provides a means of quantifying uncertainties in temperature measurement in
order to optimise sensor and/or system accuracies.
Uncertainties result from various factors including:
a) Sensor tolerances which are usually specified according to published standards and manufacturers specifications.
b) Instrumentation (measurement) inaccuracies, again specified in manufacturers specifications.
c) Drift in the characteristics of the sensor due to temperature cycling and ageing.
d) Possible thermal effects resulting from the installation, for example thermal voltages created at interconnection junctions.
A combination of such factors will constitute overall system uncertainty. Calibration procedures can be applied to sensors and instruments separately or in combination. Calibration can be performed to approved recognised standards (National and International) or may simply constitute checking procedures on an “in-house” basis. Temperature calibration has many facets, it can be carried out thermally in the case of probes or electrically (simulated) in the case of instruments and it can be performed directly with certified equipment or indirectly with traceable standards. Thermal (temperature) calibration is achieved by elevating (or depressing) the temperature sensor to a known, controlled temperature and measuring the corresponding change in its associated electrical parameter (voltage or resistance). The accurately measured parameter is compared with that of a certified reference probe; the absolute difference represents a calibration error. This is a comparison process. If the sensor is connected to a measuring instrument, the sensor and instrument combination can be effectively calibrated by this technique. Absolute temperatures are provided by fixed point apparatus and comparison measurements
are not used in that case. Electrical Calibration is used for measuring and control instruments which are scaled for temperature or other parameters. An electrical signal, precisely generated to match that produced by the appropriate sensor at various temperatures is applied to the instrument which is then calibrated accordingly. The sensor is effectively simulated by this means which offers a vary convenient method of checking or calibration. A wide range of calibration “simulators” is available for this purpose; in many cases, the operator simply sets the desired temperature and the equivalent electrical signal is generated automatically without the need for computation. However this approach is not applicable to sensor calibration for which various thermal techniques are used.
Temperature Scale of 1990
Resistance temperature detectors (RTDs) operate on the inherent propensity of metals to exhibit a change in electrical resistance as a result of a change in temperature. We are all aware that metals are conductive materials. It is actually the inverse of a metal's conductivity, or its resistivity, that brought about the development of RTDs. Each metal has a specific and unique resistivity that can be determined experimentally. This resistance, R, is directly proportional to a metal wire's length, L, and inversely proportional to the cross-sectional area, A:
R =ρL/A (1)
ρ = the constant of proportionality, or the resistivity of the material
Principle of Operation
RTDs are manufactured from metals whose resistance increases with temperature. Within a limited temperature range, this resistivity increases linearly with temperature:
ρt = ρ0 [1 + a (t – t 0 )] (2)
ρt = resistivity at temperature, t
ρ0 = resistivity at a standard temperature, t 0
a = temperature coefficient of resistance (°C –1 )
Combining Equations 1 and 2, setting t 0 to 0°C, and rearranging to the standard linear y = mx + b form, it is clear that resistance vs. temperature is linear with a slope equal to a:
R/R0 = αt + 1 (3)
In theory, any metal could be used to measure temperature. The metal selected should have a high melting point and an ability to withstand the effects of corrosion. Platinum has therefore become the metal of choice for RTDs. Its desirable characteristics include chemical stability, availability in a pure form, and electrical properties that are highly reproducible.
Platinum RTDs are made of either IEC/DIN-grade platinum or reference-grade platinum. The difference lies in the purity of the platinum. The IEC/DIN standard is pure platinum that is intentionally contaminated with other platinum group metals. The reference-grade platinum is made from 99.99% pure platinum. Both probes will read 100 Ω at 0°C, but at 100°C the DIN grade platinum RTD will read 138.5 Ω and the reference grade will read 139.02 Ω. International committees have been established to develop standard curves for RTDs. The committees have defined a mean temperature coefficient to be between 0°C and 100°C. Solving Equation (3) for a:
α = (R 100 – R 0 ) / R 0 t (4)
IEC/DIN grade platinum: a = 0.00385 Ω/Ω/°C
reference grade platinum: a = 0.003926 Ω/Ω/°C (max.)
The relationship between resistance and temperature can be approximated by the Callendar-Van Dusen equation:
T = temperature (°C)
R = resistance at temperature T
R0 = resistance at the ice point
α = constant (gives the linear approximation to the R vs. T curve)
β= constant (b = 0 when T is >0°C)
The actual values for the coefficients,α, δ, and β are determined by testing the RTD at four temperatures and solving the equations. The Callendar-Van Dusen equation can be simplified to:
Rt = R0 [1 + At + Bt2 + C(t – 100°C)]t 3 (6)
In the positive quadrant, temperatures over 0°C, the behavior of a PRT may be described by a quadratic equation in the form:
Rt = R0 (1 + At + Bt2 ) (7)
As written, the above implies that valid equations may be generated from empirical data taken using 0°C plus two arbitrarily selected positive temperatures. For a single PRT, the constants A and B could be slightly different, depending on the temperatures selected.
Callendar resolved the issue by defining two additional fixed points:
The coefficients A, B, and C depend on the wire material (i.e., platinum) and its purity. International standard IEC 751 describes the specifications that permit universal interchangeability among platinum RTDs.
The coefficients for platinum RTDs according to the IEC 751-2 (ITS90) Standard are:
A = 3.9083 × 10–3 C–1
B = –5.775 × 10–7 C–2
C = –4.183 × 10–12 C–3
©Industrial Temperature Sensors Ltd.