Digital.data.Measurement

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Chapter 1 Introduction

Chapter 1Introduction


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Th is h an dboo k is inten ded for newcom ers to th e field of data acquisition an d signalcond ition ing. Em ph asis is given to gen eral discussion s of ADC m easurem ent an d th esign al con dition in g requirem en ts of selected transdu cer typ es. For mo re detailed de-

scriptions of the signal conditioning schemes discussed, contact IOtech for Applica-tion s Notes an d Product Specification Sh eets. Addition al in form ation on IOtech prod-ucts is available in Ch apt er 9, a prod uct selection guide.

Most m easurem ent s begin with a tran sducer, a device that con verts a m easurable ph ysi-cal qu ality, such as tem peratu re, strain , or acceleration , to an electrical sign al. Tran s-du cers are available for a wide ran ge of m easurem en ts, an d com e in a variety of shap es,sizes, and specification s. Th is boo k is int en ded t o serve as a prim er for m aking m easure-m ent s by in terfacin g transducers to a com pu ter usin g sign al con dition ing.

S i g n a l c o n d i t i o n i n g c o n v e r t s atran sducer s sign al so th at an an alog-to-digital con verter (ADC) can m ea-sure th e signal . Sign al con dit ion ingcan include amplif icat ion, f i l ter ing,different ial app lication s, isolation , si-m ultan eous sam ple and h old (SS&H),current- to-voltage conversion, volt-age-to-frequen cy con version , l in ear-iza t ion an d mo re . Sign al cond i t ion -ing also includes excitation or bias for

t ransducers tha t requi re i t .

Figure 1.01 depicts a generic data ac-qu isition sign al-con dition ing con figu-

ration . Th e tran sducer is con n ected to th e in pu t of th e sign al cond ition ing electron ics.Th e outpu t of th e sign al con ditionin g is con n ected to an ADC in pu t. Th e ADC con -verts th e an alog voltage to a d igital sign al, wh ich is tran sferred to th e com pu ter forprocessing, graphing, and storage.

Analog-to-Digital Conversion. Chapter 2 includes a discussion of the four basic ADC

types, as well as issues such as accuracy, n oise redu ction , an d d iscrete sam plin g con sid-eration s. Top ics such as in pu t and sou rce im ped an ce, different ial voltage m easure-m ent s, sim ultan eous sam ple and h old, selectable inp ut ranges, m ultiplexing, and isola-tion are also discussed. A section on discrete sam plin g con sideration s, wh ich coversaliasin g, wind owin g, fast Fou rier tran sform s (FFTs), stan dard Fou rier tran sform s, anddigital filtering, is also included.

Fig. 1.0 1: Generic signal-conditioning scheme

SignalConditioning

Computer

Transducer

ADC


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Chapter 2 Analog-to-Digital Conversion

Chapter 2Analog-to-Digital Conversion....


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Fig. 2.0 1: 2-bit parallel converter

Th is ch apter exam ines general con sideration s for an alog-to-digital con verter (ADC) m ea-suremen ts. Discussed are th e fou r basic ADC types, providin g a gen eral description of each wh ile com parin g th eir speed and resolution . Issues such as calibration , linearity,

m issing cod es, an d n oise are discussed, as are th eir effects on ADC accuracy.

This chapter also includes information on simultaneous sample and hold (SS&H) andselectable in pu t ran ges. Finally, th is chap ter cont ains a section on discrete sam pling,wh ich in cludes Fou rier th eory, aliasin g, wind owin g, fast Fou rier tran sform s (FFTs), stan -dard Fou rier tran sform s, and digital filterin g.

ADC TypesAn ADC converts an an alog voltage to a digital nu m ber. Th e digital n um ber represen ts th einp ut voltage in discrete steps with finite resolution . ADC resolution is determ ined b y th en um ber of bits th at represen t th e digital nu m ber. An n -bit ADC h as a resolution of 1 part in2 n . For exam ple, a 12-bit ADC has a resolut ion o f 1 part in 4096 (2 12 =4,096). Twelve-bitADC resolut ion correspo n ds to 2.44 m V for a 10V range. Sim ilarly, a 16-bit ADCs resolu-tion is 1 part in 65,536 (2 16 =65,536), wh ich correspon ds to 0.153 m V for a 10V ran ge.

Man y differen t typ es of ana log-to -digital con verters are available. Differin g ADC typesoffer varyin g resolu tion , accuracy, an d speed specification s. Th e m ost pop ular ADCtypes are th e parallel (flash) con verter, th e successive approxim ation ADC, th e voltage-to-frequen cy ADC, and th e integrating ADC. Description s of each follow.

Parallel (Flash) ConverterThe parallel converter is the simplestADC im plem en tation . It uses a refer-en ce voltage at th e full scale of th e in-put range and a voltage divider com-posed of 2 n + 1 resisto rs in series, wh eren is th e ADC resolut ion in bits. Th evalue of the input voltage is deter-mined by using a comparator at eachof the 2 n reference voltages created in

th e voltage divider. Figure 2.01 dep ictsa 2-bit parallel converter.

Flash converters are very fast (up to500 MHz) because the b i ts are deter-

m ined in p ara llel . Th is m eth od requi res a la rge nu m ber of com para tors, therebylim it ing th e resolut ion of m ost paral lel con verters to 8 b i ts (256 com parato rs) . Flashcon verters are com m on ly fou n d in tran sien t digi t izers an d digi tal osci lloscopes.

Comparators

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EncoderVref Vinput


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Fig. 2.0 3: Voltage-to-frequency A DC

Successive Approximation ADCA successive approximation ADC em-ploys a d ig i ta l - to-analog conver ter(DAC) an d a sin gle com parat or. It ef-fectively makes a bisection or bin om ialsearch by beginn ing with an ou tpu t of zero. It pro vision ally sets each bit of th e DAC, beginn ing with th e m ost sig-n ifican t bit. Th e search com pares th eoutp ut of the DAC to t h e voltage beingm easured. If settin g a bit to on e causesth e DAC outp ut t o rise above th e in putvoltage, th at bit is set to zero. A dia-

gram of a successive approximationADC is sh own in Figure 2.02.

Successive approxim ation is slower th an flash con version because th e com parison s mu stbe performed in a series, and th e ADC m ust pau se at each step t o set th e DAC an d waitfor it to settle. However, con version rat es over 200 kHz are com m on . Successive ap-proxim ation is relatively in expen sive to im plem en t for 12- an d 16-bit resolution . Con -sequen tly, they are the m ost comm on ly used ADCs, and can be foun d in m an y PC-baseddata acquisition produ cts.

Voltage-to-Frequency ADCFigure 2.03 depicts the voltage-to-fre-qu en cy t ech n ique . Vo l t age -to - fr e -quen cy ADCs convert an inpu t voltageto an output pulse t ra in wi th a f re-quen cy proport ion al to th e input volt-age. Ou tp ut frequen cy is determ inedby coun ting pu lses over a fixed tim e in-terval, an d t h e voltage is inferred fromth e known relat ion sh ip.

Voltage-to-frequency conversion has ahigh degree of noise rejection, becauseth e inp ut signal is effectively int egratedover th e coun tin g int erval. Voltage-to-frequency con version is com m on ly usedto con vert slow and often n oisy sign als.

Digitalpulse train

Vin Voltage-to-frequencyconverter

Timingcircuitry

Digital

outputs

Pulse

counter

Fig. 2.0 2: Successive approximation ADC

Digitaloutputs

Comparator

DAC

Controllogic &

registers+

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Fig. 2.04: Integration and discharge of an integrating ADC

It is also u seful for remo te sen sing app lication s in n oisy environm ent s. Th e in pu t volt-age is converted to a frequency at the remote location, and the digital pulse train istransm itted over a pair of wires to th e coun ter. Th is elimin ates th e no ise that can be

introd uced in th e transm ission of an an alog signal over a long distance.

Integrating ADCA n um ber of ADCs use int egrating tech -niques , which measure the t ime tocharge or discharge a capacitor t o d e-term ine inp ut voltage. Figure 2.04sho ws Dual-slope in tegration , a com -m on in tegration techn ique. Using acurrent that is proportional to the in-

pu t voltage, a capacitor is ch arged fora fixed tim e period. Th e average in pu tvoltage is determin ed by m easuring th etim e required to disch arge th e capaci-tor usin g a con stan t curren t.

Integrating th e ADC inp ut over an in terval reduces th e effect of noise pickup at th e AClin e frequen cy if th e in tegration tim e is m atch ed to a m ultiple of th e AC period. For th isreason , it is com m on ly used in p recision d igital m ultim eters an d pan el m eters. Twen ty-

bit accuracy is not u n com m on . Th e disadvan tage is a relatively slow conversion rate (60Hz m axim um , slower for ADCs th at in tegrate over mu ltiple line cycles).

Summary of ADC TypesFigure 2.05 summarizes the previously discussed ADC types and their resolut ionan d speed ran ges.

Integrationtime

Dischargetime

Fixed dischargecurrent

=

IVinput

V c a p a c

i t o r

Vref

Vinput

Td

Ti

TdTi

ADC Type TableADC Type Typical Typical

Resolution SpeedParallel Converter 4-8 bit 100 kHz-500 MHz

Successive Approximat ion 8-16 bit 10 kHz-1 MHz

Voltage-to-Frequency 8-12 bit 1-60 Hz*

Integrating 12-24 bit 1-60 Hz*

* With line cycle rejection

Fig. 2.05: Summ ary of ADC types


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AccuracyAccuracy is an im portan t con sideration wh en selecting an ADC for use in t est an d m easure-

m ent application s. Th e following section p rovides an in-depth discussion o f accuracy con -siderations, pertaining to resolution, calibration, linearity, missing codes, and noise.

Accuracy vs. ResolutionTh e accuracy of a m easurem en t is influen ced by a variety of factors. If each in depen den terror is i, th e total error is

total = i2

i

Th is calculation includ es errors resultin g from th e tran sducer, n oise pickup, ADC qu an -tization , gain , offset, an d o th er factors.

ADC resolution error is term ed qu an tization error. In an ideal ADC, an y voltage in th erange th at correspon ds to a un ique digital code is represent ed by th at code. Th e error inth is case is h alf of th e least significan t bit (LSB) at m ost. For a 12-bit ADC with a 10Vrange, this error is 2.44 m V (0.0244%). Th ere are th ree com m on m eth ods of specifyinga con tribut ion to ADC error: th e error in least sign ificant bits (LSBs), th e voltage errorfor a specified range, an d th e percen t-of-readin g error. It is im po rtan t to recogn ize th atm ost ADCs are n ot as accurat e as th eir specified resolut ion , because qu an tization erroris on ly on e poten tial sou rce of error. Non eth eless, th e accuracy of a good ADC sh ou ldapp roach its specified resolut ion .

For m ore informat ion concernin g accuracy, refer to t h e Calibration section , wh ich fol-lows. For an in -dep th discussion of errors arisin g in particular tran sducers, refer toChapt ers 3 through 8.

Figure 2.06 illustrates com m on error typ es en coun tered wh en u sin g a 3-bit ADC. If th em an ufacturer provides calibration p rocedu res, offset an d gain errors can usually be re-du ced to n egligible levels, as discussed below. However, errors in lin earity an d m issin gcodes will con tribut e to th e overall error.

CalibrationTh ere are several com m on m eth ods for calibrating an ADC. In h ardware calibration ,th e offset an d gain of th e in strum ent ation am plifier th at serves as th e ADC fron t en d isadjusted with trim p ots. (Th e gain of the ADC can also be adjusted by chan gin g thereference voltage.) In h ardware/software calibration , digital-to-an alog con verters th atn ull th e offset and set th e full scale voltages are program m ed via software. In softwarecalibration , th ere is no h ardware adjustm ent . Calibration correction factors are storedin th e no n volat ile m emory of the data acquisi t ion system or in th e com puter and usedto con vert th e reading from th e ADC.


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Even if an ADC is calibrated at th e facto ry, it will n eed to be calibrated again after a p eriodof time (typically six months to a year, but possibly more frequently for ADCs of greaterresolution th an 16 bits). Variation s in th e operating tem perature can also affect in strum en tcalibration . Calibration p rocedures vary bu t usually requ ire eith er a known referen ce sourceor a m eter of greater accuracy th an th e device being calibrated . Typically, offset is set via a0V inpu t, an d gain is set via a full-scale in pu t.

In m any m easuremen ts, th e voltage is n ot th e ph ysical quantity un der test. Con sequent ly,it may be preferable to calibrate the complete measurement system rather than its indi-vidual parts. For exam ple, con sider a load cell for wh ich th e m an ufactu rer specifies th eout pu t for a given load an d excitation voltage. On e could calibrate the ADC and com bineth is with t h e m an ufacturers specification an d a m easurem en t of th e excitation voltage;h owever, th is tech n ique is op en to error. Specifically, th ree distin ct error sou rces are pos-sible in t h is tech n ique: error in t h e ADC calibration , error in t h e man ufacturers specifica-

tion s, an d error in t h e measuremen t of th e excitation voltage. To circum vent th ese errorsources, one can calibrate th e measuremen t system usin g kn own loads an d ob tain a directrelation ship between load and ADC outp ut.

4

Ideal

Input volts

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t p u

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Fig. 2.0 6: Comm on ADC error sources. The straight line is ideal output from an ADC with inf inite-bit resolution. The step function shows the indicated error for a 3-bit ADC.


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LinearityIf inp ut voltage and ADC outp ut deviate from th e diagon al lines in Figure 2.06 mo re thanthe ideal step function, the result is ADC error that is nearly impossible to eliminate bycalibration . Th is typ e of ADC error is referred to as n on linearity error. If n on linearity ispresen t in a calibrated ADC, th e error is often largest n ear th e m iddle of the in pu t ran ge, assho wn in Figure 2.06. Th e non linearity in a good ADC sho uld be 1 LSB or less.

Missing CodesSom e ADCs h ave missing codes. In Figure 2.06, th e ADC does no t provide an ou tpu t of four for an y in pu t voltage. Th is error can result in a sign ifican t loss in resolut ion an daccuracy. A qu ality ADC shou ld h ave no m issin g codes.

NoiseMan y users are surp rised by n oise en coun tered wh en m easurin g m ill ivolt sign als orat tem pt ing accurate m easurem en ts on larger s ignals . Invest ing in an accurate ADCis on ly th e first s tep in accurately measurin g an alog inp ut s ign als. Con trol l in g n oiseis im perat ive.

Man y ADCs reside on cards that plug in to a PC expan sion bus, wh ere electrical noise canpresen t serious prob lem s. Expa n sion bu s n oise often far exceeds th e ADCs sensitivityresultin g in significant loss of measuremen t accuracy. Placin g th e ADC ou tside th e PC isoften a better solution. An ADC in an external enclosure can com m un icate with th e

com pu ter over an IEEE 488 bu s, serial po rt, or parallel po rt. If an a pp lication requ iresplacemen t of th e ADC with in t h e comp uter, th e no ise level sh ould be tested by con n ect-ing th e ADC in put t o sign al comm on and observin g deviation s in ADC outpu t. (Con -n ecting th e ADC inp ut to sign al com m on isolates th e cause of th e n oise to th e circuitcard. More careful diagn ostics are n ecessary when using an external voltage sou rce be-cause n oise can arise from th e extern al sou rce and from th e in pu t leads.)

Noise Reduction and Measurement AccuracyOn e tech n ique for reducin g no ise and ensurin g m easuremen t accuracy is with isolation ,wh ich also elim inates groun d loops. Groun d loops occur wh en two or m ore devices in

a system , such as a m easuremen t instrum ent an d a transducer, are con n ected to groun dat different p h ysical location s. Slight differences in t h e actual poten tial of each groun dresults in a curren t flow from on e device to th e oth er. Th is current , wh ich often flowsth rough th e low lead of a pair of measurem en t wires, gen erates a voltage drop wh ich candirectly lead to m easurem en t in accuracies and n oise. If at least on e device is isolated,such as th e m easuremen t device, th en th ere is no p ath for th e current flow, and t h erebyn o con tribution to n oise or inaccuracy.


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infrared em ission from an LED is detected by a ph otod iode on th e opp osite side of aqu artz barrier. Figure 2.07 illustrates an opt ically-coup led isolation am plifier. Op tocou -plers can be u sed to tran smit pu lse train s in wh ich frequen cy or pulse width vary with

an alog signal m agnitud e or wh ich cont ain n um erical data in serial pu lse trains. It iseven p ossible to tran smit an alog in form ation by varyin g LED current as in Figure 2.07.Magn etic barriers usin g tran sform ers an d capacitive barriers are gen erally in tern al andused in m on olith ic or h ybrid isolation am plifiers.

Frequency Coupled Isolation. In frequen cy coupled isolation , a h igh frequen cy carriersign al is ind uctively or capacitively coup led across th e isolation barrier. The sign al ismodulated on the input s ide and demodulated on the output s ide to reproduce theoriginal in put signal.

Isolated ADC. Wh en u sing an isolated ADC, the ADC and accom pan yin g sign al con di-tion ing are floated. Th e in put signal is converted to a d igital signal by th e ADC and th ein terface for tran sferrin g th e digital code is digitally isolated. See Ch apt er 6 for a de-tailed discussion .

Discrete Sampling ConsiderationsTh e Nyquist sam pling th eorem says th at if a sign al only con tain s frequen cies less thancutoff frequen cy f c, all the in form ation in th e sign al can be captu red by sam plin g at 2f c.Th e upshot of th is is th at captu rin g a signal with m axim um frequency com pon ent f m axrequires sampling at a rate of at least 2f m ax . In practice, for working in t h e frequen cy

dom ain, it is best to set th e sam pling rate between five an d ten tim es th e sign als highestfrequency comp on ent. However, for viewin g waveform s in th e time dom ain , it is n otun comm on to sam ple 10 times th e frequency of interest. On e reason is to retain accu-racy at th e sign als h igh er frequen cy com po n en ts.

AliasingAliasin g can also be seen in th e time do m ain. Figure 2.09 sh ows a 1-kHz sin e wavesamp led at 800 Hz. Th e app arent frequ en cy of th e sin e wave is m uch t oo low. Figure2.08 sh ows th e result of sam pling th e sam e 1-kHz sin e wave at 5 kHz. Th e sam pled waveapp ears to h ave th e correct frequen cy.

Aliasing is the main reason to sample at a rate higher than the Nyquist frequency.Aliasingthe generation of false, low-frequency signalsoccurs when an ADCs sam-pling rate is too low. In put signals are seldom ban dwidth lim ited with zero amp litud eh igh er than f m ax . A signal with frequen cy com pon ent s h igh er th an on e-h alf th e sam -pling frequen cy will cause th e am plitude to appear below on e-h alf th e sam pling fre-qu en cy in th e Fou rier tran sform . Th is is called aliasin g, an d it can cau se in accuracies insam pled signal an d also in th e Fourier transform .


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Aliasing is illustrated in Figure 2.10, which shows a square waves Fourier transform.For th e purpo se of illustration , assum e th at th e experimen t h as been d esign ed to p ro-vide on ly frequen cies of un der 2 kHz. Ideally, a Fou rier tran sform of a 500-Hz squ arewave contains one peak at 500 Hz, and another at 1500 Hz, which is one third theh eigh t of th e first peak. In Figure 2.10, ho wever, high er frequen cy peaks are aliasedin to t h e Fou rier tran sform s low-frequ en cy range.

The u se of a low-pa ss filter at 2 kHz, asshown in Figure 2.11, removes mostof th e aliased peaks. Low-pa ss filtersused for this purpose are often calledanti-aliasing filters.

Wh en t h e sam pling rate is in creased tofour times the highest frequency of in-terest, th e Fourier transform in th e rangeof in terest looks even bett er. Alth ou gha small peak remains at 1,000 Hz, it is

probably the result of an imperfectsquare wave rather than an effect of alias-in g. See Figure 2.12.

Fig. 2.08: W hen sampled at just over 2 times the frequency of the sine wave, the frequency content of the signal is retained

Fig. 2.09: W hen sam pling too slowly, the acquired waveform erroneously represents th e real sine wave

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Actual Sine Wave Sampled at about 2 times fundamental

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Actual Sine Wave Sampled at about 1/2 times fundamental

Frequency [Hz]

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Fig. 2.1 0: Fourier transform of a 500-Hz square wavesampled at 4 kHz with no filtering


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WindowingWindo wing is the m ul t ip l ica t ion of the inp ut s ign al wi th a weigh t ing funct ion toreduce spu rious oscil lat ion s in a Fou rier t ransform . Real m easurem en ts are per-formed o ver f in i te t im e in tervals. In con trast , Fou rier t ransform s are defin ed overinfin i te t im e in tervals. As such, th e Fou rier t ransform of samp led data is an ap -proximat ion . Con sequ ent ly, the resolu t ion o f th e Four ier t ransform is limi ted toroughly 1 /T, where T i s th e fin i te t ime in terval over wh ich th e m easurem ent was

m ade. Four ier t ransform resolu t ion can on ly be im proved by sam pl in g for a lon gerinterval .

Using a f ini te t ime interval also causes spurious osci l lat ions in the Fourier t rans-form. From a mat h em atical viewpoin t , spu rious oscil lat ion s are caused by th e sig-n a l be in g in st an tan eously tu rned on a t t h e beg in n ing o f th e measuremen t and th ensudden ly turn ed off a t th e end o f the m easurem ent . Figure 2 .13 i llust ra tes an ex-am ple of spu rious osci llat ion s.

Imp lem ent ing wind ow fun ctions can h elp m inim ize spu rious oscillation s of a sign al.Multiplying th e sam pled data by a win dow fun ction th at rises gradually from zero de-creases the spu rious oscillation s at th e expen se of a sligh t loss in triggering resolut ion .There are many possible window functions, all of which involve trade-offs betweenam plitude estim ation an d frequen cy resolution .

Frequency [Hz]

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1.4

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Fig. 2.11: Fourier transform of 500-Hz squarewave sampled at a 4 kHz with low-pass filter cutoff at 2 kHz

Frequency [Hz]

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Fig. 2.12: Fourier transform of 500-Hz squarewave sam pled at 8 kHz with low-pass filter cutoff at 2 kHz


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Fast Fourier TransformsTh e fast Fou rier tran sform (FFT) is so com m on tod ay th at FFT h as becom e an im pre-cise syn on ym for Fou rier tran sform s in general. Th e FFT is a digital algorith m for com -pu tin g Fou rier tran sform s of data discretely sam pled at a con stan t in terval. Th e FFTssim plest im plemen tation requires 2 n sam ples. Oth er imp lem ent ation s accept oth er spe-cial n um bers of sam ples. If th e data set to be transform ed h as a different n um ber of samples than required by the FFT algorithm, the data is often padded with zeros toach ieve th e requ ired n um ber. Th is leads to in accuracies, bu t th ey are often t olerable.

Fig. 2.16: Three common window types

Hamming Hanning Blackman

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Fig. 2.15: W hen multiplied by a window function,the frequency information is preserved whileminimizing the affect of irregularities at thebeginning and end of the sam ple segment

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Fig. 2.14: W ithout window function, abrupt beginning and end points of waveform produceerroneous f requency information

Fourier transform of a sine wave using a window functionFourier transform of a sine wave with no window function

Frequency [Hz]

A m p l i t u d e

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Fig. 2.13: A Fourier transform with window function and without window function


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Standard Fourier TransformsA standard Fourier transform (SFT) can be used in applications where the number of sam ples cann ot b e arran ged t o fall on on e of th e special n um bers required b y an FFT.Th e SFT is also u seful for app lication s th at can n ot t olerate th e inaccuracies in trod ucedby pad din g with zeros, a h an dicap of th e FFT.

The SFT is also suited to applications where the data is not sampled at evenly spacedint ervals or wh ere sam ple poin ts are missing. Finally, th e SFT can be used to providem ore closely spaced poin ts in th e frequ ency dom ain th an can be obt ain ed with an FFT.(In an FFT, adjacen t po int s are separated by h alf th e sam pling frequ en cy. Points arbi-trarily close in frequ en cy can b e obt ain ed u sin g an SFT.)

Th ere are man y stan dard n um erical int egration tech n iques available for com pu tin g SFTs

from sam pled data. Wh ich ever tech n ique is selected for th e problem at h an d, it willprob ably be m uch slower th an an FFT of a sim ilar nu m ber of poin ts. Th is is becom ingless of an issue, h owever, as the speed o f mo dern com pu ters in creases.

Digital FilteringDigital filtering is accomplished inth ree steps. First, th e signal m ust besubjected to a Fourier t ransform.Th en , the signals am plitude in t h efrequen cy dom ain m ust be m ultiplied

by th e desired frequ en cy respon se. Fi-n ally, th e tran sferred sign al m ust beinverse Fourier tran sform ed back int oth e tim e dom ain. Figure 2.17 showsthe effect of digital filtering on then oisy sign al. Note th at th e solid lin erepresen ts th e un filtered sign al, wh ileth e two dashed lin es represent differ-en t digital filters.

Digital filtering is advantageous because the filter itself can be easily tailored to anyfrequen cy respon se witho ut in trodu cin g ph ase error. However, one disadvan tage of digital filtering is th at it can n ot b e used for ant i-aliasing.

Analog FilteringIn con trast to digital filterin g, analog filterin g can be u sed for an ti-aliasin g, but it is moredifficult t o ch an ge th e frequen cy respon se curves, since all analog filters int rodu ce som eelem en t of ph ase error.

Time [seconds]

V o

l t s

1.546

1.534

1.536

1.538

1.54

1.542

1.544

0 0.05 0.1 0.15 0.250.2

50Hz low-pass digital filter5Hz low-pass digital filter

Unfiltered signal

Fig. 2.1 7: The effect of digital filtering on the noisy signal


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18

Sampling HintsTh ere are several im portan t sampling h ints to observe when design ing an application .Th ese hin ts are n ot absolutes n or do th ey guaran tee optim al results. However, th ey doprovide a useful starting point for planning frequency analysis of a physical process.Th ese sampling h ints in clude:

A Fo u r ie r t r a n s fo r m s h i gh e st m e a n i n g fu l fr eq u e n c y i s o n e -h a lf o f t h esam pl ing f requ ency

Th e samp l in g r a t e sh ou ld be a t lea st t h ree to five t im es th e h igh est fr equen cyof in terest

An an ti-al iasing low-pass fi lter is typically required; th e cuto ff frequen cy shou ldbe close to th e signals high est frequen cy of interest

Dig it a l fi lt e ring can be used to sm ooth th e data o r to r em ove n o i se in a speci -f ied ran ge after acquisi t ion ; h owever, aliasin g can on ly be preven ted with an

an alog low-pass filter If t h e ph ase r el at ionsh ip between m ul t ip l e sign a ls i s impor t an t , a simul t a -

n eous sam ple and h old c ircui t shou ld be used (see mu l t ip lexin g in Ch apter 3) Four ie r t r ans fo rm reso lu t ion i s i nve rse ly p ropor t ion a l t o measuremen t t ime ;

acquir ing data over a longer period of t ime results in narrower peaks in theFou rier t ran sform .


19/90


20/90

Chapter 3 Multiplexing

20

MultiplexingA multiplexer is a switch that allows a

single ADC to measure many inputchan n els. Th is switch can be imp le-m en ted via relays or solid-state switch es.A relay is a m echan ical switch , so ratesare relatively slow (less than 1 kHz forreed relays, which are the fastest type),but large voltages and high isolation(several kV) can be achieved. Th e cur-rent capacity of a relay is determin ed byits size an d con tact type. Current s of 3Aare typical in relays used in laboratoryinstrum en ts. Much larger currents canbe switch ed with th e larger relays com -m on in indu strial applications.

Solid-state switches are much faster than relays, and speeds of several MHz are com-m on . However, th ese small devices are easily destroyed by voltages larger th an 25V,an d th ey are a poo r ch oice for isolated ap plication s. Solid-state switches typically sup-port current s less than 1 m A.

A m ultiplexing sch eme such as th at shown in Figure 3.01 elim inates the h igh cost of

h aving m ultiple ADCs. A program m able gain am plifier (PGA) allows each ch an n el toh ave a different gain an d inp ut ran ge. Multiplexing reduces th e rate at which dat a canbe acquired from an individual channel, because multiple channels are scanned se-qu en tially. For exam ple, an ADC th at can sam ple a sin gle ch an n el at 100 kHz is lim itedto a 12.5-kHz per-chan n el sam pling rate when sam pling eight ch an n els.

IOtechs 100-kHz and 1-MHz data acquisition systems are examples of systems that usesoftware selectable ch an n el an d gain sequen cin g. IOtech s 100-kHz system s provide a512-location scan sequ encer th at allows you t o select, via software, each chan n el and itsassociated inpu t am plifier gain for both th e built-in chan n els and th e expansion chan n els.The sequencer circuitry circumvents a major limitation encountered with many plug-indata acquisition boardsa drastic reduction in th e scan rate for expan sion chan n els. Allchan n els are scan n ed, in clud ing expan sion chan n els, at 100 kHz (10 s/channel). Digitalinputs can also be scanned using the same scan sequence employed for analog inputs,enab lin g the tim e correlation of acquired digital data to acqu ired an alog data. Th ese prod-ucts permit each scan group, con tain ing up to 512 ch ann el/gain combin ation s, to be re-peated imm ediately or at programm able int ervals of up to 12 h ours. With in each scangroup , consecutive ch an n els are m easured at a fixed 10 s/ch an n el rate. Figure 3.02 illus-trates a 512-location scan sequ encer operatin g in a 100-kHz data acquisition system.

Analoginputs

PGA

ADC

Muxcontrol lines

Mux

Gaincontrol lines

Fig. 3.0 1: The multiplexer (Mux) is a fast switch that directs different input signals to the ADC for digitizing


21/9021


#2 #4 #7 #2 D #18 #19 #16x1 x8 x8 x2 x100 x10 x1000Uni Uni Bi Uni Bi Bi Uni

Channel 1Gain 2

Unipolar or Bipolar 3

4 5

1. Unipolar or bipolar operation can be programmed for each channel dynamically by the sequencer2. Gain can be programmed for each channel dynamically by the sequencer3. Channels can be sampled dynamically by the sequencer4. Expansion channels are sampled at the same rate as on-board channels

Scan groupAll channels within a scan group aremeasured at a fixed scan rate

Programmable

Constantscan rate

t

t

Fig. 3.0 2: 512-location scan sequencer exam ple

Un fortun ately, m ultiplexing may in trodu ce problems. A h igh source imp edan ce can com -bine with stray capacitan ce to cause settlin g problems an d crosstalk between ch an n els. Mul-tiplexer im pedan ce can also lead to signal degradation. A solid state mu ltiplexer can h ave animp edan ce of tens of Oh m s, wh ereas a relay typically has a resistan ce of less th an 0.01 Oh m .

Sequence vs. Software Selectable RangesMost data acquisition system imp lem ent ations perm it differen t inp ut ran ges, altho ughth e man n er in wh ich t h ey do so varies con siderably. Som e data acqu isition system sallow th e in put ran ge to be switch ed or jum per selected on th e circuit board. Oth ersprovide software selectable gain ; th is is m ore conven ien t, but a distin ction shou ld bem ade between data acquisition system s wh ose chan n els mu st all have th e sam e gain,an d system s th at allow you to sequen tially select the in pu t range of each chan n el. It isoften ad van tageous to h ave different inp ut ran ges on different ch an n els, especially wh enm easuring sign als from different tran sducers. Th erm ocou ples an d strain gages requ ireinp ut ranges of tens of m illivolts, wh ile oth er transducers might out pu t several volts.

A data acquisition system with a software selectable ran ge can be used t o m easure differ-en t ran ges on different chan n els at a relatively slow rate by issuing a software com m an d

to ch an ge th e gain between sam ples.Th ere are two problem s with th is tech n ique. First , i t is s low; issuin g a softwarecom m an d to ch an ge th e ga in of a PGA can take tens or hu n dreds of m i ll isecon ds ,lowerin g th e sam ple rate to several Hz. Secon d, th e speed of th is sequ en ce is oftenind eterm inate , due to var iant s in th e PC ins t ruc t ion cycle t im es. So cycl in g th roughi t con t inu ously wi ll give sam ples wi th an un even (an d u n kno wn ) spacin g in t ime.This complicates time-series analysis and makes FFT analysis impossible since theFFT requires even ly spaced sam ples.


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22

As discussed earlier, a bet ter im plem en -tation provides a sequencer that con-trols the channel selection and gain.

Th e m axim um acquisi t ion rate can bea c h i e v e d w i t h sequence - se l ec t ab leranges, whereas the acquisition ratewill slow considerably with software -selectable ranges if channels requiredifferent ran ges. IOtech s 100 -kHzdata acquis i t ion sys tems provide a512-location scan sequencer that al-lows you to selec t each chan n el an dassoc ia t ed inpu t ampl i f i e r ga in a t

rand om . Th ese prod ucts perm it eachscan group to be repeated immedi-ately or at program m able in tervals.

Input BufferingTh e imp act of source im pedan ce and stray capacitance can be estim ated via a sim pleform ula: the tim e con stant associated with a source imp edan ce (R) and stray capaci-tan ce (C) is T=RC.

For example , suppose you want to know the maximum to lerable input impedance

for a 100-kHz m ul t ip lexer. Th e t im e between m easuremen ts on adjacen t chan n elsin t h e scan sequen ce is 10 s. In alength of t im e T=RC, th e voltage er-ror decays by a factor of 2.718. Re-ducing the error to 0.005% requireswaitin g 10T.

Con sequ en tly, a fixed tim e of 10 s be-tween scans (T scan ) and an error of 0.005%would appear to require a time of T=1s. In a typical mu ltiplexed data acqu i-sition system, th is would yield errors du eto insufficien t settlin g tim e. The differ-en ce can be explained as follows. Most100-kHz converters require 2 s (T samp )to sam ple th e inp ut signal. Subt ractin gth is from th e scan t ime results in a set-tling tim e of: T settle=Tscan -Tsamp , Tsettle=8 s.

Fig. 3.03: Multiplexer scheme with sequence selectable gain

Analoginputs

PGA

16to1

Mux

x1, x2, x4, & x8To dataacquisitionsystem

2

4

Expansionchannel addressing

Expansiongain addressing

24

Hardwaresequencer

CLK

Triggeringcircuitry

Fig. 3.04: Buffering signals before the m ultiplexer increases accuracy, especially with high-impedancesources or fast multiplexing

Inputs

PGA

ADC

Buffer

Buffer

Buffer

Buffer

Mux


23/9023


Fig. 3.0 5: DBK45 4-channel, low-pass filtering with sim ultaneoussample and hold card block diagram

Channel address lines

Sample enable

MuxTo dataacquisitionsystem

Switched bias resistors(per channel)

Ch 4IA S/H

Ch 3IA S/H

Ch 2IA S/H

Ch 1IA S/H

LPF

LPF

LPF

LPF

If we assume a typical 16-bit data acquisi t ion system, the internal set t l ing t ime(T in t) may be 6 s . Th e external se t t l in g t im e may th en be com put ed as fo l lows:Tex t = Tsettle 2-T in t 2 , T ex t =5.29 s.

For a 16 -b i t da t a acqu i s i t i on sys t em wi th 100 p ico fa rad o f inpu t capac i t ance(C in ) and a m ult iplexer resistan ce (R m u x ) of 100 Oh m s, the m axim um extern al resis-tan ce is calculated as follows: R ex t= (T ex t / C in 1n(2

16 ))-R m u x , R ex t =4,670 Oh m s.

Th e above exam ples are simp lified an d d o n ot in clud ed an y effects du e to m ultiplexercharge injection or in ductive reactan ce in th e measuremen t wiring. In actual practiceth e practical up per lim it on source resistan ce is between 1,500 and 2,000 Oh m s.

Most input signals have source impedances of less than 1.5 KOhm, so such a maximum

source im ped an ce is usually no t a problem . However, faster m ultip lexer rates requ ire lowersource im ped an ces. For exam ple, a 1-MHz m ultip lexer in a 12-bit system requires a sou rceimp edan ce of un der 1.5 KOh m . If th e source im pedan ce exceeds this value, bufferin g isn ecessary to obtain accurate measuremen ts. A buffer is an am plifier with h igh inp ut im -pedan ce and very low outpu t impedan ce. Placing a buffer on each chan n el between th etran sducer and th e mu ltiplexer elim inates inaccuracies by prevent ing th e mu ltiplexers straycapacitan ce from h aving to discharge th rough t h e im pedan ce of th e tran sducer. IOtech sWaveBook, LogBook, Personal Daq, and select signal conditioning options are all high-speed devices th at use th is con figuration . Th is arran gemen t is illustrated in Figure 3.04.

Simultaneous Sample and Hold (SS&H)A m ultiplexed ADC m easurem en t int rodu ces a time skew amo n g ch an n els, wh ich is int ol-erable in som e application s. Em ploying sim ultan eous sam ple and h old (SS&H) on m ultiplechannels remedies time-skewp r o b l e m s . S i m u l t a n e o u ssam ple and h old requires thateach chan n el be equipped witha buffer that samples the sig-n al at th e beginn ing of th e scansequ en ce. Th e signal at th ebuffer output is held at thesam pled value wh ile th e m ul-tiplexer switches through allchan n els and th e ADC digitizesth e readin gs. In a good simu l-t a n e o u s s a m p l e a n d h o l dimplementation, all channelsare sam pled with in 100 n s of each oth er.


24/90


24

Figure 3.05 sh ows a com m on sch em e for sim ultan eous sam ple and h old; this design is usedon IOtech s DBK45 sim ultan eous sam ple and h old card, an expan sion opt ion for IOtech s100-kHz data acquisition system s. Each inp ut signal passes th rough an instrum ent ation

am plifier (IA) an d in to a samp le an d h old buffer (S/H). Wh en t h e sam ple enable line goesh igh , each S/H sam ples its inp ut signal an d h olds it wh ile th e m ultiplexer switches throu ghth e readin gs. Th is sch em e ensures th at all th e sam ples are taken with in 50 n s of each oth er,even with up to sixty-four DBK45s con n ected to a sin gle instrum ent . A system con figuredwith sixty-four DBK45s would provide 256 sim ultan eous ch an n els.

Current MeasurementsMan y transdu cers can be con figured tooutput a 4-20 mA current with a lin-

ear relationsh ip to the qu an tity beingm easured. A shun t resistor con vertsthe current to a voltage for measure-m en t by an ADC. Figure 3.06 illus-trates curren t measuremen t. If th e cur-rent (I) is passed through a resistance(R), the voltage across the resistor isV=IR. Con sequen tly, a 500 Oh m re-sistor is sufficien t t o m ap a 20 m A full-scale curren t in to a 10 VFS volt age formeasurement with a data acquisition

system. Usin g a transdu cer con figuredfor current out pu t can yield h igh n oise imm un ity and accuracy, particularly if th ere is alarge distance between th e data acquisition system an d t h e transducer. Lon g leads pick up n oise and suffer an oh m ic voltage drop.

Th e curren t value inferred from m easuring th e voltage across a sh un t resistor is on ly asaccurate as th e resistor. Com m on resistor accuracies are 5%, 1%, 0.1%, and 0 .01%.Resistors are commonly specified according to their accuracy and stability when ex-posed to ch an gin g tem peratures. All resistors chan ge with tem perature. Th is ph eno m -enon can be used to measure temperature, as discussed in Chapter 4, however, this

effect is un desirable when m easuring current. Man y resistor m an ufacturers m ake aneffort to lower th e effects of ch an ging tem peratu res on resistan ce. Th is specificationmeans that the actual resistance is within the specified tolerance of the given resis-tan ce. In add ition , a 0.1% resistor usually h as a lower tem peratu re coefficien t an dbetter long-term stability than a resistor with lower accuracy, due to its constructiontechn ique, which is usually wire woun d or m etal film vs. carbon com position .

Fig. 3.0 6: Current m easurement using a shunt resistor and a differential amplifier

100k Ohm

R + ADC

i


25/9025

Chapter 4 Temperature Measurement

Chapter 4Temperature Measurement


26/90

Chapter 4 Temperature M easurement

26

Th is chap ter examin es various tran sducers for m easuring tem perature: th ermo couples, andRTDs. It also discusses th e required signal con dition ing, as well as various techn iques foropt imizin g th e accuracy of your tem perature measuremen t.

ThermocouplesThermocouples are probably the mostwidely used an d least un derstood o f alltemperature measuring devices. Ther-mocouples provide a simple and effi-cient means of temperature measure-m ent by gen erating a voltage th at is afun ction o f tem peratu re. All electricallycon ductin g m aterials produ ce a therm alelectrom ot ive force (em f or voltage dif-ference) as a function of the tempera-tu re gradien ts with in th e m aterial. Th isis called th e Seebeck effect. Th e am ou n tof the Seebeck effect depends on thechemical composition of the materialused in th e th erm ocouple.

Wh en two d ifferen t m aterials are con n ected to create a TC, a voltage is generated.Th is voltage is th e difference of th e voltages generated b y th e two m aterials . In

pr inc ip le , a therm ocouple can be m ade from a lm ost an y two meta ls. In prac t ice,several thermocouple types have become de facto standards because they possessdesirable quali t ies, such as high ly predictable outp ut voltages an d large voltage-to-tem peratu re rat ios. Som e com m on th erm ocou ple typ es are J, K, T, E, N28, N14, S, R,an d B. Figure 4.01 depicts a Type T th erm ocou ple. In th eory, th e tem peratu re canbe inferred from such a voltage by con sult ing stan dard t ables or using l inearizat ionalgori th m s. In pract ice, th is voltage can n ot be direct ly used, because th e con n ec-t ion of the thermocouple wires to the measurement device cons t i tu tes a thermo-couple providing an oth er th ermal em f th a t m ust be com pen sated for ; co ld jun ct ioncomp ensat ion can be used for th is purpose.

Cold Junction Compensation . Figure 4.02 sh ows a th ermocou ple that h as been p lacedin series with a secon d th ermocou ple, wh ich h as been placed in an ice bath. Th is icebath is called th e referen ce jun ction . An d wh en p roperly con structed, an ice bath canprod uce an extrem ely accurate 0C tem peratu re. Th is reference jun ction is requiredbecause all th erm ocou ple em f tables, as pu blish ed by NIST (Nation al In stitute of Stan -dards and Techn ology), are referen ced to th e emf outp ut o f a th ermocou ple which is

Fig. 4.0 1: Illustration of a Type T thermocouple

Metal A (copper)

Metal B (constantan)

+

-

Type Te AB


27/9027


h eld at a temp erature of 0.00 degreesCelsius. In f igure 4.02, the ch rom el/ copper and a lumel / copper the rmo-

couples in the ice ba th have a 0 .0Vcon tribution to th e voltage measuredat th e meter. Th e voltage read is en -t i rely from th e ch rom el/a lum el th er-m ocoup le. Th e copper wi res con -n ected to th e copper te rm inals on th em e t e r d o n o t c o n s t i t u t e a t h e r m o -c o u p l e b e c a u s e t h e y a r e t h e s a m em eta l conn ect ion and both te rm inalsare th e sam e temp erature .

Main ta in ing an i ce ba th an d an ad -di t ional referen ce th ermocoup le forevery th ermocoup le probe i s n ot prac t ica l in m ost system s. I f we know th e temp era-ture a t th e poin t wh ere we con n ect to our th ermocoup le wires, ( th e referen ce jun c-t ion ) , an d i f both conn ect ing wires are a t th e sam e temp erature , then th e ice ba thcan be e l im inated . In such a case, the op posin g th ermoelect r ic vol tage gen erated byth e non zero temp erature of th e referen ce jun ct ion can s im ply be added to t h e ther-m ocouple emf . Th is i s co ld jun ct ion com pen sat ion (CJC).

CJC is an essen tial part of accurate th erm ocoup le readings. CJC m ust be im plem en ted

in an y system th at h as n o ice-poin t referen ce jun ction . Th e tech n ique works best if theCJC device is close to th e termin al blocks th at con n ect th e extern al th erm ocoup les, an dif th ere are n o tem perature gradients in t h e region cont ain ing th e CJC an d term inals.

Thermocouple Linearization. Th ermocoup le vol tage i s propor t ion al to , but n ot l in-early propor t ion al to , the temp erature at th e th ermocoup le conn ect ion . Th ere areseveral tech n iques for th erm ocou ple l in earizat ion . An alog tech n iques can providea vol tage propor t ion al to tem pera ture f rom th e therm ocouple in put . In addi t ion , avol tage measurem ent can b e made wi th an ADC and th e tempera ture looked up in atable, as in t h e above examp le. To speed th is process, th e looku p tab le can be stored

in com pute r m emory and th e search pe r fo rmed wi th an a lgo ri thm . Th erm ocoup lel inear iza t ion can a lso be accompl ished us ing a polynomial approximat ion to thetem peratu re versus voltage curve. Figure 4.03 on t h e next p age i llustrates a port ionof th e NIST Polyn om ial Coefficien ts table for som e com m on th erm ocou ples.

Fig. 4.0 2: Thermocouple circuit with ice bath

+

-

+

-Copper

CopperCopper

V

Volt meter

Ice Bath

CopperAlumel

V1

Chromel


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28

Temperature conversion equation: T = a 0 + a1x + a2x2 + ... + anx2Nested polynomial form: T = a0 + x(a1 + x(a2 + x(a3 + x(a4 + a5x)))) (5th order)

NIST Polynomial Coefficients

160C to 400 C0.5C

7th ordera0a1a2

a4

a3

a5a6a

7a8a9

0C to 760 C1C

5th order

Type JIron(+) vs.

Constantan()

0.04886825219873.14503

218614.5353

264917531.411569199.78

2018441314

0C to 1370 C0.7C

8th order

Type KNickel-10%

Chromium(+) vs.Nickel5%()

(Aluminum Silicon)

0.22658460224152.1090067233.4248

860963914.92210340.682

4.83506E + 10 1.18452E + 12

1.38690E + 13 6.33708E + 13

0C to 1000 C0.5C

8th order

Platinum-13%Rhodium(+) vs.

Platinum()

0.263632917179075.491

48840341.37

4.82704E + 121.90002E + 10

7.62091E + 14 7.20026E + 16

3.71496E + 18 8.03104E + 19

Type R

0C to 1750 C1C

9th order

Platinum-10%Rhodium(+) vs.

Platinum()

0.927763167169526.5150

31568363.94

1.63565E + 128990730663

1.88027E + 14 1.37241E + 16

6.17501E + 17 1.56105E + 19

1.69535E + 20

Type SCopper(+) vs.Constantan()

0.10086091025727.94369

767345.8295

924748658978025595.81

6.97688E + 11 2.66192E + 13

3.94078E + 14

Type T

100C to 1000 C0.5C

9th order

Type ENickel-10%

Chromium(+) vs.Constantan()

0.10496724817189.45282

282639.0850

448703084.612695339.5

1.10866E + 10 1.76807E + 11

1.71842E + 12 9.19278E + 12

2.06132E + 13

For example, IOtechs DBK19 thermocouple card includes a software driver that con-tains a temperature conversion library that converts raw binary thermocouple chan-n els, an d CJC informat ion into tem perature. Included DaqView software provides au-

tom atic lin earization an d CJC for th ermocou ples attached t o th e system .

Additional ConcernsCare mu st be t aken wh en usin g th erm ocouples to m easure tem perature. Sources of mi-n or error can add u p to h igh ly inaccurate readings. Add ition al con cern s include:

Thermocouple Assembly. Th erm ocou ples are assemb led via twistin g wires to geth er, sol-dering, or welding; if don e im prop erly, all of these tech n iques can int rodu ce errors inth e temp erature measurem ent.

Twisting Wires Together. Th ermocoup le jun ction s sh ould n ot be form ed by twisting th ewires togeth er. Th is will produ ce a very poo r th ermo coup le jun ction with large errors.

Soldering. For low tem perature work th e th ermocou ple wires can be joined b y solder-ing, h owever, soldered jun ction s lim it the m aximu m tem perature that can be m easured(usually less th an 200 degrees Celsius). Soldering th erm ocou ple wires in trod uces a thirdm etal. Th is shou ld no t int roduce any app reciable error as long as both sides of th e

jun ction are th e sam e temp erature.

Fig. 4.0 3: Portion of an NIST lookup table


29/9029


Welding. Welding is th e preferred meth od of conn ecting jun ctions. Wh en weldin gth ermocou ple wires togeth er, care mu st be taken to p revent an y of th e characteristics of th e wire from ch an ging as a result of th e weldin g process. Th ese con cerns are com pli-

cated by the differen t com position of the wires being joined. Com m ercially man ufac-tured th ermocou ples are typically welded using a capacitance-discharge techn ique th atensures uniformity.

Decalibration of Thermocouple Wire. Decalibration is an oth er serious fault cond ition .Decalibration is particularly troublesom e because it can result in an erron eous tem pera-ture readin g that ap pears to be correct. Decalibration o ccurs when th e ph ysical makeupof th e th ermocou ple wire is altered in such a way th at th e wire no longer m eets NISTspecification s. Th is can o ccur for a variety of reason s in cludin g, tem peratu re extrem es,cold-workin g of th e m etal, stress placed on th e cable during in stallation , vibration, o r

tem perature gradients.Insulation Resistance Failure. Tempera-ture extremes can also introduce errorbecause th e insulation resistance of th eth ermo couple will often decrease expo-nentially as the temperature increases.Th is can lead to two types of errors: leak-age resistance with an open thermo-coup le and leakage resistan ce with smallth erm ocou ple wire. Figure 4.04 illus-

trates insu lation resistan ce failure.

Leakage Resistance with an Open Ther- mocouple . In h igh temp erature appli-cation s, th e insulation resistan ce candegrade to the point where the leak-age resistan ce R L will com plete th e cir-cuit and give an erron eous reading.

Leakage Resistance with Small Thermocouple Wire. In high temperature applications using

small th ermo couple wire, th e in sulation R L can degrade to th e point wh ere a virtual jun c-tion T 1 is created an d th e circuit ou tpu t voltage will be proportion al to T 1 instead of T 2.

Furthermore, high temperatures can cause impurities and chemicals within the ther-m ocoup le wire in sulation t o diffuse in to th e therm ocouple m etal, chan gin g the charac-teristics of th e th ermocou ple wire. Th is causes th e tem perature-voltage depen den ce todeviate from p ublish ed values. Wh en th ermocou ples are used at h igh t em peratures,

Fig. 4.04: Illustration of a virtual junction resulting frominsulation resistance failure

To DVM

Virtual junction

To DVM

(Open)

Leakage resistance

Rs

Rs

Rs

Rs

RL

T1

T2

RL


30/90


30

th e atm osph eric effects can be m inim ized by cho osin g th e proper protective in sulation.Due to th e range of th ermocou ple ch oices, therm ocouple quality is an issue. Select theth ermocou ple th at m eets your app lication criteria (i .e., high or low tem perature range,

proper groun din g, etc.)

Other Thermocouple M easurement IssuesFor h igh -accuracy and instrum ent ation -qu ality th ermocou ple m easurem en ts, issues suchas thermocouple isolation, auto-zero correction, line-cycle noise rejection, and openth ermocou ple detection m ust be addressed.

Thermocouple Isolation. Th ermocou ple isolation reduces noise and th e error effects of ground loops. Especially in cases where many thermocouples are bolted directly to adistan t m etallic object, l ike an engine block. Th e engine block and t h e therm ocoup le-

m easurem ent in strum ent m ay have different groun d referen ces. Witho ut som e form o f isolation , a groun d loop would be created th at wou ld cause th e readings to be in error.

Auto-Zero Correction. To minimize the effects of time and temperature drift on thesystem s analog circuitry, a shorted chan n el sh ould b e con stantly m easured an d sub-tracted from th e readin g. Altho ugh very small, th is circuit drift can become a substan -tial percen tage of th e low-level voltage sup plied by a th erm ocou ple.

One method of subtracting the offsetdue to drift is employed by IOtechs

Tem pScan /110 0, MultiScan/ 1200, an dCh artScan/ 1400, a h igh ly accurate ana-log scheme is used to automaticallysubt ract th e system offset. Before read-ing an y ch ann el, the in ternal chan n elsequen cer first switch es to a referen cenode and stores the offset error on acapacitor. As th e th ermo couple chan -n el is switched on to th e analog path,th e circuit h olding th e offset voltageis applied to the offset correction in-pu t of a differen tial am plifier, nu llin gou t th e offset aut om atically. Figure4.05 illustrates th is tech n ique.

Line-Cycle Noise Rejection. Because of the relat ively small voltage generated bym ost th erm ocou ples, n oise is always an issue. Th e m ost pervasive source of noise isfrom power l ines (50 Hz or 60 Hz). Since thermocouples have a bandwidth lower

Ch x

Ch ground

A

Amplifier'soffset correction

Differential amplifier

To A/D

A

A

BB

Control for "A" muxes

A/D sample

Control for "B" muxes

Auto zerophase

Samplingphase

Fig. 4.0 5: Diagram of auto-zero correction


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th an 50 Hz, a simp le per-chan n el fi l-te r in g schem e can reduce th e in com -in g AC lin e n oise. For system s with

a m ult iplexed fron t en d, an RC fil teri s n ot recom m ended. Al though m orecom plicated, an act ive fi lter m ade upof an o p-am p an d a few pass ive com -pon ent s can a lso be used; h owever,th is m eth od in curs s igni fican t add i -t ion al expen se. Furth erm ore, setu pis comp l ica ted b ecause each chan n eln eeds to be cal ibrated due to gain an doffset error. For th ese reason s active

filters are gen erally n ot u sed. Figure4.06 is a diagram of an active filter.

On e un ique l ine-cycle averagin g techn ique for reducing n oise i s em ployed by th eTem pScan/ 1100, Mult iScan /120 0 and Ch artScan /140 0. A ph ase-lock-loop circuitm on i tors an d synch ron izes th e system s in ternal sam pl ing ra te to th e m ul t ip le of th e power line frequ en cy. Durin g each l ine cycle, th e CJC is samp led alon g withoth er inp ut ch an n els th a t a re sam pled 32 t im es an d averaged. Th is h as th e effect of reducin g th e l in e cycle n oise by 82%.

Open Thermocouple Detection.Open thermocouple de tec t ion i s es -pecia l ly impor tant in sys tems wi thh igh ch an n el coun ts . Due to age, v i-b r a t i o n , a n d h a n d l i n g , t h e r m o -couples can b reak or become h igh lyresist ive. O pen th erm ocou ple detec-t ion can be accom pl ish ed by provid-ing a low level curren t pa th to a ca-pacitor across th e th ermocoup le te r-m inals. If th e th ermocoup le i s open ,

th e capaci tor charges up an d d r ivesth e am plifier to i ts rai l, in dicat ing afa u l t . W h e n t h e t h e r m o c o u p l e i sp r o p e r l y c o n n e c t e d , t h e l o w - l e v e lcurren t goes th rough th e therm ocouple ra th er th an ch arging th e capacitor. Figure4 .07 i llust ra tes an open th ermocoup le ci rcui t .

Fig. 4.0 6: Diagram of active filter

R1

R2

+

Fig. 4.0 7: Open thermocouple circuit

TCTo differentialamplifier

+0.13V

10 M

10 M

0.13V

4700 pF

One of 32 channels

TempScan/1100open TC Detect


32/90


33/9033


Resistance Temperature Detectors (RTD)RTDs fun ction on th e basic ph ysical prin ciple th at a m etals resistan ce increases with

tem peratu re. Most RTDs are simp ly wire-wou n d or th in-film resistors m ade of a wirewith a kn own resistan ce versus tem perature relationship. Platin um is th e m ost com -m on ly used m aterial for RTDs. RTDs are available in a w ide ran ge of accuracy specifica-tion s; th e m ost accurate RTDs are used as tem perature stan dards at NIST.

Platinum RTDs have resistance values ranging from 10 Ohms for a birdcage model toten th ousan d Oh m s for a film m odel. Th e mo st com m on value for RTDs is 100 Oh m s at0C. Platinu m wire h as a stan dard tem perature coefficien t of = 0.00385 / / C,wh ich m eans a 100 Oh m wire h as a temperature coefficient of +0.385 / C at 0 C; th evalue for is actually th e average slop e from 0 C to 100 C. Ch em ically pu re platinu mwire has an of + 0.00392 / / C. Th e slop e an d th e absolute value are relativelysmall, when you consider the fact that the measurement wires leading to the sensorm ay be ten s of Oh m s. With th is in m ind , even a small lead imp edan ce can cause anappreciable error in tem perature m easurem ent .

Th e followin g equation states th at th e chan ge in resistan ce is equ al to m ultiplied by th echan ge in tem perature.

R =

In th e above measuremen t exam ple, a 10 Oh m lead im pedan ce suggests a 10/0.385 @ 26 Cerror. In add ition to th e im pedan ce, th e lead wires tem perature coefficient can also con -

tribute a measurable error.

To elim inate th e possibility of error as aresult of add itional resistan ce from th ecurren t-carryin g excitation leads, an ad-ditional set of voltage-sensing leadssho uld be located as close as possible toth e sen sor. (Recall that th e tem peraturecoefficien t is 0.39 / C, so a 0.39 errorin the resistance measurement yields a1C error in th e measured temp erature.)This configuration is called a four-wireRTD m easuremen t because four wires arerequired between th e RTD and th e mea-suremen t instrum entation . Placin g th esen se leads at th e curren t supp ly in steadof th e RTD provides a less accurate con -figuration bu t on ly requires con n ectin gtwo wires to th e RTD.

RTD

R line

R line

Ohmmeter

Fig. 4.0 8: Two-wire RTD measurement


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34

The f ive common types of circuits ,which are used for RTD measurementare sh own in Figure 4.08 th rough 4.12.

Following are descript ions of eachcircuits operation .

Figure 4.08 (shown on the previouspage) sh ows a sim ple two-wire resistan cem easurem en t. Th e RTD resistan ce isread directly from t h e Oh m m eter. Th iscon n ection is rarely used since th e leadwire resistan ce mu st be a kno wn valuean d it is very difficult to d etermin e th e

tem perature coefficien t of the lead wires.Figure 4.09 sh ows a four-wire m easure-m en t using a current source. Th e RTDresistan ce is volts/current . Th is con n ec-tion requires a high stability currentsource an d fou r lead wires.

Figure 4.10 sh ows a t h ree-wire m ea-surem ent u sin g a current source. Th eRT D r e s i s t a n c e i s d e r i v e d u s i n gKirchhoff 's voltage law as fol lows:RTD in Oh m s = V a- (2 * V b) /current .Th e benef it of th is conn ect ion overFigure 4.09 is th e elimin ation of on e-lead wire. Th is con n ection assum esthat the two-current car ry ing wiresh ave th e sam e resistan ce.

Figure 4.11 shows a four-wire mea-suremen t u sin g a voltage source. Th eRT D r e s i s t a n c e i s d e r i v e d u s i n gKirchhoff 's voltage law as fol lows:RTD in Ohms = V a-((V a - V b )+(V c -Vd ))/(V d / RSENSE). Th e voltage sou rce inthis circuit can vary as long as thesense resistor (R SENSE ) is stable. Thiscon n ection requires fou r-lead wires.

Fig. 4 .10 : Three-wire RTD measurement with a current source

RTD

R line

Va

Vb

R line

R line

Highimpedancevoltmeter

Currentsource

CurrentsourceRTD

Rline

Rline

Rline

Rline


Fig. 4.09 : Four-wire RTD m easurement with a current source

RTD

R line

Va

Vb

Vc

Vd

R line

R line

R line


Voltagesource

Rsense

Fig. 4.1 1: Four-wire RTD measurement using a voltagesource


35/9035


Figure 4.12 shows a th ree-wire measure-m en t u sin g a voltage sou rce. Th e RTDresistance is derived using Kirchhoff's

voltage law as follows: RTD in Oh m s =Va-((2 * (V a - V b))+(V c - V d))/(V d /RSENSE).The voltage source in this circuit canvary as lon g as th e sense resistor (R SENSE)is stable. Th is con n ection assum es th atth e two-current carryin g wires have th esame resistance.

Wh ile th e RTD is m ore lin ear th anth e th ermocoup le, its operating range

is smaller th an a th ermo coup les. Form aximu m accuracy in RTD app lica-tion s you sho uld u se curve-fittin g viath e Callend ar-Van Dusen equation,wh ich follows:

R T = R 0 + R 0 [ ](T T100 1) )( T100 ( T100 1) )( T 3100Where:RT = resistance at temperature TRo = resistance at T = 0 C = temperature coefficient at T = 0 C

typically +0.00392 / / C = 1.49 (typical value for .00392 platinum) = 0, When T>0

0.11 (typical) When T


36/90


36

An oth er sou rce of error in RTD m easurem en ts is resist ive heatin g. A current , I,th rou gh a resistan ce, R, dissipates po wer P = I 2R. For exam ple, a 1 m A curren t th rou gha 100 RTD generat es 100 watt of power. Th is m ay seem in sign ifican t , but i t canraise th e tem perat ure of som e RTDs a sign ifican t fraction of a degree. (A typ ical RTDh as self-h eating of 1 C/m W. Sm aller RTDs offer fast t ime respon se, but can h avelarger self-heat in g errors.)

Since lower curren ts gen erate less heat; currents between 100 an d 500 A are comm on lyused. Th is lowers th e power dissipation to between 10 and 25 W, wh ich is tolerable form ost application s. Furth er reducin g th e current inh ibits accurate measuremen t becauseas th e curren ts becom e sm aller they are susceptible to n oise and m ore difficult to m ea-sure. The RTDs h eat can b e redu ced below 10 W by switching the current on onlywh en th e measuremen t is m ade. In a m ultich ann el system , th e excitation curren t can

be mu ltiplexed m uch like the an alog in put s. For exam ple, in a 16-chan n el system , thecurrent will only excite each RTD 1/16th of the time, reducing the power delivered toeach RTD from 100% t o 6%, (P* 1 /X wh ere X = th e n um ber of chan n els).

Two practical m eth ods of m easurin g an RTD in clud e: con stant current an d ratiom etric.An examp le of a cons tan t current topo logy can be foun d in th e Tem pScan/ 1100sRTD scann ing m odu le, th e Tem pRTD/16B (see f igure 4.14), wh ich provides a s in glecons tan t current source of approximate ly 500 am ps, wh ich i s swi tch ed am on g it s

sixteen ch an n els. A series of fron tend mul t ip lexers d i rec t the currentto each channel sequent ia l ly whi le

t h e m e a s u r e m e n t i s b e i n g t a k e n .Both 3- and 4-wire con n ect ion s ares u p p o r t e d t o a c c o m m o d a t e b o t htyp es of RTDs. By ap plyin g curren tto on ly a s in gle RTD at a t im e, errorsdue to resist ive heat ing becom e n eg-l igible. Advan tages of th e con stan t-curren t m eth od in c lude c i rcui t sim-pl ic ity an d n oise imm un i ty. Th e d is-advant age of using cons tan t current

i s th e expense of bui ld ing or b uyinga h igh ly stable current sou rce. Fig. 4.1 4: TempRTD/16B card in a TempScan/1100

Constant currentCh x

To A/D

24 Channels

RTD

Ch x +1

RTD


37/9037


Fig. 4.16: Diagram of DBK9 front end with 3-wireconfiguration

RTD

Constantvoltage

Precisionresistor

V100 RTDV500 RTD

V1000 RTD

Va

Vb

Vc

iS

RdiS

Vd

RL

RL

The DBK9 RTD measurement card forIOtech s LogBook, DaqBoard , DaqBook,an d Daq PC-Card based data acqu isition

products uses th e ratiom etric m eth od form easuring RTDs. A sim ple constant volt-age source provides a curren t, I s, th roughthe RTD and resistor R d . Fou r readin gs,Va, Vb, Vc, and V d, are taken for eachRTD chan n el. Th e curren t th rough t h eRTD, I s, is V d /Rd. The voltage across theRTD, V rtd , is equ al to V b-Vc. The RTD re-sistan ce is, th erefore, V rtd / Is.

For a 3-wire connection scheme, thevoltage Va-Vc includ es th e voltage dropacross on ly on e of th e leads. Since th e2 extension wires to th e transdu cer aremade of the same metal, one can as-sume th at th e drop in th e first wire isequal to the drop in the second wire.Therefore, the real voltage across theRTD wou ld be V RTD =Va-2(V a-Vb)-Vd. Theresistan ce of th e RTD can be calculatedby R RTD =Rd[VRTD /Vd].

Fig. 4.15: Ratiometric DBK9 front end with 4-wireconfiguration

RTD

Constantvoltage

Precisionresistor

Va

Vb

Vc

Vd

iS

RdiS

V1000 RTD

V500 RTDV100 RTD

RL

RL


38/90


38

Small Resistance vs. Large Resistance RTDsSmall RTD Large RTD

Response Time Fast SlowThermal Shunting Low PoorSelf-heating Error High Low

Practical PrecautionsRTDs require the same precaution s th at app ly to th ermocoup les, includin g th e use of shields an d t wisted-pair wire, proper sheath ing, avoiding stress and steep gradient s, an dusing large exten sion wire.

In add it ion , th e fol lowing issues com e in to play: th e RTD is m ore fragile th an t h eth ermocoup le and n eeds to be prot ected d ur ing u se , and RTDs are n ot se lf-powered.An exci ta t ion curren t m ust be provided to t h e device to obta in a m easurem ent . Th ecurrent causes Jou le heatin g with in t h e RTD, and th is chan ges th e RTDs temp era-ture . Th is se lf-h eat in g appears as a measurem ent er ror an d m ust be inc luded in th ecalculat ion s th at determ ine m easurem en t. A typical value for self-h eatin g error is1C per mil l iwatt in free air. An RTD im m ersed in a th ermally con du ctive m ediumwill distr ibute this heat to the medium and the result ing error wil l be smaller. The

sam e RTD th at rises 1 C p er m ill i-watt in free air will rise on ly 1/10 Cper m ill iwatt in air that is f lowin gat th e rate of on e meter per second .Using th e m inimum exci tat ion cur-rent th a t p rovides th e des ired reso-lu t ion an d u s in g the la rgest ph ysi -cally practical RTD will h elp red uceself-h eatin g errors.

Thermal Shunting. Th ermal shu n ting results in an altered tem perature reading as a resultof introducing a measurement transducer. Thermal shunting is of greater concern withRTDs because RTDs are larger th an th erm ocou ples.


39/9039

Chapter 5 Strain & Acceleration

Chapter 5Strain & Acceleration


40/90


40

Th is ch apter exam ines th e various transducers for m easurin g strain an d acceleration . Italso d iscusses th e required sign al con dition ing, as well as various techn iques for en sur-ing m easurem en t accuracy.

Strain GagesStrain gages are used in a variety of test and m easurem en t app lication s. Strain gagescan m easure m ost ph ysical phen om ena th at elon gate or con tract a solid m aterial. Strain -gage techniques are also used in many accelerometer and pressure-transducer designs.Strain is defin ed as th e ch an ge in length per un it length . For examp le, if a 1m long baris stretched t o 1.000002 m , th e strain is defin ed as 2 m icrostrains.

Strain can b e measured by bon din g a resist ive strain gage to th e test m aterial. Wh enth e test m aterial is s train ed i t t ran sfers th at s train to th e resist ive strain gage, ch an g-ing i ts resistan ce sl ight ly. Th e gage factor is th e fract ion al chan ge in resistan cedivided by th e strain . For exam ple, two m icrostrain app lied to a gage with a gagefactor o f two causes a fract ion al resistan ce chan ge of 4x10 -6 O h m . C o m m o n ga geresistan ce values are from 120 Oh m to 350 Oh m , but in som e appl ica t ions , res is-tan ce can be as low as 30 Oh m or as h igh as 3000 Oh m .

The Wheatstone Bridge. To m ake an accurate strain m easurem en t, very sm all resistan cechan ges m ust be m easured. As in th e previous examp le, if two m icrostrain are applied to agage, a ch an ge in resistan ce of on ly 4 Oh m would need to be m easured. Th e Wh eatston ebridge con verts a ch an ge in resistan ce in to a voltage ready for ADC measurem en t. If all

four resistors are equal, then V ou t = 0. Wh en o n e of th e resistors ch an ges sligh tly (by afraction al amou n t X), th en a m easurable voltage is produced.

Full-Bridge Configuration. Th e opt im al strain -gage con figurat ion is th e ful l bridge.Th is con figurat ion provides th e high est sen sit ivity an d th e fewest error com po n en ts.Since th e ful l bridge configurat ion also p rovides th e greatest ou tp ut , n oise is less of a factor in the measurement. For these reasons, wherever possible, the ful l bridgeconf igura t ion i s recom m end ed.

A full bridge contains four strain gages mounted on a test member, two on the tensilesurface and two on th e opp osite com pressive surface. As th e m em ber deflects, two gagesincrease in resistan ce wh ile th e op posite gages decrease in resistan ce, maxim izing t h ebridges output.

In this configuration, the following equation applies: V ou t = V ex c * X wh ere X is th echan ge in resistan ce ( R). Figure 5.01 illustrates a full-bridge con figurat ion .


41/9041


Poten tial error com pon ents such as tem perature ch an ge are nu lled by th e bridge sinceall four strain gages have th e same tem perature ch aracteristics. In a full-bridge con figu-ration , the resistan ce in th e lead wires h as n o effect on th e accuracy of the m easurem en tas long as th e in put am plifier has a h igh inpu t imp edance. For exam ple, with an inpu tresistan ce of 100 MOh m , very little current flows th rough th e measurem en t leads, min i-m izing th e possible voltage drop du e to lead resistan ce.

Half-Bridge Configuration. Wh en ph ysical con sideration s do n ot allow for a full bridge, ah alf bridge can be em ployed. In th is con figuration, two strain gages are mo un ted on a testm em ber wh ile two resistors are used t o com plete th e bridge.

In th is con figuration , th e following equ ation app lies: V bridge = V excitation * X/2 w h ere X isapproximately the change in resistance ( R). For large R, half-bridge and quarter-bridge con figuration s can in trodu ce an addition al n on lin earity error. Figure 5.02 illus-trates a h alf-bridge con figuration .

On e pot en tial error source with h alf bridges is th at, because of th e dissim ilar tem pera-tu re characteristics of bridge comp letion resistors an d strain gages, as th eir temp eraturech an ges, th eir resistan ce m ay no t chan ge prop ortion ately. Furth erm ore, bridge com ple-tion resistors are typically n ot in th e sam e ph ysical location as the strain gages, addin g toth e error in duced by tem perature ch an ges.

In system s with lon g lead wires, it is recom m en ded th at th e bridge com pletion resistorsbe attach ed close to th e gages; h owever, this may n ot always be practical due to en viron -m ental condit ion s.

Fig. 5.0 1: Full bridge and gage locations

+

+

Vexc

R1

R3

R2 R4

VOUT

R1R4

R2R3


42/90


42

Quarter-Bridge Configuration. A qu ar t e r b r idge uses on e st r a in gage an d th reeb r i d ge co m p l e t io n r e si st o r s . I n t h i s c o n fi gu r a t i o n , t h e f o ll o w in g eq u a t i o n a p -plies: V o u t = V ex c * X/4 , wh ere X i s app rox im a te ly th e chan ge in r e si st an ce ( R).Figure 5.03 illustrates a quarter-bridge configuration.

Th is configuration h as the sm allest ou tpu t, m akin g no ise a poten tial problem. Furth er-more, all of the error sources and drawbacks in the half-bridge configuration are alsoapplicable to th e q uarter-bridge con figuration .

Excitation Source. Accurate m easurem en t requ ires a quiet (low n oise) and stable regu-lated excitation source. A regulated excitation source is necessary because th e out pu t of a strain gage is prop ortion al to th e excitation vo ltage. Th erefore, an y fluctuation in th eexcitation will result in o ut pu t errors.

Fig. 5.0 2: Half-bridge and gage locations

Straingages

+

Bridgecompletion resistors

Vexc VOUT +

R1

R2

R1

R2

Fig. 5.0 3: Quarter-bridge and gage location

+

Straingage

+

Bridgecompletion resistors

Vexc VOUT

R1R

1


43/90


44/90


44

Strain-Gage Signal ConditioningMost strain gages an d lo ad cells are specified for a full scale value of weight , force, ten -sion , pressure, torque, or deflection with an out pu t of m V/V of excitation . For examp le,a load cell with a full scale ratin g of 1,000 lbs migh t ou tp ut 2 m V per volt of excitation atfull load. For an excitation of 10V, th e full scale ou tp ut is 20 m V.

Steps m ust be taken t o con trol n oise when m easurin g mV levels. Sh ielded cables, low-pass filters, differential voltage measurement and averaging can be used to minimizen oise in strain -gage m easurem en ts.

Readin g a m V sign al with a 12-bit A/D con verter requ ires an in strum en tation am plifier.Most A/D am plifiers h ave a 10V full scale and th us, on ly provide a 2.44 m V resolut ion(10V/40 95). To m easure strain u sin g th e A/Ds full resolut ion , on e mu st adjust th e

instrum ent ation am plifier s gain so th at th e full scale out pu t of th e strain gage or loadcell covers th e en tire range of th e A/D.

Man y test system s are characterized b y th e presen ce of a quiescent load th at results in anout pu t voltage, even wh en n o force is applied. An adjustable offset can redu ce th is qu ies-cent o utp ut voltage to zero, allowing th e applied load to use th e full range of the ADC.

Fig. 5.0 5: DBK43A strain gage module block diagram

ToA/D

Exc. Adj.

6

5

2

1

DBK43A (Typical of 8 ch.)

+Sense

Sense

+Exc

ExcExcitationRegulator

BypassBypass

LPF

+

Scale Gain Adj.Input Gain Adj.

4

3

ShuntCal.

OffsetAdj.

OptionalBridgeCompletionResistors


45/9045


Flexibility is the key to maximizing the performance of a strain gage system. For ex-am ple, th e DBK43A provides adjustable excitation , gain an d o ffset p er chan n el, allowin guse of th e entire dyn am ic ran ge of th e data acquisition system. Figure 5.05 illustrates

on e-chan n el of th e DBK43A.

Common M ode Reject ion Ratio.C o m m o n m o d e r e j e c t i o n r a t i o(CMRR) is a v i ta l ins t rumenta t ionam plifier specificatio n . A strain -gages ignal in a Wheats tone br idge con-figurat ion is sup erim posed on a com -mon mode vol tage of ha l f the exci -tat ion voltage. CMRR m easures h ow

wel l the ampl i f ie r re jec ts commonm od e voltage. For exam ple, con sidera 10V excitation of a strain gage with2 m V/V ou tp ut at ful l scale. An am -plifier with a CMRR of 90 d B can in -trod uce an error of 0.158 m V, corre-spon din g to 0 .8% ful l sca le . Thism ay no t be acceptable. A CMRR of 115 dB is much better, as i t intro-duces an error of only 9 V, wh ichcorrespon ds to 0.04% of ful l scale.

dB=20log 10 (V sig /V error )Vm ax /V error =log 10

-1(dB/20)=log 10 -1(90/20)=31,622

Verror =Vm ax /log 10 -1(dB/20)=5.00/31,622=0.158 mV

%erro r= (V erro /V sig)100=(0.158 mV/20 mV)100=0.79%

IOtech s DBK43A pro vides a regulated excitat ion source with op tion al Kelvin excitatio n .Provision is made for on-board bridge-completion resistors when using quarter- andh alf-bridge strain gages. Two in strum en tation am plifiers provide inp ut an d scalin g gainadjustm en ts. An o ffset adjustm en t perm its n ullin g of large quiescent loads, so th at th einp ut sign al uses th e full ran ge of the dat a acquisition system . Th is allows th e measure-m ent to h ave the full resolution of the ADC.

Many strain-gage signal conditioners provide fixed gain, offset, and excitation settings;typically the manufacturer suggests that the user adjust the system via software. Theprob lem with th is solution is th at its gen eralized; fixed settin gs do n ot take advan tage of th e m axim um dyn am ic ran ge of the A/D. Th is decreases the actual available resolution of the measurement .

Gain = 200

5.02 V

5.00 V350

347

350

350

20 mV

+10 V

+V

V

IA Vout = 200 (0.02)= 4.00 V

Fig. 5.06: A strain-gage signal in a W heatstone bridgeconfiguration superimposed on a comm on m ode voltageof half the excitation voltage


46/90


46

For exam ple, man y gen eric strain-gage sign al-con dition ing m odu les can b e configuredwith a fixed 3 m V/V rating. At 10V, th e excitation , offset, an d gain trim m ing are fixedand n o adjustm ents are available.

The excitation adjustment provides a means for the user to set the excitation to them axim um allowed by th e man ufacturer, m aximizin g th e bridges ou tpu t. Th e offset ad-

justm en t allows th e user to zero th e out pu t offset caused by a slight bridge im balance orquiescen t deformation of the m ech an ical mem ber. Th e gain adjustm ents allow th e userto set a gain th at will provide a full scale outp ut u n der m axim um load, optim izing th edyn am ic range of the A/D.

The DBK43A pro vides a sh un t calibrationfeature, illustrated in Figure 5.07, th at al-

lows the use r to swi t ch use r- supp l i edshun t r e s i s to r s in to e i the r o f the twolower legs of th e bridge via software. Th isis useful because in som e in stan ces, i t isn ot po ssib le to provide a m aximum loadto se t the opt im um gain . A sh un t resis-tor va lue can be ca lcula ted so th a t wh enit is switched in, i t wil l s imulate a ful lload, al lowin g an accurate gain t o be set .For an y balan ced bridge, th ere is a resis-tan ce va lue tha t can be app l ied in p ara l-

lel with on e of the four br idge e lemen tsto crea te predic table imbalance an d o utp ut vol tage . For examp le, a 350 Oh m 2 m V/ V strain gage wil l del iver ful l out pu t i f on e leg drops by 0.8% (about 2.80 Oh m ) to347.2 Oh m . A 43.75K Oh m resistan ce sh un ted across on e or th e o th er lower br idgeelem en ts will result in ful l po sit ive or ful l n egative out pu t .

An app ropriate formu la for th e shu n t-cal resistan ce value is:

Rshun t = R bridge arm [V excitation / 4 (V ou t)]For exam ple:

Rshun t = 350 [10 / 4 (0.020)] = 43,750 Oh m

Man y prod ucts provide calibration software. The DBK43A ships with a Wind ows-basedprogram th at provides th ree calibration m eth ods, on-line instructions, and a diagn osticscreen for testing th e calibrated system .

Ron

350 350

43.75K

Closeto shunt

350Voltage 20 mV

when shunted

+10 V

(+)

()RTN

Fig. 5.0 7: Schematic of a shunt bridge


47/9047


Load Cells and Torque SensorsStrain gages are commercially available in prefabricated modules such as load cells,con figured to m easure force, tension , com pression , and torqu e. Load cell man ufactur-ers provide calibration an d accuracy in format ion . Load cells typically use a full-bridgecon figuration an d h ave four leads for bridge excitation an d m easurem ent .

Strain Diaphragm Pressure Gages. A strain diaph ragm pressure gage consists of two orfour strain gages on a th in diaph ragm. Th e strain gages are wired in a Wh eatston e bridgeconfiguration, including bridge completion resistors if necessary, so that the pressuregage is electrically equ ivalent to a load cell. The ou tp ut voltage is specified as a m illivoltsper volt of excitation for a full scale pressure differential across the diaphragm.

If th e referen ce pressure is open to air, th e gage com pares th e inlet pressure to th e am bient

pressure. Am bien t pressure is app roxim ately 14.7 lbs/in 2 at sea level. If th e gage is goin g tobe used to m easure ambien t pressure, it is n ecessary to use a sealed reference ch am ber witheith er vacuu m reference pressure (0 lbs/in 2) or sea-level referen ce pressure (14.7 lb

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