Technical Note 15-95ASIssued 18.11.05

USING THERMISTOR TEMPERATURESENSORS WITH CAMPBELL SCIENTIFIC DATALOGGERS

deployed in a bridge circuit (see 107 InstructionManual). This has a 1kΩ resistor chosen to reducethe input resistance of the sensor (as seen by thedatalogger) and to minimise settling errors which canoccur when the cable length is large.

The 107 probe is normally used with Instruction 11,which applies a precise excitation voltage to thebridge before making a single-ended voltage meas-urement across the 1k resistor. When usingInstruction 11, the measured voltage is converted totemperature through a fifth order polynomial conver-sion. An additional resistor is included in the bridgeto optimise the fit of the polynomial over the fulltemperature range of -40°C to +56°C; the errorsintroduced are typically ±1.0°C over the range-40°C to +56°C, but reduce to ±0.1°C over therange -23°C to 48°C.

NOTE: The linearisation errors can be reducedin critical applications by using a software correc-tion (see Technical Note 21-95AS).

Good quality polyurethane cable is used withCampbell Scientific’s 107 probes and the cablescreen is only connected at the datalogger, whichprovides good interference immunity.

In some applications the physical construction of the107 probe is not ideal; here the simplest option is tobuild a probe which mimics the circuit of the 107,and to use Instruction 11 to read the temperature.Points to note for the construction are:

1. The resistors must be either bought or selectedto 0.02% tolerance and must also have a lowtemperature coefficient, i.e. 10 ppm or preferably5 ppm/°C.

2. The sensor must be well sealed against theingress of water; any moisture in the probe willaffect the reading because the thermistor has alarge resistance, comparable to that of a film ofwater when it bridges the conductors.

In many applications, thermistor probes represent aconvenient and reliable method of measuring tem-perature. The change in electrical resistance of athermistor with temperature is significant (unlike aPRT) and, when the thermistor is deployed within asuitable bridge, a millivolt output may be obtained incontrast to the microvoltages supplied by a thermo-couple.

Unfortunately, the change of resistance with tempera-ture is non-linear for a thermistor, and thecharacteristic response curve varies with thermistortype. The non-linear response can be compensatedfor by using an appropriate algorithm or by carefullyselecting the value of the bridge resistors to providelinearisation over a limited range, or by a combinationof both techniques. Furthermore, most manufactur-ers produce a range of ‘unicurve’ thermistors withclosely matched characteristics; this allows the userto interchange temperature probes without the needfor recalibration.

Virtually any thermistor can be used with CampbellScientific dataloggers providing sufficient attention ispaid to the construction of the probe and the lineari-sation method. Many users, however, prefer to use asingle type of probe which is interchangeable and forwhich an output in degrees Celsius is easily obtainedand recorded. Campbell Scientific’s 107 probes fulfilthese requirements and are available at a reasonablecost. This Technical Note provides the user withdetailed information on the construction, use andlimitations of the 107 probe and offers advice onmethods of using alternative thermistors withCampbell Scientific equipment.

CAMPBELL SCIENTIFIC’S 107THERMISTOR PROBEThis probe is based around a precision thermistorand is designed to measure over a wide temperaturerange. The thermistor has a resistance of 100kΩ at25°C and has a highly reproducible response curve.The large resistance is useful in minimising theeffects of long cable runs and the thermistor is

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small enough to be ignored. For more critical appli-cations the ‘almost-linear’ voltage output provides agood basis for fitting a non-linear function. Generallya third or fourth order polynomial provides an excel-lent fit and the function can be used in Instruction 55(Polynomial) to convert the measured voltage into atemperature.

The method of calculating the optimum value oflinearising resistor for a given temperature range wasoriginally published by Burke (Electronics, 2nd June1981). First define the thermistor resistance at thelowest (R

a), middle (R

b) and highest (R

c) tempera-

tures to be measured. Rref

is then

R = R (R + R ) - 2R R

R + R - 2 Rrefb a c a c

a c b

Generally the value of Rref

as calculated is not a‘preferred value’ and so the resistor cannot easily beobtained. The closest possible value must thereforebe selected. Knowing this value it is possible topredict the output voltage for any bridge excitationvoltage. (Refer to Burke’s paper or to CampbellScientific for further details of how to calculate R

ref,

the output voltage and the errors that would beincurred if this was accepted as a linear response.)

A worked example using this linearisation techniqueis given in Appendix B.

CHOOSING THE EXCITATIONVOLTAGEGenerally, you should choose a voltage so that thehighest output voltage, at the lowest temperature, isclose to the top of one of the voltage ranges of thedatalogger, thereby increasing the sensitivity. Forvery low bridge resistances the possibility of self-heating of the thermistor should also be considered.In practice the datalogger only powers the sensor fora few milliseconds, which ensures that self-heating isnegligible, but for fast, continuous logging it would besafer to reduce the excitation voltage and measurethe output on a more sensitive voltage range. Thisprocess also reduces power consumption.

THE EFFECTS OF CABLE LENGTHLong cable runs can cause two sources of error inthe measured temperature. Firstly, the cable resist-ance will add to the thermistor resistance and causean error in the absolute accuracy of the measure-ment if not accounted for. The error is generallynegligible unless extremely long cables are used and/or the base resistance of the thermistor is low (2k orless).

DESIGNING OTHER THERMISTORPROBESWith other thermistors there are two options forcalculating the probe temperature.

OPTION 1: HALF BRIDGE WITH NON-LINEAR OUTPUTConfigure the thermistor in a half bridge with a fixedreference resistor (see Fig. 1). Instruction 4 (Excite,Delay and Measure) can be used to measure theoutput voltage. Alternatively, Instruction 5 (AC HalfBridge) may be used to measure the ratio (X) of thevoltage across the thermistor to the excitation voltage.This may then be converted to the thermistorresistance (Rt) by the simple algorithm:

Rt = Rref [X/(1-X)]

NOTE: This is a built-in function of thedatalogger instruction set (Instruction 59).

ein

eout

0V

Rref

Rt

x = eout

= Rt

ein

Rref

+ Rt

FIGURE 1

Individual readings of resistance can be stored bythe datalogger and then converted to a tempera-ture at a later stage, e.g. on a computer using a fittedcurve. Beware of averaging the measuredresistances; a mean resistance will not be easy toconvert to mean temperature because the relation-ship between resistance and temperature isnon-linear.

A worked example using the 21X to accuratelymeasure snow and ice temperatures using thistechnique is given in Appendix A.

OPTION 2: HALF BRIDGE WITHLINEARISED OUTPUTConfigure the thermistor in a half bridge (as above)but select the reference resistor so that the relation-ship between the voltage output and temperature is‘almost linear’ over the desired temperature range.For many applications the non-linearity errors are

2

In such instances the thermistor might either beconfigured as a 3-wire half bridge (see Instruction 7),which compensates for the lead resistance, oralternatively the cable resistance could be measuredonce during the sensor construction and this resist-ance added to the thermistor resistance beforecalculating the calibration coefficients. The firsttechnique is undoubtedly the most accurate, but itrequires an additional input channel.

The second effect of long cables is to increase anysettling errors in the voltage measurement (a fulldiscussion of these errors is given in the dataloggermanuals). Settling errors can be reduced by using ahigh quality cable with a low capacitance. Secondly,when using Instruction 4, a delay can be introducedbefore the measurement is made to allow the readingtime to settle. The settling error can also be reducedby dividing R

ref into two components (as in the 107

probe). The resistance across the input terminalsshould be 1000 ohms or less, although the total valueof R

ref should remain unchanged. The calibration

coefficients must, of course, be corrected whenusing this latter technique.

THERMISTOR BRIDGESBurke (1981) describes how to construct multi-thermistor bridges which have errors in non-linearitywhich are an order of magnitude better than for asingle thermistor. However, apart from the cost ofusing two or more thermistors and precision resis-tors, similar accuracy can be achieved by fitting apolynomial to the output of a single thermistor bridge.It follows that the construction of multi-thermistorbridges is rarely justified, especially as ready made,linearised, multi-thermistor probes and bridges haverecently become available from manufacturers suchas Fenwall. These sensors may be used directly witha Campbell datalogger, but note that settling errorsand cable length must be considered as with anyother high resistance sensor.

ABSOLUTE ACCURACY OFTHERMISTOR PROBESWhichever linearisation technique is used, theabsolute accuracy (as opposed to the linearisationaccuracy) is dependent on the quality of the thermis-tor used. Most thermistors are only guaranteed to bewithin ±0.2°C absolute accuracy over a limitedtemperature range. For improved tolerance, thethermistors must either be selected carefully frombatches, or else each probe must be calibratedindividually and corrections made when calculatingthe linearisation coefficients.

In the case of the 107 probe, individual calibrationscan usually be catered for by a linear correctionwhereby the multiplier and offset are changed fromone and zero to give the corrected reading.

RESISTOR SELECTIONFinding a supplier for resistors with non-standardvalues and a low temperature coefficient can bedifficult, and often these components are availableonly in large quantities. One compromise is to buyresistors with a low tolerance and select to thespecification required. It is often the case that onefifth of resistors sold with a 1% tolerance are actuallywithin 0.1% of the marked value.

In many applications, the use of resistors with atemperature coefficient of 50 ppm will be quiteacceptable as the error introduced over a 50°Crange of temperature rarely exceeds 0.1°C.

Several suppliers offer resistors with less commonvalues, and Campbell Scientific Ltd. are willing tosupply the resistors used in the 107 probe.

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APPENDIX A. WORKED EXAMPLE USING HALF BRIDGEWITH NON-LINEAR OUTPUT

An accurate measurement of ice temperature isrequired using a precision thermistor. Power dissi-pation in the thermistor must not exceed 1µW. Leadwire resistance is to be measured separately. A 21Xwill be used.

Required measurement range 9kΩ-40kΩ

Max. power dissipation in the thermistor 1 x 10-6w

Resolution required 0.05% of thereading

Accuracy required (thermistor 0.25% of themeasurements) reading

As lead wire resistance is measured separately andused in the subsequent calculations to obtain icetemperature, a standard 2-wire half-bridge configura-tion is considered adequate. This produces onesingle-ended output per thermistor allowing up to 16thermistors to be connected to a 21X datalogger.

Max. power dissipated, I2Rt = 1 x 10-6W

if Rt = 40 kohms,

l = √ 0.25 x 10-10 = 5 x 10-6 A

Therefore current through a thermistor must notexceed 5µA. Assume an excitation voltage (for thebridge) of 2.0V.

if: Rt = 40k Ω

i = 5μA

then (R + Rt) = 400k Ω

R

Rt

2.0V

eo

Thus R = 360kΩ

Now consider the extreme cases:

2.0V

eo

360k

9k

0

4

e = 2. 99 = 360

= 48.780 mV

2.0V

eo

360k

0

40k

e = 2. 4040 = 360

= 200mV0

Unfortunately, the ranges on the 21X do not matchwell with these outputs, and some adjustment isrequired to get the best resolution for the measure-ments. We select the 50mV range on the 21X andreduce the bridge excitation voltage to 0.5V. Thebridge output voltages are now 12.19mV (9kΩ) and50.0mV (40kΩ) which makes the fullest use of the50mV range.

RESOLUTIONOn the 50mV range, the resolution is 6.66µV (for asingle-ended measurement).

When RT = 9kΩ, resolution is

0.00612.19

x 100 = 0.05%rdg

When RT = 40kΩ, resolution is

0.00650.0

x 100 = 0.01%rdg

Thus the required resolution is achieved over the fullworking range.

ACCURACYThe accuracy of voltage measurement on the 21X is0.1% FSR which exceeds the required specification.Note, however, that accuracy depends on thecharacteristics of the 360k resistor. A precisionwirewound resistor would be ideal (a few ppmtemperature coefficient and ±0.1% accuracy).

CONVERTING BRIDGE OUTPUT TORESISTANCEA multiplier in the measuring instruction is used toscale the bridge output initially and a Bridge Trans-form instruction is subsequently used to calculateresistance for each thermistor.

eo

360k

0

0.5V

eo

=x

R

x = R(360k + R)

x 0.5

R =

x0.5

1 - x

0.5

x 360k)

((

)

The following program illustrates the use of Instruc-tions 4 and 59 to calculate the resistance of a singlethermistor.

*1 Enter Table 110 Execution interval is 10 seconds

P4 Excite, delay and measure1 Reps3 Range = 50mV1 Input Channel1 Excitation Channel10 Delay by 0.1 sec500 Excitation is 500mV

1 Location to store0.002 Multiplier (to give X/0.5)0.0 Offset

P59 Bridge Transform X/(X-1)1 Reps1 Location of X360 Multiplier

Output (in kohms) is stored in location 1.

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APPENDIX B. WORKED EXAMPLE USING HALF BRIDGEWITH LINEARISED OUTPUT

In practice it is better to select a temperature rangefor the linearisation which is slightly less than thatactually required. This procedure reduces errorsslightly; in the example above, choosing a range of -5 to +25°C reduces the linear error to ±0.2°C withinthat range, yet the errors at the extremes of the spanare increased only slightly.

Consider the Fenwall Unicurve UUA4lJl thermistor.This has a resistance of 10k ohms at 25°C. For thetemperature range of -10 to +30°C the optimumbridge resistance is calculated at 15677 ohms. Theclosest value commercially available from a standardrange is 15800 ohms. Using this value and 2.5Vexcitation, the maximum error in assuming a linearrelationship between temperature and output (Temp= 36.35 * V - 30.2) is ±0.6°C.

By fitting a polynomial to the output:

Temp = -38.79 + 65.1V - 28.55V2 + 8.65V3

the error can be reduced to ±0.03°C.

6

CSL 115