1. ME 322: Instrumentation Lecture 19
March 4, 2015
Professor Miles Greiner
LabVIEW program, A/D converter characteristics, actual measured grounded output, Input resolution error

2. 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?

3. 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
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

4. LabVIEW Five Main Acquisition Steps
Measurement I/O, NI DAQmx
Create a channel
Timing
Start Process
Read Data analog waveform
1 Channel
N-Samples
Output voltage – convert to ̊ C
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.

5. LabVIEW program

6. 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 ( …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

7. How “could” an A/D Converters work?
VRL
VRU t TS
2TS
3TS
IOUT = 1
IOUT = 2
IOUT = 5
VMeasured
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

8. 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 sub-ranges
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

9. Sampling Rate Sampling Frequency Sampling Period myDAQ
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

10. myDAQ Absolute Voltage Uncertainty
(0.11%FS)
(0.19%FS)
(0.12%FS)
(0.22%FS)
More information myDAQ
user guide, page 36-38
Demonstration
Short myDAQ Analog Input 1 and observe signal
What “should” the reading be when shorted?
In my office:
±10 V range: V ~ to V = 1.7 ± 0.9 mV (0.009% FS)
±2 V range: V ~ to V = 0.6 ± 0.3 mV (0.02% FS)
Is it larger at higher voltages?
Same in class?

11. 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 = 𝑉 𝑅𝑈 − 𝑉 𝑅𝐿 𝑀 = 10𝑉 −(−10𝑉) = 20𝑉 4 =5 𝑉
How do we interpret IOUT (VDigitized) and what is its uncertainty?
A/D Converter
Transfer Function

12. Input Resolution Error
𝐼𝑅𝐸= 𝐹𝑆 2 𝑁 = 𝑉 𝑅𝑈 − 𝑉 𝑅𝐿 2 𝑁+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 2 𝑁+1
For N = 16, 𝐼𝑅𝐸 𝐹𝑆 = =7.6× 10 −6 , IRE = 0.000,76%FS

13. 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

14. 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= 𝐹𝑆 2 𝑁 = 𝑉 𝑅𝑈 − 𝑉 𝑅𝐿 2 𝑁+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

15. myDAQ Uncertainties 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?

17. Example (cont)
Break Range into 4 Steps How to interpret Iout and its error 𝑉 𝑜𝑢𝑡𝐷 = 𝐼 𝑜𝑢𝑡 𝑉 𝑟𝑢 − 𝑉 𝑟𝑙 2 𝑁 + 𝑉 𝑟𝑙 = 𝐼 𝑜𝑢𝑡 𝑉 + −10 𝑉

18. Transfer Function
First Order: Generic Where

19. Example

20. Second Order
ζ ≡ damping ration ωn ≡ natural frequency without damping

21. Example

22. Second Order