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/labview-student-edition/779252-02.html?utm_source=google&utm_medium=ppc&kpid=371806&gclid=COPM1Pym-bwCFdBqfgodUF4A4A 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 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.

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? VRL VRU t TS 2TS 3TS IOUT = 1 IOUT = 2 IOUT = 5 0 1 2 3 4 5 6 7 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

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

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

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 = 𝑉 𝑅𝑈 − 𝑉 𝑅𝐿 𝑀 = 10𝑉 −(−10𝑉) 2 2 = 20𝑉 4 =5 𝑉 How do we interpret IOUT (VDigitized) and what is its uncertainty? A/D Converter Transfer Function

Input Resolution Error 𝐼𝑅𝐸= 1 2 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 = 1 2 17 =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 2 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

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?

Example (cont) Break Range into 4 Steps How to interpret Iout and its error 𝑉 𝑜𝑢𝑡𝐷 = 𝐼 𝑜𝑢𝑡 + 1 2 𝑉 𝑟𝑢 − 𝑉 𝑟𝑙 2 𝑁 + 𝑉 𝑟𝑙 = 𝐼 𝑜𝑢𝑡 + 1 2 5 𝑉 + −10 𝑉

Transfer Function First Order: Generic Where

Example

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

Example

Second Order