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 Authors : A.V. Seryakov
 Paper ID : IJERTV2IS70260
 Volume & Issue : Volume 02, Issue 07 (July 2013)
 Published (First Online): 09072013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A New Method For Temperature Measurement Using Thermistors
A.V. Seryakov
Scientific laboratory, Special Relay System Design and Engineering Bureau, Nekhinskaya Street, 55, 173021, Velikiy Novgorod, Russia.
This article considers the question of improving the accuracy of temperature measurement using thermistors. Improvement is carried out by binding the temperature to the inflection point Tinf of the functional dependence of the logarithm of the thermistor resistance lnRC and measurement of the temporal drift of the decomposition coefficients Ai(d).
A new method is proposed to derive a precise temperature of the thermistor since it provides a closer approximation to the actual temperature then simpler equations, and is useful over the entire working temperature range of the sensor.
Keywords: temperature measurement, inflection point of the functional dependence of the logarithm of the thermistor resistance, drift coefficients of decomposition.
Thermistors refer to equipment with a strong dependence of electrical resistance to temperature. At limiting high temperatures the thermistor resistance becomes almost constant and independent of temperature. This means that thermistor calibration has a constant at value at infinity, or has a reference point at very high temperature. This causes inconvenience in use and leads to significant errors at measurement and calculation of temperature using thermistors, at low and medium temperatures.
We offer to make a second constant value point, or reference point of thermistor calibration, which was determined by us to be at the inflection point of the functional dependence of the logarithm of the thermistor resistance lnRC.
The difficulty of temperature measurement using thermistors, which are used in the research
of many thermal processes and in thermal equipment, is of high interest at this time, and improving the accuracy of measurements is considered very important.
In view of this, calibration of the thermistor T319 within the temperature range of 0200Â°C was made by verifying indicated values recorded in equilibrium thermodynamic conditions using the model platinum resistance temperature sensor [1, 2].
EXPERIMENTAL
Thermistors CT319 are represented as thermally sensitive elements [68], made of ceramic oxide materials based on nickel, magnesium and cobalt, denoted in composition by the formula (Ni0.2Mn0.7Co0.1)3O4, with negative temperature coefficient (NTC) and resistance of about 10 kOhm at room temperature. The thermistor bead of a CT319 is coated with a thin layer of molybdenum glass and welded on output traverses (0.3 mm) by thin platinum wires (0.01 mm).
The sensitive element of the standard Platinum Resistance Thermometer PRT10 is used as a resistance temperature sensor. The quartz helicoid with platinum spiral is placed in a 4mm diameter thinwalled cylinder made of molybdenum glass. Before sealing, the cylinder with helicoid was filled with helium under a pressure a little less than atmospheric. After manufacturing, the resistance thermometer is calibrated again in temperature range 0200Â°C at Siberian Scientific Research Institute of Metrology (SSRIM) in Novosibirsk. The absolute error of temperature measurement using the platinum resistance thermometer is Â± 0.02 K.
The thermometer together with a thermistor are placed in a heavy copper cylinder, 100 mm in length and 70 mm in diameter, which is located in a vacuum chamber on rigid hangers fixed on the internal surface of upper flange of the chamber. Two pipes are welded to the upper flange of the
vacuum chamber, through one of which the chamber is evacuated, though the other one all sensing wires exit. The pressure in the chamber is maximum 1.3Â·103Pa (105torr).
The vacuum chamber and copper unit are placed in liquid thermal bath with a capacity of 40 litres, which has is allowed to reach equilibrium temperatures in the range of 0200Â°C with temperature gradients of less than 1Â·103K/cm.
The cooling unit was a conditioner BK1500, for which the standard flashheat exchanger was replaced with a subdivided loop.
The working fluid in the thermal bath was silicone oil PESV2, which allows operation at temperatures of 0200Â°C. The temperature variation inside the bath over a period of several hours of monitoring was not more than 1Â·103K, and rate of temperature drift was less than 1Â·104K/h.
MEASURING
Calibration of the thermistor CT319 was carried out over more than two years. Measurements were made in stable conditions under an isothermal cover [910], with gradual increase of temperature from 0Â°C to 200Â°C in increments of 10Â°C. The duration of one continuous
cycle of temperature rise and measuring run was up to 48 hours. In total there were 21 cycles of measurements .
Calibration of the thermistor is in the precise measuring of the thermistor resistance RC, (Ohm), using the standard potentiometric method, in a stationary state under fixed temperature T, (K), determined by the platinum resistance temperature thermometer PRT10. A high quality voltage comparator 3003, accuracy class 0.0005, is used, coupled with standard resistance coil 321 accuracy class 0.01, located in a temperatureinsulated box. A pack of batteries Backen in a grounded metal enclosure worked as a current source.
A total of 500 experimental points were obtained, which were formed into a source data array of temperatures T, and the logarithms of the resistance of the thermistor lnRC. The maximum random error of measurement of temperature with thermometer PRT10 does not exceed (23)Â·103K, thermistor resistance 5Â·104Ohm.
All temperature measurements, conducted using platinum resistance thermometer PRT10, including calibration at SSRIM, were made when measuring a current value of 1 mA (1Â·103), and sensor dissipation is WPRT = (1017)Â·106 W.
Fig. 1 shows the results of one cycle of thermistor resistance RC measurement, against temperature. For easier viewing, the graphic is presented as a reciprocal temperature function 104/T, 1/, of lnRC. This relationship is close to linear, but at high temperatures around T~473K, where
lnRC ~45, and at low temperatures around T~273K, where lnRC~910, some deviations are noticed. At moderate temperature, at the range of lnRC ~68, an inflexion point possibly exists.
Fig.1. Experimental dependence of the logarithm of thermistor CT319's resistance on the reciprocal temperature 104/T, 1/K. The straight line is the calculation according to equation (6), the curve calculation according to equation (9).
Considering the temperature detector as a system with lumped parameters, the thermistors equation is written as follows [1,2]
TC + C T C = WC + T0 ; C = CC
(1)
KC KC
Where TC thermistor temperature, K; derivative with respect to thermistors time temperature in dynamic conditions of measurement; C thermistors characteristic lag time, s;
WC electrical heating output, W ; KC heattransfer coefficient between thermistor and copper unit, W/K; T0 measurement with thermometer PRT10 temperature of copper unit or, for example, heat pipe; time, s; CC – thermistors heat capacity, J/K.
Solution of equation (1) is the following formula [3], in which at moment in time = * the
thermistors temperature is considered to be equal to .
T = T exp + WC + T 1 exp (2)
C C C
KC 0 C
The electrical heating output WC, generated on the thermistor by the act of measuring the current, s constant during all calibration tests and equals 20Â·106W, and the thermistors overheating TC is calculated by the formula:
TC = WC = C WC
(3)
KC CC
To define the thermistors overheating special tests were performed: when in a stationary state at temperatures from 2Â°C to 195Â°C, the thermistors (and thermometer's) heating and cooling temperature was measured during a staged evolution of the electrical heating output WC. With the help of a measuring system liquid calorimeter, described in [9,10], detailed measurements of the relaxational characteristics of the sensors were made. Calculation of the thermistors response (lag) time C, according to equation (2) using ordinary least squares technique (OLS) [1114], gave the results shown in Figure 2.
Fig.2 . Experimentally defined thermistors CT319 lag time C.
An approximation to the curve in Figure 2 is given by a polynomial formula
C(t) = 3.3963027Â·105Â·t2 – 1.39779Â·102Â·t + 2.261388 minutes (4)
where t temperature Celsius, experimental points mean squared departure ~ 0.18 min.
The heat capacity of the thermistor CC~0.3 J/K, weak dependence of the heat capacity of the thermistor temperature; heattransfer coefficient KC~(2Ã·5)Â·103 W/K; and the overheat value caused by the measurement current not more than TC~(104)Â·103, and is considered in all measurements. The temperature difference between the copper cylinder and its isothermal cover, was not more than 0.050.1 K; temperature change during calibration was less than 107K/s. Therefore, the
thermodynamic state of the temperature sensors inside the copper unit during this period was quasi stationary.
ELABORATION
The functional dependence of the electrical resistance of the oxide semiconductor thermistor RC on temperature T is quite difficult, and at first approximation it is represented as a resistance of an
ideal semiconductor with strictly the same number of holes and charge carriers in the exponential form:
C
C
R = A exp B (5)
T
where RC electric resistance of thermistor, Ohm, at temperature T, ; A thermistors resistance value, Ohm, at infinite temperature;
B thermistors sensitivity parameter, dependent upon temperature in general way, .
At temperature T=1Â°C thermistors CT319 resistance RC~30 kOhm; at temperature T=200Â°C RC~50 hm; B~4000 , A~0.013 Ohm. Taking logs in equation (5):
1 = 1 lnA + 1 lnRC (6)
T B B
To clarify the question of inflection of the experimental curve in Fig.1, the derivative was calculated d(1/T)/d(lnRC), and analyzed with the whole array of experimental points. Derivative value d(1/T)/d(lnRC), calculated according to the results of one cycle of thermistors resistance measurement dependent upon lnRC, are shown in Fig.3.
According to the results of numerical differentiation [15] of the entire array of experimental points, curve minimum was defined for the value lnRC min=7.63Â±0.01, which corresponds to the temperature of inflection point, Tinf = 336.34K or 63.19Â°C.
Fig.3. Calculated derivative dependence d(1/T)/d(lnRC)Â·104, 1/ dependent upon logarithm of thermistors CT319 resistance lnRC.
Expanding the derivative d(1/T)/d(lnRC) to a series form at a point minimum:
1 2 3
1 2 3
1/ = + 7.63 2 + 7.63 3 + (7)
where ai the expansion coefficients.
After integration the expansion (7) leads to the following form
T
T
1 = A0 d + A1 d lnRC 7.63 + A2 d lnRC 7.63 3 + A3 d lnRC 7.63 4 (8)
where Ai(d) the expansion coefficients, d time drift of the coefficients.
Thus, the calibration of the thermistor CT319 essentially consists of determining the numerical values of polynomial (8) Ai(d) coefficients and taking account of their drift through time d.
The main feature of the calculation according to the equation (8) is in binding the temperature to the
inflection point Tinf of the functional dependence of the logarithm of thermistors resistance.
Calculation of coefficients Ai(d) was made using ordinary least squares technique (OLS) [1114]. The absolute errors of calculation coefficients Ai(d) are following:
A0~1Â·103, A1~1Â·103, A2~1Â·104, A3~1Â·105.
For quality control and calibration and long term stability, after each of the 21 defining set of coefficients Ai(d) from formula (8), the derivatives d(1/T)/d(lnRC) were calculated. With dispersion of not more than ~5Â·107 all the values of derivatives lie on the curve in Fig. 3. In the low
temperature area at values of the logarithms lnRC~910, the dispersion of calibration is a bit higher, and reaches ~(57)Â·107. This is due to the higher thermistor resistance RC, and the steeper temperature dependence dRC/dT, then the lower density of experimental points, since the calibration of the thermistor was mostly performed at intervals of 10Â°C.
Fig.4 shows the time history of coefficients Ai(d), and the temporal drift of the thermistors calibration. The first eight measurement cycles were made when heating the thermistor up to 200Â°C. As a result of such heating there was significant calibration drift and change of coefficient Ai(d) , for example: dA0/d~6Â·104 1/month. After the limiting high temperature was decreased to 190Â°C,
temporal drift of coefficients decreased notably, for example the rate of change of coefficient A0(d) became only dA0/d~1.5Â·104 1/month. Values of temporal coefficients drift Ai(d) are shown below, d months.
Fig.4. Time history of coefficients Ai(d) at heating up to 200Â°C left part of graphics, heating up to 190Â°C right part of graphics.
Coefficients A0(d)
A0 = 6.21997Â·104Â·d + 29.824488 at heating up to 200Â°C A0 = 2.3075444Â·104Â·d + 29.8213 at heating up to 190Â°C
Coefficients A1(d)
A1 = 4.051207Â·105Â·d + 2.4893 at heating up to 200Â°C A1 = 1.5876991Â·105Â·d + 2.4895 at heating up to 190Â°C
Coefficients A2(d)
A2 = 2.2266277Â·105Â·d + 0.00227 at heating up to 200Â°C A2 = 1.0559017Â·105Â·d + 0.00218 at heating up to 190Â°C
Coefficients A3(d)
A3 = – 3.98635Â·108 Â· (d)2 + 1.771915Â·106 Â·d + 6.3241 Â·105 at heating up to 190Â°C and to 200Â°C
Substitution of the coefficients Ai(d), calculated when heating the thermistor up to 190Â°C, into equation (8) reduces the dispersion of derivatives d(1/T)/d(lnRC) of the curve in Fig.3 to the value ~(23)Â·107, and allows to define the minimum point more accurately: lnRC min = 7.632Â±0.01, thus reducing the calculation error when temperature measurement using thermistor CT319.
Thus, the recommended equation for calculating temperature using the thermistor CT319, taking account of both inflection point Tinf = 336.34K to functional dependence of the logarithm lnRC of thermistors resistance, and temporal drift of the polynomial decomposition coefficients Ai(d), at periodic heating thermistor up to 190Â°C, is as follows:
T
T
1 = A0 d + A1 d lnRC 7.63 + A2 d lnRC 7.63 3 + A3 d lnRC 7.63 4 (9)
DISCUSSION OF THE RESULTS
There is the wellknown cubic polynomial SteinhartHart equation [4], designed to calculate
C
C
temperature using thermistors, by incorporating linear and cubic components using the logarithm of the resistance lnRC:
1
TSH
= A + B lnRC + C lnR3 (10)
where A, B, C the expansion coefficients.
The useful temperature range of this equation with one set of coefficients is not more than 5075K [4,5]. Using sets of numerical coefficients of the SteinhartHart equation, available in internet publications, a comparison of temperature calculation data was made based on the SteinhartHart equation and on our biquadratic equation of logarithms of thermistor resistance (9). Fig.5 shows
temperature relative differences = (TSH T)/TÂ·100% , dependent upon lnRC. Comparison f results shows that temperature differences , depending upon lnRC, have an alternatingsign nature. Minimum values of temperature differences on the order of 0.25% are observed at a value lnRC~6 of thermistor CT319. Maximum values of differences , reaching 0.81%, occur at the edges of applicability of the equation interval (9).
Fig.5. Temperature relative difference , calculated according to the SteinhartHart equation and biquadratic equation under point of inflection of thermistor characteristic (9).
The error, when defining temperature (temperature differences) using thermistor T319 with the biquadratic equation (9) subject to the inflection point at lnRC = 7.632, is not more than (35)Â·104 K.
CONCLUSIONS
The use of the biquadratic polynomial equation (9) with temperature binding to the inflection point of the functional dependence logarithm of thermistor resistance, can extend the range and increase accuracy of the temperature definition.
Account of temporal drift decomposition coefficients polynomial (9) Ai(d), allows to improve the accuracy of the minimum point definition lnRC min=7.632Â±0.01 of thermistor characteristics, and thus the accuracy of the temperature definition.
The use of SteinhartHart cubic polynomial equation increases temperature calculation error, using thermistor, at range limits 273K – 473K to 1.52K.
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