Z-19

Practical Temperature Measurements*

□ Self-powered □ Most stable □ High output □ Most linear□ Simple □ Most accurate □ Fast □ Highest output□ Rugged □ More linear than □ Two-wire ohms □ Inexpensive□ Inexpensive thermocouple measurement □ Wide variety□ Wide temperature

range

□ Non-linear □ Expensive □ Non-linear □ T<200°C□ Low voltage □ Current source □ Limited temperature □ Power supply □ Reference required required range required□ Least stable □ Small Δ R □ Fragile □ Slow□ Least sensitive □ Low absolute □ Current source □ Self-heating

resistance required □ Limited configurations□ Self-heating □ Self-heatingDi

sadv

anta

ges

Adva

ntag

es

TABLE OF CONTENTSAPPLICATION NOTES-PRACTICAL TEMPERATURE MEASUREMENTS

Figure 1

Page

Common Temperature Transducers....................................................................................Z-19

Introduction ...........................................................................................................................Z-20Reference Temperatures ...................................................................................................Z-21

The Thermocouple ................................................................................................................Z-21Reference Junction............................................................................................................Z-22Reference Circuit...............................................................................................................Z-23Hardware Compensation...................................................................................................Z-24Voltage-to-Temperature Conversion..................................................................................Z-25

Practical Thermocouple Measurement ...............................................................................Z-27Noise Rejection .................................................................................................................Z-27Poor Junction Connection .................................................................................................Z-29Decalibration......................................................................................................................Z-29Shunt Impedance ..............................................................................................................Z-29Galvanic Action..................................................................................................................Z-30Thermal Shunting ..............................................................................................................Z-30Wire Calibration .................................................................................................................Z-30Diagnostics ........................................................................................................................Z-31Summary ...........................................................................................................................Z-32

The RTD .................................................................................................................................Z-33History ...............................................................................................................................Z-33Metal Film RTD's ...............................................................................................................Z-33Resistance Measurement..................................................................................................Z-343-Wire Bridge Measurement Errors...................................................................................Z-35Resistance to Temperature Conversion ............................................................................Z-35Practical Precautions.........................................................................................................Z-36

TEMPERATURE

RE

SIS

TAN

CE

R

TTEMPERATURE

VO

LTA

GE

V

TTEMPERATURE

RE

SIS

TAN

CE

R

TTEMPERATURE

VO

LTA

GE

T

or C

UR

RE

NT

V or I

* Copyright © 1997, 2000 Agilent Technologies, Inc. Reproduced with Permission.

Thermocouple RTD Thermistor I. C. Sensor

Z-20

Z

The Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-36Linear Thermistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-37Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-37

Monolithic Linear Temperature Sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-37Appendix A-The Empirical Laws of Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-37Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-38

Thermocouple Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-38Base Metal Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-38

Standard Wire Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-39Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z-40

TABLE OF CONTENTSAPPLICATION NOTES-PRACTICAL TEMPERATURE MEASUREMENTS (conʼt)

Synthetic fuel research, solar energy conversion andnew engine development are but a few of theburgeoning disciplines responding to the state of ourdwindling natural resources. As all industries place newemphasis on energy efficiency, the fundamentalmeasurement of temperature assumes new importance.The purpose of this application note is to explore themore common temperature monitoring techniques andintroduce procedures for improving their accuracy.

We will focus on the four most common temperaturetransducers: the thermocouple, the RTD, the thermistorand the integrated circuit sensor. Despite thewidespread popularity of the thermocouple, it isfrequently misused. For this reason, we will concentrateprimarily on thermocouple measurement techniques.

Appendix A contains the empirical laws ofthermocouples which are the basis for all derivationsused herein. Readers wishing a more thoroughdiscussion of thermocouple theory are invited to readREFERENCE 17 in the Bibliography.

For those with a specific thermocouple application,Appendix B may aid in choosing the best typeof thermocouple.

Throughout this application note, we will emphasizethe practical considerations of transducer placement,signal conditioning and instrumentation.

Early Measuring Devices - Galileo is credited withinventing the thermometer, circa 1592.1, 2, 3 In an opencontainer filled with colored alcohol he suspended along narrow-throated glass tube, at the upper end ofwhich was a hollow sphere. When heated, the air inthe sphere expanded and bubbled through the liquid.Cooling the sphere caused the liquid to move up the tube.1 Fluctuations in the temperature of the sphere could then be observed by noting the position of the liquid inside the tube. This “upside-down” thermometerwas a poor indicator since the level changedwith barometric pressure and the tube had no scale. Vast improvements were made in temperaturemeasurement accuracy with the development of the

1, 2, 3 Refer to Bibliography 1,2,3.

Florentine thermometer, which incorporated sealedconstruction and a graduated scale.

In the ensuing decades, many thermometric scaleswere conceived, all based on two or more fixed pointsOne scale, however, wasnʼt universally recognized untilthe early 1700ʼs, when Gabriel Fahrenheit, a Dutchinstrument maker, produced accurate and repeatablemercury thermometers. For the fixed point on the lowend of his temperature scale, Fahrenheit used a mixtureof ice water and salt (or ammonium chloride). This wasthe lowest temperature he could reproduce, and helabeled it “zero degrees”. For the high end of his scale, he chose human blood temperature and called it 96 degrees.

Why 96 and not 100 degrees? Earlier scales hadbeen divided into twelve parts. Fahrenheit, in anapparent quest for more resolution divided his scale into 24, then 48 and eventually 96 parts.

The Fahrenheit scale gained popularity primarilybecause of the repeatability and quality of thethermometers that Fahrenheit built.

Around 1742, Anders Celsius proposed that themelting point of ice and the boiling point of water beused for the two benchmarks. Celsius selected zerodegrees as the boiling point and 100 degrees as themelting point. Later, the end points were reversed andthe centigrade scale was born. In 1948 the name wasofficially changed to the Celsius scale.

In the early 1800ʼs William Thomson (Lord Kelvin),developed a universal thermodynamic scale basedupon the coefficient of expansion of an ideal gas. Kelvinestablished the concept of absolute zero and his scaleremains the standard for modern thermometry.

The conversion equations for the four moderntemperature scales are:

°C = 5/9 (°F - 32) °F= 9/5 °C + 32

K = °C + 273.15 °R= °F + 459.67The Rankine Scale (˚R) is simply the Fahrenheit

equivalent of the Kelvin scale, and was named after an early pioneer in the field of thermodynamics, W.J.M. Rankine.

INTRODUCTION

Z-21

We cannot build a temperature divider as we can avoltage divider, nor can we add temperatures as wewould add lengths to measure distance. We must relyupon temperatures established by physical phenomenawhich are easily observed and consistent in nature. TheInternational Practical Temperature Scale (IPTS) isbased on such phenomena. Revised in 1968, itestablishes eleven reference temperatures.

Since we have only these fixed temperatures to useas a reference, we must use instruments to interpolatebetween them. But accurately interpolating betweenthese temperatures can require some fairly exotictransducers, many of which are too complicated orexpensive to use in a practical situation. We shall limitour discussion to the four most common temperaturetransducers: thermocouples, resistance-temperaturedetectorʼs (RTDʼs), thermistors, and integratedcircuit sensors.

IPTS-68 REFERENCETEMPERATURESEQUILIBRIUM POINT K 0CTriple Point of Hydrogen 13.81 -259.34

Liquid/Vapor Phase of Hydrogen 17.042 -256.108

at 25/76 Std. Atmosphere

Boiling Point of Hydrogen 20.28 -252.87

Boiling Point of Neon 27.102 -246.048

Triple Point of Oxygen 54.361 -218.789

Boiling Point of Oxygen 90.188 -182.962

Triple Point of Water 273.16 0.01

Boiling Point of Water 373.15 100

Freezing Point of Zinc 692.73 419.58

Freezing Point of Silver 1235.08 961.93

Freezing Point of Gold 1337.58 1064.43

Table 1

THE THERMOCOUPLEWhen two wires composed of dissimilar metals are

joined at both ends and one of the ends is heated, thereis a continuous current which flows in the thermoelectriccircuit. Thomas Seebeck made this discovery in 1821.

If this circuit is broken at the center, the net opencircuit voltage (the Seebeck voltage) is a function of thejunction temperature and the composition of the twometals.

All dissimilar metals exhibit this effect. The mostcommon combinations of two metals are listed inAppendix B of this application note, along with theirimportant characteristics. For small changes intemperature the Seebeck voltage is linearly proportionalto temperature:

ΔeAB = αΔT Where α, the Seebeck coefficient, is the constant ofproportionality.

Measuring Thermocouple Voltage - We canʼtmeasure the Seebeck voltage directly because we mustfirst connect a voltmeter to the thermocouple, and thevoltmeter leads themselves create a newthermoelectric circuit.

Letʼs connect a voltmeter across a copper-constantan(Type T) thermocouple and look at the voltage output:

We would like the voltmeter to read only V1, but byconnecting the voltmeter in an attempt to measure theoutput of Junction J1, we have created two moremetallic junctions: J2 and J3. Since J3 is a copper-to-copper junction, it creates no thermal EMF(V3 = 0), but J2 is a copper-to-constantan junction whichwill add an EMF (V2) in opposition to V1. The resultantvoltmeter reading V will be proportional to thetemperature difference between J1 and J2. This saysthat we canʼt find the temperature at J1 unless we firstfind the temperature of J2.

Reference Temperatures

Metal A

Metal B

eAB

+

–

J1

–V2

+

–

+

–V1

+

J2

J1

+

–v

Cu

Cu

Cu

C

J1

–V2

+

–V1

+

J2

EQUIVALENT CIRCUITS

–V3

+

J3

V3 = 0

Cu

Cu C

Cu

Cu C

Cu

J2

J3

V1

MEASURING JUNCTION VOLTAGE WITH A DVMFigure 4

eAB = SEEBECK VOLTAGEFigure 3

Metal A Metal C

Metal B

THE SEEBECK EFFECTFigure 2

Z-22

Z

One way to determine the temperature of J2 is tophysically put the junction into an ice bath, forcing itstemperature to be 0˚C and establishing J2 as theReference Junction. Since both voltmeter terminaljunctions are now copper-copper, they create nothermal emf and the reading V on the voltmeter isproportional to the temperature difference between J1and J2.

Now the voltmeter reading is (see Figure 5):V = (V1 - V2) ≅ α(tJ1

- tJ2)

If we specify TJ1in degrees Celsius:

TJ1(˚C) + 273.15 = tJ1

then V becomes:V = V1 - V2 = α [(TJ1

+ 273.15) - (TJ2+ 273.15)]

= α (TJ1- TJ2

) = α (TJ1- 0)

V = αTJ1

We use this protracted derivation to emphasize thatthe ice bath junction output, V2, is not zero volts. It is afunction of absolute temperature.

By adding the voltage of the ice point referencejunction, we have now referenced the reading V to 0˚C.This method is very accurate because the ice pointtemperature can be precisely controlled. The ice point isused by the National Bureau of Standards (NBS) as thefundamental reference point for their thermocoupletables, so we can now look at the NBS tables anddirectly convert from voltage V to Temperature TJ1

.

The copper-constantan thermocouple shown inFigure 5 is a unique example because the copper wireis the same metal as the voltmeter terminals. Letʼs usean iron-constantan (Type J) thermocouple instead of thecopper-constantan. The iron wire (Figure 6) increasesthe number of dissimilar metal junctions in the circuit, asboth voltmeter terminals become Cu-Fe thermocouplejunctions.

EXTERNAL REFERENCE JUNCTIONFigure 5

The Reference Junction

J1

+

–

J4

J3Fe

C

v

Ice Bath

Fe

Cu

Cu

J2

V1 = Vif V = Vi.e., ifTJ3

= TJ4

Voltmeter

+

–v V1

V3

V4

J3

J4

+-

+-

3 4

+

–T1

V2

Fev

Ice Bath

Cu

Cu

Voltmeter

C

TREF

Fe

J3

J4

Cu

Cu

Isothermal Block

J1

–V2

+

–

v

T=0°C

+

–V1

+ T

J2

–

+J1V1

V2

–+

+

–

Cu

C

v

Ice Bath

Cu

Cu

Cu

J2

Voltmeter

REMOVING JUNCTIONS FROM DVM TERMINALSFigure 8

IRON-CONSTANTAN COUPLEFigure 6

If both front panel terminals are not at the sametemperature, there will be an error. For a more precisemeasurement, the copper voltmeter leads should beextended so the copper-to-iron junctions are made onan isothermal (same temperature) block:

The isothermal block is an electrical insulator but agood heat conductor, and it serves to hold J3 and J4 atthe same temperature. The absolute block temperatureis unimportant because the two Cu-Fe junctions act inopposition. We still have

V = α (T1 - TREF)

JUNCTION VOLTAGE CANCELLATIONFigure 7

Z-23

Letʼs replace the ice bath with another isothermalblock

The new block is at Reference Temperature TREF, andbecause J3 and J4 are still at the same temperature, wecan again show that

V = α (T1-TREF)

This is still a rather inconvenient circuit because wehave to connect two thermocouples. Letʼs eliminate theextra Fe wire in the negative (LO) lead by combiningthe Cu-Fe junction (J4) and the Fe-C junction (JREF).

We can do this by first joining the two isothermalblocks (Figure 9b).

We havenʼt changed the output voltage V. It is still

V = α (TJ1 - TJREF )

Now we call upon the law of intermediate metals (seeAppendix A) to eliminate the extra junction. Thisempirical “law” states that a third metal (in this case,iron) inserted between the two dissimilar metals of athermocouple junction will have no effect upon theoutput voltage as long as the two junctions formed bythe additional metal are at the same temperature:

This is a useful conclusion, as it completely eliminatesthe need for the iron (Fe) wire in the LO lead:

Again, V = α (TJ1 - TREF), where α is the Seebeckcoefficient for an Fe-C thermocouple.

Junctions J3 and J4, take the place of the ice bath.These two junctions now become the ReferenceJunction.

Now we can proceed to the next logical step: Directlymeasure the temperature of the isothermal block (theReference Junction) and use that information tocompute the unknown temperature, TJ1.

A thermistor, whose resistance RT is a function oftemperature, provides us with a way to measure theabsolute temperature of the reference junction.Junctions J3 and J4 and the thermistor are all assumedto be at the same temperature, due to the design of theisothermal block. Using a digital multimeter undercomputer control, we simply:

1) Measure RT to find TREF and convert TREF

to its equivalent reference junction voltage, VREF , then

2) Measure V and add VREF to find V1,and convert V1 to temperature TJ1

.

This procedure is known as Software Compensationbecause it relies upon the software of a computer tocompensate for the effect of the reference junction. Theisothermal terminal block temperature sensor can beany device which has a characteristic proportional toabsolute temperature: an RTD, a thermistor, or anintegrated circuit sensor.

It seems logical to ask: If we already have a devicethat will measure absolute temperature (like an RTD orthermistor), why do we even bother with athermocouple that requires reference junction

Reference Circuit

J3

J4

Cu

CuJ1

C

T REF

Fe

–

+v

J3

J4

Cu

CuVoltmeter

HI

LO

Isothermal Block

J1

C

T REF Isothermal Block

J REF

Fe

Fe

J3

J4

Cu

Cu

J1

C

Isothermal Bloc k @ T REF

J REF

Fe

Fe

HI

LO +

–J1

+

–V1v

Voltmeter

C

FeJ3

RT

Cu

Cu

Block Temperature = TREF

J4

Isothermal Connection

T REF

T REF

Thus the low lead in Fig. 9b: Becomes:

Metal A Metal CMetal B =Metal CMetal A

Cu CFe =CCu

ELIMINATING THE ICE BATHFigure 9a

JOINING THE ISOTHERMAL BLOCKSFigure 9b

LAW OF INTERMEDIATE METALSFigure 10

EQUIVALENT CIRCUITFigure 11

EXTERNAL REFERENCE JUNCTION-NO ICE BATHFigure 12

Z-24

Z

compensation? The single most important answer tothis question is that the thermistor, the RTD, and theintegrated circuit transducer are only useful over acertain temperature range. Thermocouples, on theother hand, can be used over a range of temperatures,and optimized for various atmospheres. They are muchmore rugged than thermistors, as evidenced by the factthat thermocouples are often welded to a metal part orclamped under a screw. They can be manufactured onthe spot, either by soldering or welding. In short,thermocouples are the most versatile temperaturetransducers available and, since the measurementsystem performs the entire task of referencecompensation and software voltage to-temperatureconversion, using a thermocouple becomes as easy asconnecting a pair of wires.

Thermocouple measurement becomes especiallyconvenient when we are required to monitor a largenumber of data points. This is accomplished by usingthe isothermal reference junction for more than onethermocouple element (see Figure 13).

A reed relay scanner connects the voltmeter to thevarious thermocouples in sequence. All of the voltmeterand scanner wires are copper, independent of the typeof thermocouple chosen. In fact, as long as we knowwhat each thermocouple is, we can mix thermocoupletypes on the same isothermal junction block (oftencalled a zone box) and make the appropriatemodifications in software. The junction blocktemperature sensor RT is located at the center of theblock to minimize errors due to thermal gradients.

Software compensation is the most versatiletechnique we have for measuring thermocouples. Manythermocouples are connected on the same block,copper leads are used throughout the scanner, and thetechnique is independent of the types of thermocoupleschosen. In addition, when using a data acquisitionsystem with a built-in zone box, we simply connect thethermocouple as we would a pair of test leads. All of theconversions are performed by the computer. The onedisadvantage is that the computer requires a smallamount of additional time to calculate the referencejunction temperature. For maximum speed we can usehardware compensation.

Hardware CompensationRather than measuring the temperature of the

reference junction and computing its equivalent voltageas we did with software compensation, we could inserta battery to cancel the offset voltage of the referencejunction. The combination of this hardwarecompensation voltage and the reference junctionvoltage is equal to that of a 0°C junction.

The compensation voltage, e, is a function of thetemperature sensing resistor, RT. The voltage V is nowreferenced to 0°C, and may be read directly andconverted to temperature by using the NBS tables.

Another name for this circuit is the electronic ice pointreference.6 These circuits are commercially available foruse with any voltmeter and with a wide variety ofthermocouples. The major drawback is that a unique icepoint reference circuit is usually needed for eachindividual thermocouple type.

Figure 15 shows a practical ice point reference circuitthat can be used in conjunction with a reed relayscanner to compensate an entire block of thermocoupleinputs. All the thermocouples in the block must be of thesame type, but each block of inputs can accommodatea different thermocouple type by simply changing gainresistors.

Pt

Isothermal Block(Zone Box)

Fe

C

Pt - 10% Rh

RT

All Copper Wires

Voltmeter

HI

LO

+

–

T

Fe

Fe

C

T

Cu

Cu

Fe

C

RT

e

Cu

Cu+–

Cu

+Cu

-

–

+

–

+

v

Fe

Fe

C

T

Fe

+–

Cu

Cu

v

0°C

= =

6 Refer to Bibliography 6.

HARDWARE COMPENSATION CIRCUITFigure 14

ZONE BOX SWITCHINGFigure 13

Z-25

The advantage of the hardware compensation circuitor electronic ice point reference is that we eliminate theneed to compute the reference temperature. This savesus two computation steps and makes a hardwarecompensation temperature measurement somewhatfaster than a software compensation measurement.

Voltage-To-Temperature ConversionWe have used hardware and software compensation

to synthesize an ice-point reference. Now all we have todo is to read the digital voltmeter and convert thevoltage reading to a temperature. Unfortunately, thetemperature-versus-voltage relationship of athermocouple is not linear. Output voltages for the morecommon thermocouples are plotted as a function oftemperature in Figure 16. If the slope of the curve (theSeebeck coefficient) is plotted vs. temperature, as inFigure 17, it becomes quite obvious that thethermocouple is a non-linear device.

A horizontal line in Figure 17 would indicate aconstant α, in other words, a linear device. We noticethat the slope of the type K thermocouple approaches aconstant over a temperature range from 0°C to 1000°C.Consequently, the type K can be used with a multiplyingvoltmeter and an external ice point reference to obtain amoderately accurate direct readout of temperature. Thatis, the temperature display involves only a scale factor.This procedure works with voltmeters.

By examining the variations in Seebeck coefficient,

we can easily see that using one constant scale factorwould limit the temperature range of the system andrestrict the system accuracy. Better conversionaccuracy can be obtained by reading the voltmeter andconsulting the National Bureau of StandardsThermocouple Tables4 on page Z-203 in this Handbook- see Table 3.

T = a0 +a1 x + a2x2 + a3x3 . . . +anxn

whereT = Temperaturex = Thermocouple EMF in Voltsa = Polynomial coefficients unique to each

thermocouplen = Maximum order of the polynomialAs n increases, the accuracy of the polynomial

improves. A representative number is n = 9 for ± 1˚Caccuracy. Lower order polynomials may be used over anarrow temperature range to obtain higher systemspeed.

Table 4 is an example of the polynomials used toconvert voltage to temperature. Data may be utilized inpackages for a data acquisition system. Rather thandirectly calculating the exponentials, the computer isprogrammed to use the nested polynomial form to saveexecution time. The polynomial fit rapidly degradesoutside the temperature range shown in Table 4 andshould not be extrapolated outside those limits.

0°

Mill

ivo

lts

500° 2000°1500°1000°

Temperature °C

Type Metals+ –

E Chromel vs. ConstantanJ Iron vs. ConstantanK Chromel vs. AlumelR Platinum vs. Platinum

13% RhodiumS Platinum vs. Platinum

10% RhodiumT Copper vs. Constantan

20

40

60

80

R

S

E

J

K

THERMOCOUPLE TEMPERATUREvs.

VOLTAGE GRAPHFigure 16

4 Refer to Bibliography 4.

OMEGA TAC-Electronic ice point™ andThermocouple Preamplifier/Linearizer Plugsinto Standard Connector

OMEGA ice point™ Reference Chamber.Electronic Refrigeration Eliminates Ice Bath

PRACTICAL HARDWARE COMPENSATIONFigure 15

Integrated TemperatureSensor

Cu

Cu

RH

Fe

C

TABLE 2

HARDWARE COMPENSATION SOFTWARE COMPENSATION

Fast Requires more computer Restricted to one thermocouple manipulation time

type per card Versatile - accepts any thermocouple

OMEGA Electronic ice point™ Built into Thermocouple Connector -”MCJ”

Z-26

Z

NBS POLYNOMIAL COEFFICIENTSTable 4

TYPE E TYPE J TYPE K TYPE R TYPE S TYPE TNickel-10% Iron(+) Nickel-10% Chromium(+) Platinum-13% Rhodium(+) Platinum-10% Rhodium(+) Copper(+)

Chromium(+) Versus Versus Versus Versus Versus

Versus Constantan(-) Nickel-5%(-) Platinum(-) Platinum(-) Constantan(-)Constantan(-) (Aluminum Silicon)

-100˚C to 1000˚C 0˚C to 760˚C 0˚C to 1370˚C 0˚C to 1000˚C 0˚C to 1750˚C -160˚C to 400˚C± 0.5˚C ± 0.1˚C ± 0.7˚C ± 0.5˚C ± 1˚C ±0.5˚C

9th order 5th order 8th order 8th order 9th order 7th order

a0 0.104967248 -0.048868252 0.226584602 0.263632917 0.927763167 0.100860910

a1 17189.45282 19873.14503 24152.10900 179075.491 169526.5150 25727.94369

a2 -282639. 0850 -218614.5353 67233.4248 -48840341.37 -31568363.94 -767345.8295

a3 12695339.5 11569199.78 2210340.682 1.90002E + 10 8990730663 78025595.81

a4 -448703084.6 -264917531.4 -860963914.9 -4.82704E + 12 -1.63565E + 12 -9247486589

a5 1.10866E + 10 2018441314 4.83506E + 10 7.62091E + 14 1.88027E + 14 6.97688E + 11

a6 -1. 76807E + 11 -1. 18452E + 12 -7.20026E + 16 -1.37241E + 16 -2.66192E + 13

a7 1.71842E + 12 1.38690E + 13 3.71496E + 18 6.17501E + 17 3.94078E + 14

a8 -9.19278E + 12 -6.33708E + 13 -8.03104E + 19 -1.56105E + 19

a9 2.06132E + 13 1.69535E + 20

mV .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 mVTEMPERATURES IN DEGREES C (IPTS 1968)

0.00 0.00 0.17 0.34 0.51 0.68 0.85 1.02 1.19 1.36 1.53 1.70 0.000.10 1.70 1.87 2.04 2.21 2.38 2.55 2.72 2.89 3.06 3.23 3.40 0.100.20 3.40 3.57 3.74 3.91 4.08 4.25 4.42 4.58 4.75 4.92 5.09 0.200.30 5.09 5.26 5.43 5.60 5.77 5.94 6.11 6.27 6.44 6.61 6.78 0.300.40 6.78 6.95 7.12 7.29 7.46 7.62 7.79 7.96 8.13 8.30 8.47 0.400.50 8.47 8.63 8.80 8.97 9.14 9.31 9.47 9.64 9.81 9.98 10.15 0.500.60 10.15 10.31 10.48 10.65 10.82 10.98 11.15 11.32 11.49 11.65 11.82 0.600.70 11.82 11.99 12.16 12.32 12.49 12.66 12.83 12.99 13.16 13.33 13.49 0.700.80 13.49 13.66 13.83 13.99 14.16 14.33 14.49 14.66 14.83 14.99 15.16 0.800.90 15.16 15.33 15.49 15.66 15.83 15.99 16.16 16.33 16.49 16.66 16.83 0.901.00 16.83 16.99 17.16 17.32 17.49 17.66 17.82 17.99 18.15 18.32 18.48 1.001.10 18.48 18.65 18.82 18.98 19.15 19.31 19.48 19.64 19.81 19.97 20.14 1.101.20 20.14 20.31 20.47 20.64 20.80 20.97 21.13 21.30 21.46 21.63 21.79 1.201.30 21.79 21.96 22.12 22.29 22.45 22.62 22.78 22.94 23.11 23.27 23.44 1.301.40 23.44 23.60 23.77 23.93 24.10 24.26 24.42 24.59 24.75 24.92 25.08 1.40

The calculation of high-order polynomials is a time-consuming task for a computer. As we mentionedbefore, we can save time by using a lower orderpolynomial for a smaller temperature range. In thesoftware for one data acquisition system, thethermocouple characteristic curve is divided into eightsectors, and each sector is approximated by a third-order polynomial.*

All the foregoing procedures assume thethermocouple voltage can be measured accurately andeasily; however, a quick glance at Table 3 shows us thatthermocouple output voltages are very small indeed.Examine the requirements of the system voltmeter:

THERMOCOUPLE SEEBECK DVM SENSITIVITYTYPE COEFFICIENT FOR 0.1˚C

(μV/˚C) @ 20˚C (μV)E 62 6.2J 51 5.1K 40 4.0R 7 0.7S 7 0.7T 40 4.0

REQUIRED DVM SENSITIVITY

Table 5

Even for the common type K thermocouple, thevoltmeter must be able to resolve 4 μV to detect a0. 1˚C change. The magnitude of this signal is an openinvitation for noise to creep into any system. For thisreason, instrument designers utilize severalfundamental noise rejection techniques, including treeswitching, normal mode filtering, integration andguarding.

–500°

See

beck

Coe

ffici

ent �

V/°

C

0° 2000°1500°1000°500°Temperature °C

Linear Region(SeeText)

20

40

60

80

100

R

S

K

T J

E

* HEWLETT PACKARD 3054A.

TEMPERATURE CONVERSION EQUATION: T = a0 +a1 x + a2x2 + . . . +anxn

NESTED POLYNOMIAL FORM: T = a0 +x(a1 + x(a2 + x (a3 + x(a4 + a5x)))) (5th order)where x is in Volts, T is in °C

TYPE E THERMOCOUPLETable 3

SEEBECK COEFFICIENT vs. TEMPERATUREFigure 17

{

aVoltage

Tem

p.

T = bx + cx + dx 2 3

a

CURVE DIVIDED INTO SECTORSFigure 18

Z-27

PRACTICAL THERMOCOUPLE MEASUREMENTNoise Rejection

Tree Switching - Tree switching is a method oforganizing the channels of a scanner into groups, eachwith its own main switch.

Without tree switching, every channel can contributenoise directly through its stray capacitance. With treeswitching, groups of parallel channel capacitances arein series with a single tree switch capacitance. Theresult is greatly reduced crosstalk in a large dataacquisition system, due to the reduced interchannelcapacitance.

Analog Filter - A filter may be used directly at theinput of a voltmeter to reduce noise. It reducesinterference dramatically, but causes the voltmeter torespond more slowly to step inputs.

Integration - Integration is an A/D technique whichessentially averages noise over a full line cycle; thus,power line related noise and its harmonics are virtuallyeliminated. If the integration period is chosen to be lessthan an integer line cycle, its noise rejection propertiesare essentially negated.

Since thermocouple circuits that cover long distancesare especially susceptible to power line related noise, itis advisable to use an integrating analog-to-digitalconverter to measure the thermocouple voltage.Integration is an especially attractive A/D technique inlight of recent innovations which allow reading rates of48 samples per second with full cycle integration.

VIN

t

VOUT

t

Guarding - Guarding is a technique used to reduceinterference from any noise source that is common toboth high and low measurement leads, i.e., fromcommon mode noise sources.

Letʼs assume a thermocouple wire has been pulledthrough the same conduit as a 220 Vac supply line. Thecapacitance between the power lines and thethermocouple lines will create an AC signal ofapproximately equal magnitude on both thermocouplewires. This common mode signal is not a problem in anideal circuit, but the voltmeter is not ideal. It has somecapacitance between its low terminal and safety ground(chassis). Current flows through this capacitance andthrough the thermocouple lead resistance, creating anormal mode noise signal. The guard, physically afloating metal box surrounding the entire voltmetercircuit, is connected to a shield surrounding thethermocouple wire, and serves to shunt the interferingcurrent.

= Signal+

–C

~

HI

DVM

NoiseSour ce

(20 Channels)

C

C

C

CTree

Switch1

TreeSwitch2

C

Next 20 Channels

Signal+

–

~

HI

DVM

Stray capacitance to noisesource is reduced nearly20:1 by leaving TreeSwitch 2 open.

NoiseSource

Signal+

–20 C C

~

HI

DVM =~

TREE SWITCHINGFigure 19

ANALOG FILTERFigure 20

Z-28

ZHI

LO

DVM

GuardWithout Guard

HI

LO

DVM

DistributedCapacitance

Without Guard

220 VAC Line

DistributedResistance

Each shielded thermocouple junction can directlycontact an interfering source with no adverse effects,since provision is made on the scanner to switch theguard terminal separately for each thermocouplechannel. This method of connecting the shield to guardserves to eliminate ground loops often created whenthe shields are connected to earth ground.

The dvm guard is especially useful in eliminatingnoise voltages created when the thermocouple junctioncomes into direct contact with a common mode noisesource.

In Figure 22 we want to measure the temperature atthe center of a molten metal bath that is being heatedby electric current. The potential at the center of thebath is 120 V RMS. The equivalent circuit is:

The stray capacitance from the dvm Lo terminal tochassis causes a current to flow in the low lead, whichin turn causes a noise voltage to be dropped across theseries resistance of the thermocouple, Rs. This voltageappears directly across the dvm Hi to Lo terminals andcauses a noisy measurement. If we use a guard leadconnected directly to the thermocouple, we drasticallyreduce the current flowing in the Lo lead. The noisecurrent now flows in the guard lead where it cannotaffect the reading:

Notice that we can also minimize the noise byminimizing Rs. We do this by using larger thermocouplewire that has a smaller series resistance.

To reduce the possibility of magnetically inducednoise, the thermocouple should be twisted in a uniformmanner. Thermocouple extension wires are availablecommercially in a twisted pair configuration.

Practical Precautions - We have discussed theconcepts of the reference junction, how to use apolynomial to extract absolute temperature data, andwhat to look for in a data acquisition system, tominimize the effects of noise. Now letʼs look at thethermocouple wire itself. The polynomial curve fit reliesupon the thermocouple wire being perfect; that is, itmust not become decalibrated during the act of makinga temperature measurement. We shall now discusssome of the pitfalls of thermocouple thermometry.

Aside from the specified accuracies of the dataacquisition system and its zone box, mostmeasurement errors may be traced to one of theseprimary sources:

1. Poor junction connection

2. Decalibration of thermocouple wire

3. Shunt impedance and galvanic action

4. Thermal shunting

5. Noise and leakage currents

6. Thermocouple specifications

7. Documentation

GUARD SHUNTS INTERFERING WITH CURRENTFigure 21

Figure 22

Figure 23

Figure 24

240 VRMS

HI

Noise Current

LO

Guard

RS

120VRMS

Noise Current

LO

HIRS

Z-29

Poor Junction Connection There are a number of acceptable ways to connect

two thermocouple wires: soldering, silver-soldering,welding, etc. When the thermocouple wires aresoldered together, we introduce a third metal into thethermocouple circuit, but as long as the temperatureson both sides of the thermocouple are the same, thesolder should not introduce any error. The solder doeslimit the maximum temperature to which we can subjectthis junction. To reach a higher measurementtemperature, the joint must be welded. But welding isnot a process to be taken lightly.

5Overheating can

degrade the wire, and the welding gas and theatmosphere in which the wire is welded can both diffuseinto the thermocouple metal, changing itscharacteristics. The difficulty is compounded by the verydifferent nature of the two metals being joined.Commercial thermocouples are welded on expensivemachinery using a capacitive-discharge technique toinsure uniformity.

A poor weld can, of course, result in an openconnection, which can be detected in a measurementsituation by performing an open thermocouple check.This is a common test function available withdataloggers. While the open thermocouple is theeasiest malfunction to detect, it is not necessarily themost common mode of failure.

Decalibration Decalibration is a far more serious fault condition than

the open thermocouple because it can result in atemperature reading that appears to be correct.Decalibration describes the process of unintentionallyaltering the physical makeup of the thermocouple wireso that it no longer conforms to the NBS polynomialwithin specified limits. Decalibration can result fromdiffusion of atmospheric particles into the metal causedby temperature extremes. It can be caused by hightemperature annealing or by cold-working the metal, aneffect that can occur when the wire is drawn through aconduit or strained by rough handling or vibration.Annealing can occur within the section of wire thatundergoes a temperature gradient.

Robert Moffat in his Gradient Approach toThermocouple Thermometry explains that thethermocouple voltage is actually generated by thesection of wire that contains the temperature gradient,and not necessarily by the junction.

9For example, if we

have a thermal probe located in a molten metal bath,there will be two regions that are virtually isothermaland one that has a large gradient.

In Figure 26, the thermocouple junction will notproduce any part of the output voltage. The shadedsection will be the one producing virtually the entirethermocouple output voltage. If, due to aging orannealing, the output of this thermocouple were found

to be drifting, then replacing the thermocouple junctionalone would not solve the problem. We would have toreplace the entire shaded section, since it is the sourceof the thermocouple voltage.

Thermocouple wire obviously canʼt be manufacturedperfectly; there will be some defects which will causeoutput voltage errors. These inhomogeneities can beespecially disruptive if they occur in a region of steeptemperature gradient. Since we donʼt know where animperfection will occur within a wire, the best thing wecan do is to avoid creating a steep gradient. Gradientscan be reduced by using metallic sleeving or by carefulplacement of the thermocouple wire.

Shunt ImpedanceHigh temperatures can also take their toll on

thermocouple wire insulators. Insulation resistancedecreases exponentially with increasing temperature,even to the point that it creates a virtual junction.

7

Assume we have a completely open thermocoupleoperating at a high temperature.

The leakage Resistance, RL, can be sufficiently low tocomplete the circuit path and give us an impropervoltage reading. Now letʼs assume the thermocouple isnot open, but we are using a very long section of smalldiameter wire.5 Refer to Bibliography 5

9 Refer to Bibliography 9 7 Refer to Bibliography 7

500˚CMetal Bath

200300400500

100˚C25˚C

Solder (Pb, Sn)

Junction: Fe - Pb, Sn - C = Fe - C

Fe

C

SOLDERING A THERMOCOUPLEFigure 25

GRADIENT PRODUCES VOLTAGEFigure 26

Z-30

ZIf the thermocouple wire is small, its series resistance,

RS, will be quite high and under extreme conditions RL

< < RS. This means that the thermocouple junction willappear to be at RL and the output will be proportional toT1 not T2.

High temperatures have other detrimental effects onthermocouple wire. The impurities and chemicals withinthe insulation can actually diffuse into the thermocouplemetal causing the temperature-voltage dependence todeviate from published values. When usingthermocouples at high temperatures, the insulationshould be chosen carefully. Atmospheric effects can beminimized by choosing the proper protective metallic orceramic sheath

Galvanic ActionThe dyes used in some thermocouple insulation will

form an electrolyte in the presence of water. Thiscreates a galvanic action, with a resultant outputhundreds of times greater than the Seebeck effect.Precautions should be taken to shield thermocouplewires from all harsh atmospheres and liquids.

Thermal Shunting No thermocouple can be made without mass. Since it

takes energy to heat any mass, the thermocouple willslightly alter the temperature it is meant to measure. Ifthe mass to be measured is small, the thermocouplemust naturally be small. But a thermocouple made withsmall wire is far more susceptible to the problems ofcontamination, annealing, strain, and shunt impedance.To minimize these effects, thermocouple extension wirecan be used. Extension wire is commercially availablewire primarily intended to cover long distances betweenthe measuring thermocouple and the voltmeter.

Extension wire is made of metals having Seebeckcoefficients very similar to a particular thermocoupletype. It is generally larger in size so that its seriesresistance does not become a factor when traversinglong distances. It can also be pulled more readilythrough a conduit than can very small thermocouple

R LTo DVM

R LTo DVM

R S R S

R S R ST 1

T 2

(Ope )

wire. It generally is specified over a much lowertemperature range than premium grade thermocouplewire. In addition to offering a practical size advantage,extension wire is less expensive than standardthermocouple wire. This is especially true in the case ofplatinum-based thermocouples.

Since the extension wire is specified over a narrowertemperature range and it is more likely to receivemechanical stress, the temperature gradient across theextension wire should be kept to a minimum. This,according to the gradient theory, assures that virtuallynone of the output signal will be affected by theextension wire.

Noise - We have already discussed line-related noiseas it pertains to the data acquisition system. Thetechniques of integration, tree switching and guardingserve to cancel most line-related interference.Broadband noise can be rejected with the analog filter.

The one type of noise the data acquisition systemcannot reject is a dc offset caused by a dc leakagecurrent in the system. While it is less common to see dcleakage currents of sufficient magnitude to causeappreciable error, the possibility of their presenceshould be noted and prevented, especially if thethermocouple wire is very small and the related seriesimpedance is high.

Wire CalibrationThermocouple wire is manufactured to a certain

specification, signifying its conformance with the NBStables. The specification can sometimes be enhancedby calibrating the wire (testing it at knowntemperatures). Consecutive pieces of wire on acontinuous spool will generally track each other moreclosely than the specified tolerance, although theiroutput voltages may be slightly removed from thecenter of the absolute specification.

If the wire is calibrated in an effort to improve itsfundamental specifications, it becomes even moreimperative that all of the aforementioned conditions beheeded in order to avoid decalibration.

LEAKAGE RESISTANCEFigure 27

VIRTUAL JUNCTIONFigure 28

Z-31

Documentation - It may seem incongruous to speakof documentation as being a source of voltagemeasurement error, but the fact is that thermocouplesystems, by their very ease of use, invite a large numberof data points. The sheer magnitude of the data canbecome quite unwieldy. When a large amount of data istaken, there is an increased probability of error due tomislabeling of lines, using the wrong NBS curve, etc.

Since channel numbers invariably change, datashould be categorized by measure and, not just channelnumber.6 Information about any given measure and,such as transducer type, output voltage, typical valueand location, can be maintained in a data file. This canbe done under computer control or simply by filling outa pre-printed form. No matter how the data ismaintained, the importance of a concise system shouldnot be underestimated, especially at the outset of acomplex data gathering project.

Diagnostics Most of the sources of error that we have mentioned

are aggravated by using the thermocouple near itstemperature limits. These conditions will beencountered infrequently in most applications. But whatabout the situation where we are using smallthermocouples in a harsh atmosphere at hightemperatures? How can we tell when the thermocoupleis producing erroneous results? We need to develop areliable set of diagnostic procedures.

Through the use of diagnostic techniques, R.P. Reedhas developed an excellent system for detecting faultythermocouples and data channels.10 Three componentsof this system are the event record, the zone box test,and the thermocouple resistance history.

Event Record - The first diagnostic is not a test at all,but a recording of all pertinent events that could evenremotely affect the measurements. An example wouldbe:

MARCH 18 EVENT RECORD10:43 Power failure10:47 System power returned11:05 Changed M821 to type K thermocouple13:51 New data acquisition program16:07 M821 appears to be bad reading

Figure 29

We look at our program listing and find that measurand#M821 uses a type J thermocouple and that our new dataacquisition program interprets it as a type J. But from theevent record, apparently thermocouple M821 waschanged to a type K, and the change was not entered intothe program. While most anomalies are not discoveredthis easily, the event record can provide valuable insightinto the reason for an unexplained change in a systemmeasurement. This is especially true in a systemconfigured to measure hundreds of data points.

Zone Box Test - A zone box is an isothermal terminalblock of known temperature used in place of an ice bathreference. If we temporarily short-circuit thethermocouple directly at the zone box, the systemshould read a temperature very close to that of the zonebox, i.e., close to room temperature.

If the thermocouple lead resistance is much greaterthan the shunting resistance, the copper wire shuntforces V = 0. In the normal unshorted case, we want tomeasure TJ, and the system reads:

V ≅ α (TJ - TREF)

But, for the functional test, we have shorted the terminalsso that V=0. The indicated temperature TʼJ is thus:

0 = α (TʼJ - TREF)TʼJ = TREF

Thus, for a dvm reading of V = 0, the system willindicate the zone box temperature. First we observe thetemperature TJ (forced to be different from TREF), thenwe short the thermocouple with a copper wire and makesure that the system indicates the zone box

temperature instead of TJ.

This simple test verifies that the controller, scanner,voltmeter and zone box compensation are all operatingcorrectly. In fact, this simple procedure tests everythingbut the thermocouple wire itself.

Thermocouple Resistance - A sudden change in theresistance of a thermocouple circuit can act as awarning indicator. If we plot resistance vs. time for eachset of thermocouple wires, we can immediately spot asudden resistance change, which could be an indicationof an open wire, a wire shorted due to insulation failure,changes due to vibration fatigue, or one of many failuremechanisms.

For example, assume we have the thermocouplemeasurement shown in Figure 31.

We want to measure the temperature profile of anunderground seam of coal that has been ignited. Thewire passes through a high temperature region, into acooler region. Suddenly, the temperature we measurerises from 300°C to 1200°C. Has the burning section ofthe coal seam migrated to a different location, or has

10 Refer to Bibliography 10

TJ

oltmeter

C

FeCu

Cu

Zone BoxIsothermal Block

+

–

V

v

Cu

Cu

TREF

Copper Wire Short

SHORTING THE THERMOCOUPLE AT THE TERMINALSFigure 30

Z-32

Zthe thermocouple insulation failed, thus causing a shortcircuit between the two wires at the point of a hot spot?

If we have a continuous history of the thermocouplewire resistance, we can deduce what has actuallyhappened.

The resistance of a thermocouple will naturallychange with time as the resistivity of the wire changesdue to varying temperature. But a sudden change in

resistance is an indication that something is wrong. Inthis case, the resistance has dropped abruptly,indicating that the insulation has failed, effectivelyshortening the thermocouple loop.

The new junction will measure temperature Ts, not T1.The resistance measurement has given us additionalinformation to help interpret the physical phenomenondetected by a standard open thermocouple check.

Measuring Resistance - We have casuallymentioned checking the resistance of the thermocouplewire as if it were a straightforward measurement. Butkeep in mind that when the thermocouple is producing avoltage, this voltage can cause a large resistancemeasurement error. Measuring the resistance of athermocouple is akin to measuring the internalresistance of a battery. We can attack this problem witha technique known as offset compensated ohms

Summary In summary, the integrity of a thermocouple system

can be improved by following these precautions:• Use the largest wire possible that will not

shunt heat away from the measurement area.• If small wire is required, use it only in the region

of the measurement and use extension wire for the region with no temperature gradient.

• Avoid mechanical stress and vibration which could strain the wires.

• When using long thermocouple wires, connect the wire shield to the dvm guard terminal and usetwisted pair extension wire.

• Avoid steep temperature gradients.• Try to use the thermocouple wire well within its

temperature rating.• Use a guarded integrating A/D converter.• Use the proper sheathing material in hostile

environments to protect the thermocouple wire.• Use extension wire only at low temperatures and

only in regions of small gradients.• Keep an event log and a continuous record of

thermocouple resistance.

measurement.

As the name implies, the voltmeter first measures thethermocouple offset voltage without the ohms currentsource applied. Then the ohms current source isswitched on and the voltage across the resistance ismeasured again. The voltmeter software compensatesfor the offset voltage of the thermocouple andcalculates the actual thermocouple source resistance.

Special Thermocouples - Under extreme conditions,we can even use diagnostic thermocouple circuitconfigurations. Tip-branched and leg-branchedthermocouples are four-wire thermocouple circuits thatallow redundant measurement of temperature, noise,voltage and resistance for checking wire integrity. Theirrespective merits are discussed in detail in REF. 8.

T1

To Data AcquisitionSystem

T = 1200˚C T = 300˚C

t1 Time

R

T1

Short

TS

Leg-Branched Thermocouple

Tip-Branched Thermocouple

BURNING COAL SEAMFigure 31

THERMOCOUPLE RESISTANCE vs. TIMEFigure 32

CAUSE OF THE RESISTANCE CHANGEFigure 33

Figure 34

Z-33

HistoryThe same year that Seebeck made his discovery

about thermoelectricity, Sir Humphrey Davy announcedthat the resistivity of metals showed a markedtemperature dependence. Fifty years later, Sir WilliamSiemens proffered the use of platinum as the element ina resistance thermometer. His choice proved mostpropitious, as platinum is used to this day as theprimary element in all high-accuracy resistancethermometers. In fact, the Platinum ResistanceTemperature Detector,15 or PRTD, is used today as aninterpolation standard from the oxygen point(-182.96°C) to the antimony point (630.74°C).

Platinum is especially suited to this purpose, as it canwithstand high temperatures while maintaining excellentstability. As a noble metal, it shows limited susceptibilityto contamination.

The classical resistance temperature detector (RTD)construction using platinum was proposed by C.H.Meyers in 1932.12 He wound a helical coil of platinum ona crossed mica web and mounted the assembly insidea glass tube. This construction minimized strain on thewire while maximizing resistance.

Although this construction produces a very stableelement, the thermal contact between the platinum andthe measured point is quite poor. This results in a slowthermal response time. The fragility of the structurelimits its use today primarily to that of a laboratorystandard.

Another laboratory standard has taken the place ofMeyersʼ design. This is the bird-cage element proposedby Evans and Burns.16 The platinum element remainslargely unsupported, which allows it to move freelywhen expanded or contracted by temperaturevariations.

Strain-induced resistance changes over time andtemperature are thus minimized, and the bird-cagebecomes the ultimate laboratory standard. Due to theunsupported structure and subsequent susceptibility tovibration, this configuration is still a bit too fragile forindustrial environments.

Metal Film RTDʼsIn the newest construction technique, a platinum or

metal-glass slurry film is deposited or screened onto asmall flat ceramic substrate, etched with a laser- trimming system, and sealed. The film RTD offerssubstantial reduction in assembly time and has thefurther advantage of increased resistance for a givensize. Due to the manufacturing technology, the devicesize itself is small, which means it can respond quicklyto step changes in temperature. Film RTDʼs arepresently less stable than their hand-madecounterparts, but they are becoming more popularbecause of their decided advantages in size andproduction cost. These advantages should provide theimpetus for future research needed to improve stability.

THE RTD

12 Refer to Bibliography 1215 Refer to Bibliography 1516 Refer to Bibliography 16

A more rugged construction technique is shown inFigure 37. The platinum wire is bifilar wound on a glassor ceramic bobbin. The bifilar winding reduces theeffective enclosed area of the coil to minimize magneticpickup and its related noise. Once the wire is woundonto the bobbin, the assembly is then sealed with acoating of molten glass. The sealing process assuresthat the RTD will maintain its integrity under extremevibration, but it also limits the expansion of the platinummetal at high temperatures. Unless the coefficients ofexpansion of the platinum and the bobbin matchperfectly, stress will be placed on the wire as thetemperature changes, resulting in a strain-inducedresistance change. This may result in a permanentchange in the resistance of the wire.

There are partially supported versions of the RTDwhich offer a compromise between the bird-cageapproach and the sealed helix. One such approachuses a platinum helix threaded through a ceramiccylinder and affixed via glass-frit. These devices willmaintain excellent stability in moderately ruggedvibrational applications.

Glass sealed Biflar Winding

Thick Film OMEGA® Film Element

Typical RTD Probes

Thin Film OMEGA® TFD Element

MYERS RTD CONSTRUCTIONFigure 35

TYPICAL RTDʼsFIgures 36 and 37

Z-34

Z

Metals - All metals produce a positive change inresistance for a positive change in temperature. This, ofcourse, is the main function of an RTD. As we shallsoon see, system error is minimized when the nominalvalue of the RTD resistance is large. This implies ametal wire with a high resistivity. The lower theresistivity of the metal, the more material we will have touse.

Table 6 lists the resistivities of common RTDmaterials.

METAL RESISTIVITY OHM/CMF(cmf = circular mil foot)_________ ___________________

Gold Au 13.00Silver Ag 8.8Copper Cu 9.26Platinum Pt 59.00Tungsten w 30.00Nickel Ni 36.00

Table 6

Because of their lower resistivities, gold and silver arerarely used as RTD elements. Tungsten has a relativelyhigh resistivity, but is reserved for very high temperatureapplications because it is extremely brittle and difficultto work.

Copper is used occasionally as an RTD element. Itslow resistivity forces the element to be longer than aplatinum element, but its linearity and very low costmake it an economical alternative. Its uppertemperature limit is only about 120˚C.

The most common RTDʼs are made of eitherplatinum, nickel, or nickel alloys. The economical nickelderivative wires are used over a limited temperaturerange. They are quite non-linear and tend to drift withtime. For measurement integrity, platinum is the obviouschoice.

Resistance Measurement The common values of resistance for a platinum RTD

range from 10 ohms for the bird-cage model to severalthousand ohms for the film RTD. The single mostcommon value is 100 ohms at 0°C. The DIN 43760standard temperature coefficient of platinum wire is α =0.00385. For a 100 ohm wire, this corresponds to +0.385 ohms/°C at 0°C. This value for α is actually theaverage slope from 0°C to 100°C. The more chemicallypure platinum wire used in platinum resistancestandards has an α of +0.00392 ohms/ohm/°C.

Both the slope and the absolute value are smallnumbers, especially when we consider the fact that themeasurement wires leading to the sensor may beseveral ohms or even tens of ohms. A small lead

impedance can contribute a significant error to ourtemperature measurement.

A ten ohm lead impedance implies 10/0.385 ≅ 26°Cerror in measurement. Even the temperature coefficientof the lead wire can contribute a measurable error. Theclassical method of avoiding this problem has been theuse of a bridge.

The bridge output voltage is an indirect indication ofthe RTD resistance. The bridge requires fourconnection wires, an external source, and threeresistors that have a zero temperature coefficient. Toavoid subjecting the three bridge-completion resistors tothe same temperature as the RTD, the RTD isseparated from the bridge by a pair of extension wires:

These extension wires recreate the problem that wehad initially: The impedance of the extension wiresaffects the temperature reading. This effect can beminimized by using a three-wire bridge configuration:

If wires A and B are perfectly matched in length, theirimpedance effects will cancel because each is in anopposite leg of the bridge. The third wire, C, acts as asense lead and carries no current.

The Wheatstone bridge shown in Figure 41 creates anon-linear relationship between resistance change andbridge output voltage change. This compounds thealready non-linear temperature-resistance characteristicof the RTD by requiring an additional equation to convertbridge output voltage to equivalent RTD impedance.

Lead

Lead

R = 5 Ω

R = 5 Ω

100 Ω RTD

–

+ DVM

RTD

–

+ DVM

RTD

ADVM

C

B

EFFECT OF LEAD RESISTANCE

WHEATSTONE BRIDGE

3-WIRE BRIDGE

Figure 38

Figure 39

Figure 40

Figure 41

Z-35

4-Wire Ohms - The technique of using a currentsource along with a remotely sensed digital voltmeteralleviates many problems associated with the bridge.

The output voltage read by the dvm is directly proportionalto RTD resistance, so only one conversion equation isnecessary. The three bridge-completion resistors arereplaced by one reference resistor. The digital voltmetermeasures only the voltage dropped across the RTD andis insensitive to the length of the lead wires.

The one disadvantage of using 4-wire ohms is that weneed one more extension wire than the 3-wire bridge.This is a small price to pay if we are at all concernedwith the accuracy of the temperature measurement.

3-Wire Bridge Measurement ErrorsIf we know VS and VO, we can find Rg and then solve fortemperature. The unbalance voltage Vo of a bridge built

with R1 = R2 is:

R3 1VO= VS ——— – VS —(R3 + Rg) (2)If Rg = R3, VO= 0 and the bridge is balanced. This can

be done manually, but if we donʼt want to do a manualbridge balance, we can just solve for Rg in terms of VO:

VS - 2VORg = R3 ————(VS + 2VO)This expression assumes the lead resistance is zero.

If Rg is located some distance from the bridge in a 3-wire configuration, the lead resistance RL will appear inseries with both Rg and R3:

Again we solve for Rg:

Vs - 2Vo 4VoRg = R3 ———— - RL ————(VS + 2Vo) (Vs + 2Vo)

Resistance to TemperatureConversion

The RTD is a more linear device than thethermocouple, but it still requires curve-fitting. TheCallendar-Van Dusen equation has been used for yearsto approximate the RTD curve:11, 13

T T T TRT=R0+R0 α T-δ —— -1 —— -β —— -1 ——[ (100 )(100) (100 )(100)3 ]

Where:RT = Resistance at Temperature TRo = Resistance at T = 0˚Cα = Temperature coefficient at T = 0˚C

(typically +0.00392Ω/Ω/˚C)δ = 1.49 (typical value for .00392 platinum)β = 0 T > 0

0. 11 (typical) T < 0

The exact values for coefficients α , β , and δ aredetermined by testing the RTD at four temperatures andsolving the resultant equations. This familiar equationwas replaced in 1968 by a 20th order polynomial inorder to provide a more accurate curve fit.

The plot of this equation shows the RTD to be a morelinear device than the thermocouple:

11, 13 Refer to Bibliography 11 and 13.

–

+

DVM

= 0100 W RTD

= 0

ii

i

The error term will be small if Vo is small, i.e., thebridge is close to balance. This circuit works well withdevices like strain gauges, which change resistancevalue by only a few percent, but an RTD changesresistance dramatically with temperature. Assume theRTD resistance is 200 ohms and the bridge is designedfor 100 ohms:

Since we donʼt know the value of RL, we must useequation (a), so we get:

6 - 1.9868Rg = 100 ————— = 199.01 ohms(6 + 1.9868)The correct answer is of course 200 ohms. Thatʼs a

temperature error of about 2.5˚C.

Unless you can actually measure the resistance of RL

or balance the bridge, the basic 3-wire technique is notan accurate method for measuring absolutetemperature with an RTD. A better approach is to use a4-wire technique.

RTD = R

R3

VO

+-+-

VS

R2

R1

g

3V

1Ω

VO

+-+-

1Ω100Ω

200Ω6V

2.0066V

RL

Rg

RLR3

VO

+-+-

VS

Figure 43

4-WIRE OHMS MEASUREMENTFigure 42

Figure 44

Figure 45