcements/Reminders
• Please fully participate in each lab and complete
the Lab Preparation Problems
– For the final you will repeat one of the last three labs,
solo, including performing the measurements, and
writing Excel, LabVIEW and PowerPoint.
– The labs help prepare you for the final
• HW 7 due Friday
• Lab 6 (wind tunnel) this week
– Please see schedule on WebCampus and be on time
– Bring Excel from HW 6
– How are things going in lab this week so far?
LabVIEW
• LabVIEW is available in the Engineering
Computer Center (ECC)
• You can buy LabVIEW on the web for around
$20, but you don’t have to
– http://www.studica.com/us/en/National-Instruments-students-ni-labview-mydaq/labviewstudent-edition/77925202.html?utm_source=google&utm_medium=ppc&kpid=371806&gclid=COPM1PymbwCFdBqfgodUF4A4A
• If you purchases it, you will need to download
and install DAQmx after installing LabVIEW
to use the Measurement I/O icons we use in
class
– http://www.ni.com/dataacquisition/nidaqmx
LabVIEW Five Main Acquisition Steps
Measurement I/O, NI DAQmx
1) Create a channel
2) Timing
3) Start Process
4) Read Data analog waveform
–
–
–
1 Channel
N-Samples
Output voltage – convert to ̊ C
5) Clear the test
Programming; Dialog and User Interface
simple error handler
• In this class we give and modify example LabVIEW programs.
• The intent is to help you quickly learn to perform data acquisition
programing.
• However, we don’t deal with structured programming.
LabVIEW program
Computer Data Acquisition (DAQ)
• Sensors detect measurands and produce signals
– Voltages, currents, resistances, pulses,…
• Conditioners convert those output signals to moderately large voltages
• Multiplexer (MUX) sweeps channel-to-channel and feeds individual signals, at
different times, to the Analog-to-Digital (A/D) converter
• A/D converter samples real voltages (7.674337…V) and converts them to integers
(0, 1, 2,…) that the digital computer can work with.
• Computer programs store and/or process the data
– In ME 322: LabVIEW and DAQmx drivers
How “could” an A/D Converters work?
VRU 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
01234567
VST
x
V
x
x
VRL
0
IOUT = 1 TS
VMeasured
IOUT = 2 2TS IOUT = 5 3TS
t
• One “method:” Saw Tooth Compare (not really used)
– Function generator produces ramps from VRL to VRU within period TS
– Converter break TS into M (= 2N, N = integer) equal sub-steps
– IOUT for each time step is the first sub-step when VST ≥ VMEASURED
• To interpret IOUT
– VDigitized = VRL + (IOUT +1/2)[(VRU-VRL)/M] ± (1/2)(VRU-VRL)/M
• Uncertainty decreases as M = 2N increase, and/or FS = VRU-VRL decreases
• Measurement is associated with center of time period
– Time uncertainty: ±TS/2
Characteristics of A/D Converters
• Full-scale range VRL ≤ V ≤ VRU
– FS = VRU - VRL
– For myDAQ the user can chose between two full-scale ranges
• ± 2 V, ± 10 V
• for Lab 7, 0 to 2.5 V, which range is used?
• Number of Bits (in its digital word) N
– The A/D converter breaks the full scale range into 2N subranges
– For myDAQ, N = 16, 216 = 65,536
– What does this mean?
• For example, a 2 bit word __ __ , in which each bit can be 0 or 1
• Has 22 = 4 combinations: 00, 01, 10, 11
• These are the digital signals (words) the A/D converter passes to the
computer
Sampling Rate
• Sampling Frequency
– fS = samples converted to digital per second [Hz]
• Sampling Period
– TS = 1/ fS; timed required to find IOUT
• myDAQ
– (fS)max = 200,000 Hz, TS = 0.000,005 sec = 5 msec
– User can chose lower rates
– If both channels are used, then (fS)max = ? Hz
myDAQ Absolute Voltage Uncertainty
(0.11%FS)
(0.19%FS)
(0.12%FS)
(0.22%FS)
• More information myDAQ
– user guide, page 36-38
– http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2007%20Boiling
%20Water%20Temperature/Lab7%20Index.htm
• Demonstration
– Short myDAQ Analog Input 1 and observe signal
• What “should” the reading be when shorted?
– In my office:
• ±10 V range: V ~ -0.0008 to -0.0026 V = 1.7 ± 0.9 mV (0.009% FS)
• ±2 V range: V ~ -0.0003 to -0.0009 V = 0.6 ± 0.3 mV (0.02% FS)
• Is it larger at higher voltages?
– Same in class?
Example
• For a ±10 Volt, N = 2 bit A/D converter, what digitized
voltages will it report for -∞ < V < +∞?
– M = 2N = __ sub-ranges
• Break input range into __ steps
• IOUT can be 0, 1, 2, 3
– Step size =
𝑉𝑅𝑈 −𝑉𝑅𝐿
𝑀
=
10𝑉 −(−10𝑉)
22
=
20𝑉
4
=5𝑉
– How do we interpret IOUT (VDigitized) and what is its
uncertainty?
IOUT
3
A/D Converter
Transfer Function
2
1
0
-15
-10
-5
0
VIN [volts]
5
10
15
Input Resolution Error
• 𝐼𝑅𝐸 =
1 𝐹𝑆
2 2𝑁
=
𝑉𝑅𝑈 −𝑉𝑅𝐿
2𝑁+1
• At edge of range 𝐼𝑅𝐸 → ∞
– Don’t go there! (by design)
• IRE quantifies the random error from digitization
process
– IRE decreases (improves) as
• N increases
•
𝐼𝑅𝐸
𝐹𝑆
=
1
2𝑁+1
• For N = 16,
𝐼𝑅𝐸
𝐹𝑆
=
1
217
= 7.6 × 10−6 , IRE = 0.000,76%FS
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?
Example (cont)
Break Range into 4 Steps
Input Range
(V)
-10 to -5
-5 to 0
0 to 5
5 to 10
Iin
B2
00
01
10
11
B10
0
1
2
3
How to interpret Iout and its error
1 𝑉𝑟𝑢 − 𝑉𝑟𝑙
𝑉𝑜𝑢𝑡𝐷 = 𝐼𝑜𝑢𝑡 +
+ 𝑉𝑟𝑙
𝑁
2
2
1
= 𝐼𝑜𝑢𝑡 +
5 𝑉 + −10 𝑉
2
Vout
(V)
-7.5
-2.5
2.5
7.5
Eror
∞
± 2.5
± 2.5
∞
Transfer Function
First Order: Generic
Where
Example
Second Order
ζ ≡ damping ration
ωn ≡ natural frequency without damping
Example
Second Order