precision thermistor measurement for thermometry

APPLICATION NOTE January 1993 / June 2000 / May 2010 TD002

Measurement Specialties Dayton www.meas-spec.com 2670 Indian Ripple Road Dayton, OH 45440-3605 USA

MEASUREMENT SCIENCE CONFERENCE TUTORIAL

THERMOMETRY FUNDAMENTALS AND PRACTICE

PRECISION THERMISTOR THERMOMETRY

John M. Zurbuchen January 20, 1993

Revised June 2000



PRECISION THERMISTOR THERMOMETRY I. Introduction. Thermistors and thermistor probe assemblies are used in diverse fields of temperature sensing, from neo-natal infant monitoring to tracking the temperature of astronauts in space, from measurement of temperature in the oceans to maintaining critical temperature parameters of satellites, from a one-time use in a disposable medical probe to decades in telecommunications cables. They are the sensors for the automatic reference junction compensators in thermocouple devices, and they are ubiquitous in electronic circuits for compensation of component changes due to temperature fluctuations. What are Thermistors: The name is derived from the devices major characteristic, a thermally sensitive resistor. There are two major types: NTC, with a negative temperature coefficient of resistance, and PTC with positive temperature coefficient. The most common type in use for temperature measurement is the NTC thermistor which exhibits a steep decrease in resistance as temperature increases. The resistance of the thermistor changes approximately three orders of magnitude in a 150C range. This provides a means to very accurately measure very small temperature variations. In comparison with other electrical temperature sensors, thermistors are the most sensitive devices available. This is shown below for a type K thermocouple, a 100 ohm platinum RTD, and a 10k ohm NTC thermistor at 25C:

Table 1. Comparison of Temperature Sensors K Thermocouple 100 RTD 10k Thermistor Sensitivity: 40 uV/C 0.392 /C 438 /C For 1mk Resolution 4x10-8 Volts 4x10-4 ohms 4x10-1 ohms Temperature Range -200C to 1300C -200C to 650C -80C to 150C Other advantages of thermistors include very low excitation power, two-wire connection, ruggedness, interchangeability, flexibility in characteristics, and a large variety of sizes. Their major disadvantages are a rather limited temperature range, and an inherent nonlinear response.



II Thermistor Types. Thermistors are made in an incredible variety of sizes, styles, and lead configurations, all dependent upon their final application. There are beads, chips, disks, wafers, flakes, rods; with parallel leads or axial leads; epoxy coated or glass encapsulated. For temperature measurement, two types of thermistors, beads and disks, constitute the major portion of the market volume, with disks the dominant type. In recent years the thermistor chip has gained popularity. Its characteristics are like those of a disk thermistor, but with a trend to smaller size. The characteristics that distinguish bead thermistors from disks are size, interchangeability, dissipation constant, time constant, and stability. Beads are usually very small, not interchangeable, and have a very fast response time, but very lower power handling without self-heat. They are normally quite stable, with drift rates on the order of 5mK per year. They can operate at higher temperatures. Disks, on the other hand, can be made interchangeable, have higher power handling capability, have a longer time constant, but until recently, were somewhat less stable, with drift rates about 50mK per year. These differences arise from the differing processes used in their manufacture, and are summarized in Table 2.

Table 2. Comparison of Bead and Disk Thermistor Properties Typical 10 mil

Glass coated Bead Typical

Epoxy Coated Disk Diameter/Width 0.25 mm 2.5 mm

Time Constant (still air) 0.5 sec --------- Dissipation Constant (air) 0.09 mW/C 1.0 mW/C

Time Constant (water) 10 msec 1.0 sec Dissipation Constant (oil) 0.45 mW/C 8.0 mW/C

Max. Operating Temperature 300C 150C



III. Thermistor Theory. NTC thermistors consist of mixed metal oxide semiconductors. These are prepared by intimately mixing fine powders of transition metal oxides, and firing these mixtures at high temperatures, in the 1000C to 1300C range. In this sintering process, the metal oxides undergo a solid state chemical reaction, forming the spinel crystallographic structure, which is the electrically active material. Spinels of the transition metal oxides, such as manganese, iron, cobalt, and nickel, all exhibit a large change in resistance with temperature. The name derives from the mineral spinel, which has the structure MgAl2O4, where Mg occupies tetrahedral, or A sites in the crystal lattice and AI occupies octahedral, or B sites. This is a normal spinel, and contains one 2+ metal ion on the A site, two 3+ metal ions on the B sites and four oxygens. This is commonly written as Mg[Al2,]O4, where the elements inside the bracket represent the B sites. An inverse spinel has half the trivalent ions on the A sites and the divalent ions on the B sites, such as nickel ferrite, Fe[NiFe]O4. Various degrees of inversion can occur depending on the metal ions, the temperature, of reaction, and any annealing cycles to which the material was subjected. A common thermistor material is nickel manganite, NiMn2O4, a partially inverse spinel where the nickel atoms prefer the octahedral sites, thus forcing some manganese to occupy tetrahedral sites. In order to maintain charge neutrality, the remaining manganese present on the B sites must be in a distribution of 3+ and 4+ states. These types of materials are referred to as valence controlled semiconductors. Conduction occurs when ions having multiple valence states occupy equivalent crystallographic sites. It must be the same element and differ in valence by one unit and occupy B sites. The conduction mechanism is a thermally activated electron hopping process, in which the electrons hop from one cation (Mn3+) to another (Mn4+) in the B lattice sites under the influence of a potential gradient across the material. The conductivity is a product of charge density and mobility. Charge density is determined by the number of charge carriers, the density of B sites, and the probability of a B site being active. The mobility is determined by the distance between nearest neighbor B sites, the activation energy (needed for the electron to move from one site to another), and a frequency factor (how often it tries to jump). Charge carriers are also produced by other defects such as non- stoichiometry and grain boundaries. By considering the effects of all the above factors, an expression for conductivity can be derived:

= x(-q/kT) where is the infinite temperature conductivity (which includes consideration of charge density and mobility), -q is the activation energy, k is Boltzmanns constant, and T the absolute temperature.



For thermistors, the resistivity (and hence resistance) is of more interest; therefore, the expression becomes

= x(q/kT) By replacing resistivity with resistance values and combining the activation energy and Boltzmanns constant terms, the familiar thermistor expression is obtained R = A(B/T) where A includes dimensional factors and infinite temperature resistance, B is the material constant Beta, and T is the absolute temperature. These electrical properties, the material constant Beta (or slope) and the resistivity (Ohm-cm), are controlled by composition, sintering temperature, and oxygen partial pressure during sintering; that is, by the manufacturing process. The resistance (Ohm) is a function of the resistivity and the physical dimensions of the device.

R = 1/A where R is the resistance in Ohms, is the resistivity (ohm-cm), 1 is the distance between opposite electrodes, and A is the contact area. Although the slope and resistivity are fixed by composition and firing temperature, the resistance can be adjusted by varying the dimensions of the device. Thus, precision interchangeable thermistors can be manufactured. In this manner, thermistor manufacturers provide a series of materials covering a range of R v. T characteristics to provide the appropriate sensor for the temperature range of interest. Figure 1 shows R v. T for a series of different thermistor compositions in the temperature range of -80C to 150C. Although the expression R = A(B/T) gives good agreement with experiment over short temperature spans, a better method of interpolation over larger temperature ranges is necessary for accurate temperature measurements. Such an equation was developed by J. S. Steinhart and S. R. Hart of the Woods Hole Oceanographic Institute in 1968 (see Ref. 12).



Figure 1. Resistance versus temperature for different thermistor compositions. Note that temperature range for high resistance materials can extend beyond 150C.

The Steinhart & Hart equation is an empirical expression that has been determined to be one of the best mathematical expressions for the resistance-temperature relationship of a negative temperature coefficient thermistor. It is usually written explicit in T:

1 = a + b * (1nR) + c * (1nR)3 T

where T is the Kelvin temperature, a, b, and c are the coefficients derived from measurement, and lnR is the natural logarithm of resistance in ohms. To find a, b, and c, the resistance of a thermistor should be measured at three evenly spaced temperatures. These three temperatures and resistances are then used to solve three simultaneous equations.



Knowing a, b, and c, for the thermistor allows one to use the equation in two ways. if resistance is known and temperature is desired, use the above equation. If temperature is known and the expected resistance is desired use the equation below.

R = e[(2/4+3/27)1/2-/2]1/3-[(2/4+3/27)1/2+/2]1/3 where = (a -1/T)/c and = b/c, in which a, b, and c, are the coefficients of the Steinhart and Hart equation. Listed below is a spreadsheet program with cell assignments which will calculate the coefficients for the Steinhart and Hart equation. A1: 'SPREADSHEET METHOD FOR SOLVING STEINHART & HART EQUATION. A2:'1/T = a + b(lnR) + c(lnR)^3 A4: 'Input temperature and resistance B5: 'Temp (C) C5: 'Resistance D5: 'T(K) E5: 'ln(R) A6: 'Low B6: 0 C6: 7355 D6: +B6+273.15 E6: @LN(C6) A7: 'Mid B7: 40 C7: 1199 D7: +B7+273.15 E7: @LN(C7) A8: 'High B8: 70 C8: 394.5 D8: +B8+273.15 E8: @LN(C8) A10: 'Solve three simultaneous equations to obtain coefficients a,b,c: A12: 'ln(R1) - ln(R2) B12: +E6 -E7 C12: 'Coefficients: A13: 'ln(R1) - ln(R3) B13: +E6-E8 C13: 'a= D13: 1/D6-D15*E6^3-D14*E6 A14: '(1/T1)-(1/T2) B14: 1/D6 - 1/D7 C14: 'b=



D14: (B14-D15*(E6^3-E7^3))/B12 A15: '(1/T1) - (1/T3) B15: 1/D/6-1/D8 C15: 'c= D15: (B14-B12*B15/B13)/((E6^3-E7^3)-B12*(E6^3-E8^3)/B13) A17: 'Solving for R, given T: A19: 'For T (Deg C) = B19: 25 C19: +B19+273.15 D19: '=T (K) A21: 'R = exp{[A^2/4 + B^3/27)^(1/2) - (A/2]^(1/3) A22: ' - [(A^2/4 + B^3/27)^(1/2) + A/2]^(1/3)} A24: 'A =(a -1/T)/c B24: (D13 - (1/C19))/D15 D24: 'A squared = E24: +B24^2 A25: 'B = b/c B25: +D14/D15 D25: 'B cubed= E25: +B25^3 A27: 'R = B27: @EXP((@SQRT(E24/4+E25/27)-B24/2)^(1/3)-(@SQRT(E24/4+E25/27)+B24/2) ^(1/3)) C27: 'Ohms A28: 'dR/dT= B28: -1*B27/(C19^2*(D14+3*D15*(@LN(B27))^2)) A29: '%dR/dt= B29: +B28/B27*100 A31: 'Solving for Temperature given R: A32: 'Ohms = B32: 2252 A34: 'Temperature (C) = B34: 1/(D13+D14*@LN(B32)+D15*(LN(B32))^3)-273.15 Note: Cells that start with an apostrophe ' are labels. Boxed cells indicate data you must enter. Other cells are formulas. For better legibility, increase column A width to 18 characters.



IV. A. Material Characteristics. The steepness of the change in resistance with temperature, or the material characteristics are expressed in numerous ways. Beta, alpha, resistance ratio, all describe the slope of the R v. T curve. One can determine the Beta constant by measuring the resistance at two temperatures and using equation

R = A(B/T)

rewritten as B = 1n(R1/R2)

(1/T1-1/T2) The temperature coefficient of resistance is determined by

= 1 dR R dT

and is usually expressed in terms of % change in resistance per degree. The coefficient of resistance and material constant B are related to each other by

= -B T2

Beta and are two different ways of expressing the same property. Different manufacturers give different temperature ranges for these material constants which sometimes make direct comparisons difficult. In most instances, however, Beta is given for the temperature range of 0C to 50C. Resistance ratio is usually given as the resistance @25C divided by the resistance @125C. Table 3 shows the relationship of the different material characteristics for a series of different compositions. Note the trend of increasing material constants with increasing resistance. A given composition, however, can be made in a series of resistance values with identical Betas. This provides a designer with great flexibility in the choice of thermistor sensor. Another method often used is to give a table of multiplying factors of the resistance at 25C to obtain the resistance at another temperature. Some manufacturers simply provide the complete R v T characteristics as a table of resistances at one degree increments. The nominal resistance value of a thermistor is normally specified as the zero power resistance at 25C.



Table 3. Material Characteristics for Selected Compositions Material R @25

Ohms Alpha @25C (%/C)

Alpha @50C (%/C)

Beta 0-50 (K)

Resistance Ratio

(R25 / R125) a 2252 -4.40 -3.80 3891 29.26 b 10k -4.03 -3.53 3574 23.51 c 100k -4.50 -3.96 3988 34.82 d 300k -4.83 -4.26 4276 46.02 e 1meg -5.19 -4.58 4582 61.96

IV .B. Device Characteristics; Dissipation Constant and Time Constant. The dissipation constant is defined as the power required to raise the temperature of a thermistor 1C above its ambient temperature.

D = P ___ (T Tamb)

Usually expressed in milliWatts per C, it is highly dependent on the thermistors environment, its mounting method, heat capacity, and thermal conductivity. Thus, when a dissipation constant is given, the conditions should be specified. Most thermistor catalogs list the dissipation constant of a thermistor suspended by its leads in still air. Additionally, it may also specify the value for a thermistor in a well-stirred fluid. For example, assume the dissipation constant is approximately 8mW/C and that one wishes to limit self heat to less than 0.01C. Since

P = D delta T

where P is the power applied in mW, D the dissipation constant in mW/C, and delta T is the allowed self-heat error, then a maximum of 0.08 milliwatts, or 80 microwatts, could safely be applied to the thermistor.

The best rule of thumb for accurate temperature measurement is to operate at the lowest possible power consistent with the needed accuracy and the limitations of the read-out device.

As power is applied to a thermistor, Joule heating occurs with an accompanying change in resistance. Since these are negative temperature coefficient devices, the resistance drops as the power increases. As long as the self-heat power is less than the heat dissipation, the resistance is constant. When self heating becomes appreciable, the voltage increase lags against the current increase until a point is reached when the voltage no longer increases. This is the turnover point. Beyond this point, as the current is increased further, the resistance drops faster than the current increase, resulting in a falling current-voltage region with negative resistance. This is a type of thermal runaway condition.

For temperature measurement one should stay well below this "turnover" voltage. (See Fig. 2.)



The thermal time constant is the time required for a thermistor to reach 63.2% of the final temperature change when subjected to a step change in temperature. Its magnitude depends on the same environmental and thermal conditions as the dissipation constant. These properties are device related, as they depend upon mass, heat capacity, and thermal conductivity. A very tiny bead thermistor may have a time constant in the millisecond range, but can only handle tenths of microwatts of power without substantial self-heat. Figure 2. Static V-I characteristics for a 10k ohm thermistor at 25 C. A dissipation constant of 1 mW/C is assumed.

IV. C. Stability Thermistors are not only extremely sensitive, they are also very stable. Their drift rate is surprisingly small, normally on the order of milliKelvins per year at room temperature. Discussion of stability, or drift, in themistors refers to the change in resistance at a given temperature over time. It does not refer to short term variations, sometimes called noise. Unless there is a defect in the device, thermistors are very quiet.



Figure 3. a) Increasing thermometric shift of bare disk thermistor aged at 150C (from Ref. 7). b) Constant thermometric shift at various measuring temperatures. Glass coated thermistors aged at 200C (data from Ref. 8). The major causes of calibration drift are contact degradation and changes in the bulk material. Contact degradation usually manifests itself as a constant % increase in resistance at all measuring temperatures. The effect is to have a larger thermometric error at the higher measuring temperatures. (See Figure 3a.) Changes in bulk material properties are due to crystallographic changes, shifts in phase equilibrium, grain boundary effects, and changes due to cation distribution and oxygen balance. Material changes usually appear as a constant thermometric change. (See Figure 3b.)



Figure 4. Effect of aging temperature on stability (data from Ref. 8). Stability is temperature dependent. The higher the working temperature of a thermistor the more rapidly it will drift. (See Figure 4.) Manufacturing conditions and the type of thermistor construction will also affect stability. In increasing order of stability, one may list bare thermistors, organic-material coated chips or disks, glass coated disks, and glass encapsulated beads.



Figure 5. Stability of disk thermistor probes. Samples were at room temperature between measurements. Figure 5 shows the remarkable stability of ordinary disk thermistor probes. The graph represents the average of five probes that were measured by NBS over a 13-year period. The average drift rate is approximately 5mK/year.



Figure 6. Median drift rates of beads and disks versus aging temperature (from Ref. 10). The NIST (then the NBS) has carried out a long-term (2 year, 1974-1976) study of the stability of thermistors. They obtained both bead and disk sample thermistors in four different resistance values from each of five different manufactures. This study verified the better stability of beads, but also showed the large variation in drift rate of disk thermistors from different suppliers. The better disk samples had median drift rates equal to that of some bead types. Figures 6, 7a, and 7b are some examples of the drift rates taken from that study.



Figure 7. Plot of thermometric change with time for 30C aging. Top: Best bead type. Bottom: Best disk type. Note magnitude of scale. (From Ref. 10.)



Figure 8. Long-term stability of glass coated thermistors. Top: Beads at 30C (from Ref. 10). Bottom: Interchangeable glass coated disks at 25C (from Ref. 4).

In 1981YSI introduced very stable interchangeable glass coated disk thermistors. The drift rate was specified at less than 5 mK/year for temperatures up to 70C, which is a stability approaching that of the better glass coated beads. This was confirmed in a paper presented by J.A. Wise of NIST at 1992 International Temperature Symposium in Toronto. Figure 8 shows a plot from that study compared with results to beads from the 1976 study.



V. Tolerance, Calibration For precision thermometry, the Beta value and the resistance must be controlled over a narrow range. Thermistors are often specified like resistors, with a resistance tolerance of 20%, 10%, 5% of R at 25C. The Beta tolerance should be specified as well. These are normally referred to as point matched thermistors, and are only accurate at the one point, with deviations growing rapidly on either side. (See Fig. 9.) In interchangeable or curve matched thermistors, the R v T curve is reproducible over a given temperature range. This means both the Beta constant and the resistance value have to be tightly controlled. For highly precise interchangeable thermistors the Beta constant is maintained within 0.3%. If the required accuracy and precision of the temperature measurement is on the order of 0.1C or broader, then the use of interchangeable thermistors is a decided advantage since they are pre-calibrated. By interchangeability, we mean that any thermistor may be replaced by any other, of the same type, and the error in temperature measurement will be within the specified tolerance over the specified temperature range on a nominal curve. [For example, a YSI 44031, a tenth degree device, will give resistance values that differ by no more than 0.1C between 0C and 70C from the nominal curve.] For some glass coated disk thermistors, the interchangeability has been tightened to 0.05C. The effect of the temperature scale change from IPTS-68 to ITS-90 in the temperature range for which most interchangeable thermistors are produced is not significant. At worse, it takes up about 20% of the tolerance band at the high temperature end. (See Fig. 10.) For temperature tolerance tighter than 0.05C or 50 mK, calibration at specific temperature points of interest should be done in a constant temperature bath against a reference thermistor thermometer or a SPRT. For accuracies in the mK range, and in conformance to ITS-90, one may calibrate thermistors in fixed point cells, such as the triple point of mercury, the triple point of water, and the melting point of gallium. This is a convenient range with which to bracket 0C. Such a thermistor probe could then be used to track temperature variations on the order of tenths of milliKelvins in triple point of water cells, for instance. For the biological or medical range, calibrations may be done with TpH20, gallium, and succinonitrile cells. This covers the range from 0C to 60C, which brackets the human body temperature nicely.



Figure 9. Top: Effect of resistance and beta tolerance on temperature measuring tolerance (from Ref. 1). Bottom: Tolerance of interchangeable thermistor, 0.1 from 0-70C (from YSI catalog).



Figure 10. Interchangeables tolerance envelope relative to T-90 / T-68 differential.



VI. Measurement Methods The simplest circuit for measuring temperature with a thermistor is a constant voltage power supply, an ammeter and a thermistor connected in series. As the temperature increases, the current through the thermistor increases, which can be read as temperature on the ammeter. This type of design was (and may still be) used in automobile engine coolant temperature gauges. Direct reading electronic thermistor thermometers have been available for many years; from the first YSI Telethermometers of the 1950s to the more recent high precision digital devices. These are usually designed for a specific application or thermistor type, such as YSI 400 Series, which has become a world standard for medical thermometry. For metrology, digital electronic thermistor thermometers of high accuracy and precision have recently appeared on the market. Some of these thermometers have resolution down to 10 microKelvin, accuracy of 0.001K, have built in linearization and interpolation algorithms, computer interface capabilities, and we assume, have taken care of self-heat considerations. For greater flexibility, or if one doesnt have a Telethermometer available, the most convenient and handy device in the laboratory for the measurement of a thermistor or thermistor probe is a good DMM. A commercial 4.5 digit meter will give about 10mK resolution with slight self-heat, depending on the nominal resistance of the thermistor. A 5.5 digit multimeter will provide 2 mK, or better resolution at the expense of increased self-heat. It should be kept in mind that the major determinant of self-heat is the dissipation constant of the thermistor or probe being measured. Meter manufacturers can often modify their measurement circuits to reduce current to the unknown in ohms mode for reduced self-heat errors. Examples are given in the tables below.

Table 4. Self-heat Errors for Different DMMs Assume a thermistor at 1200 with = -48.3/C and 8mW/C dissipation constant

Keithley 172-A (4.5 Digit)

Range (ohms) 3k 30k 300k Resolution 2 mK 21 mK 0.2C Self-heat, Hi ohms 150 mK 1.5 mK



Table 5. Modified Keithley 197 DMM Self-Heat Errors (mK)

Assuming Thermistor with Dissipation Constant of 8mW/C Meter Range Thermistor

Resistance 200 2k 20k 200k 2meg 100 12.4 200 22.9 219 24.8 1.3

1,000 5.2 0.1 1,200 6.0 0.1 2,000 8.9 0.2 2,199 9.5 0.2 0.2

10,000 0.6 0.7 20,000 1.0 1.1 21,199 1.1 1.2 1.2 100,000 0.0 2.0

Admittedly, DMMs give read-outs in ohms, not in temperature. The temperature then must be obtained from the R v. T tables available with interchangeable thermistors. For more accurate determination of temperature, one can determine the resistance at three temperatures, either experimentally or from the R v. T tables, and use Steinhart & Hart interpolation equation to obtain temperature from a given resistance. The major drawback of DMMs is their inability to adjust the power to the thermistor, thus offering no control over self-heat. However, the speed at which measurements can be taken may be an offsetting factor. A simple voltage divider, or half-bridge, where resistance (of a value close to that of the thermistor at temperature mid-point) is placed in series with the thermistor, is a convenient calibration set-up. The fixed resistor is a standard resistor and the power supply is a very stable current source. Using a precision voltmeter, one can determine the current by measuring the voltage across the standard resistor. Then, by measuring the voltage across the thermistor and using Ohms Law, one can calculate the resistance of the thermistor. In this set-up, the connection to the standard resistor and thermistor is 4-wire. Such a set-up was used at NIST to measure drift rates in glass coated thermistors. One of the traditional methods for very precise temperature measurements is the use of a good DC Wheatstone bridge with adjustable input power and a sensitive null detector. In this manner, self-heat can be controlled, and zero power resistance can be determined by operating at several power levels and extrapolating to zero. The disadvantage is slow data acquisition.



Figure 11. Half bridge and Wheatstone bridge circuits for thermistor measurement. With the precision and accuracy of modern DMMs approaching that of a Wheatstone bridge, the choice of which to use depends on the relative importance of convenience versus power control. With the advent of modern digitizing techniques, the recommendation is to perform an A/D conversion at the earliest possible step, and use look-up tables in ROM and/or calculations to provide a temperature output. We have not covered linearization techniques or circuit designs. Information on the YSI 4800LC Linearizing Circuit and Thermilinear networks are available from YSI.



VII. Sources of Error Self-heat, or the energy dissipated by the thermistor due to I2R heating, is probably the major source of error in thermistor temperature measurement. If possible, one should operate at a power level about 100 times below the dissipation constant. This will normally give a self-heat error of 10mK or less. Alternatively, one can reduce self-heat error by operating the thermistor at the same power level that was used for calibration. In our metrology laboratory, we calibrate thermistor reference probes with both an ESI 230B bridge and a modified Keithly 197 DMM. The calibration tag then carries the proper R v. T information for either apparatus that may be used in the readout of the constant temperature baths. Switching ranges on a DMM may alter the degree of self-heat errors. The lower ranges give better resolution at the expense of more power to the thermistor, while the higher range sacrifices resolution for lower self-heat. The choice depends on the application. (Note examples from Table 4.) Additionally, one should be aware of the accuracy and precision specifications of the instrument being used. A quick calculation of the possible percent resistance uncertainty can be made and converted to a temperature uncertainty by dividing by 4%/C. This 4%/C is a good rule of thumb since practically all thermistors have that sensitivity at their midpoint. Stem effects should be familiar to all temperature metrologists. For thermistor probes, immersion should be at least ten times the diameter of the probe. Sample volume should be 1,000 times the mass of the sensor. The Steinhart & Hart interpolation equation can introduce errors, especially if the calibration points are far apart. Figure 12 is a deviation plot for Steinhart & Hart interpolation over 100C with calibration points at 0C, 50C, and 100C. The deviation is less than 10mK in a 100 degree span, or one part in ten thousand. By using closely spaced calibration points these errors can be made vanishingly small. (A 7C span in SH&Hs paper gave



Figure 12. Interpolation errors for Steinhart & Hart equation with calibration points at 0, 50, and 100C.

Table 6. Error in Observed Temperature Due to 0.5 Lead Resistance Measuring Thermistor % Change in alpha Thermometric

Temperature Resistance Resistance %DR/C Error (mK) 0.0 7355 0.007 -5.15 -1

25.0 2252 0.022 -4.39 -5 40.0 1200 0.042 -4.05 -10 70.0 394.5 0.127 -3.45 -37

EMFs may originate from temperature gradients at connections of thermistor leads to extension wires r the measuring equipment if made of dissimilar metals. DC bridges normally have zero offset capabilities. With DMMs the simplest method is to switch to DC volts mode in the lowest range and look for small voltages. A good thermistor (or probe) should show 0. If a voltage does appear, one can obtain correct resistance readings by reversing the connections and averaging the two resistance readings.



Bibliography

Books 1. David C. Hill and Harry L. Tuller, Ceramic Sensors: Theory and Practice; pp. 249-347 in Ceramic

Materials for Electronics. Edited by Revla C. Buchanan. Marcel Dekker, Inc., New York, 1991. The following texts are good, but unfortunately out of print: 2. Eric D. Macklen, Thermistors, Electrochemical Publications, Ayr, Scotland, 1979. 3. Herbert B. Sasche, Semiconducting Temperature Sensors and their Applications, John Wiley & Sons, New

York, 1975. Papers 4. J.A. Wise, Stability of Glass-encapsulated Disk-type Thermistors, presented at the International

Symposium on Temperature, Toronto, 1992.

5. Brian E. Code, Thermistor Probes for Severe Moisture Environments, Sensors, October 1986.

6. Harry L. Trietley, All About Thermistors, Parts 1, 2, and 3, Radio Electronics, January, February, and March 1985.

7. J.M. Zurbuchen and D.A. Case, Aging Phenomena in Nickel Manganese Oxide Thermistors; pp. 889-896 in Temperature, Its Measurement and Control in Science and Industry, Vol. 5. Edited by J.F. Schooley. American Institute of Physics, New York, 1982.

8. T.H. LaMers, J.M. Zurbuchen, and H. Trolander, Enhanced Stability in Precision Interchangeable Thermistors; pp. 865-873 in Temperature, Its Measurement and Control in Science and Industry, Vol. 5. Edited by J.F. Schooley. American Institute of Physics, New York, 1982.

9. Meyer Sapoff, Thermistors for Resistance Thermometry, Measurements and Control, Vol. 14, Nos. 2, 3, 4, 5, and 6, 1980.

10. S.D. Wood, B.W. Mangum, J.J. Filliben, and S.B. Tillet, An Investigation of the Stability of Thermistors, Journal of Research of the National Bureau of Standards, Vol. 83, No. 3, 247-263, 1978.

11. Ray Haruff and Charles Kimball, Temperature Compensation Using Thermistor Networks, Analytical Chemistry, Vol. 42, No. 7, 73A-75A, 1970.

12. J.S. Steinhart and S.R. Hart, Calibration Curves for Thermistors, Deep Sea Research, Vol. 15, 497-503, 1968.

precision thermistor measurement for thermometry

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