Measuring temperature: Platinum Resistance thermometers 
Algorithms  Temperature  
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Monday, 06 December 2010 13:45  
Platinum resistance thermometersWithin a limited range several metals and alloys have an approximately linear resistivity alteration depending on temperature. Resistance thermometers are sensors that allow determining temperature by measuring the electrical resistance of the sensor, assuming that it is in thermal equilibrium with the medium to measure. Thus, respective sensors can be used within their specific range to calculate temperature by polynomial approximation. Platinum has a positive temperature coefficient, meaning that electrical resistance increases with raising temperature. Platinum Resistance Thermometers (PRT) are often manufactured of coiled platinum wire or as film thermometers with a layer of platinum applied on non conductive substrates. They are used in the range 200°C ≤ t ≤ 850°C. Outer these bounds polynomial approximation is not assured and higher temperatures are often problematic for proper use. Depending on the application the platinum freely extends into the medium to measure, is mounted on non conductive materials or encapsulated in housings for rugged use. PRT sensors are characterised by their specific electrical resistance R_{0} at 0°C. The calibration is easily accomplished by length and thickness of the used wire or coating area and thickness. Common types are:
The advantage of PRT’s is their exchangeability without necessitating recalibration. To measure temperature the easy measurable property of the electrical resistance needs to be gauged. Within a given tolerance this resistance can be converted to temperature for the respective PRT type. Tolerances according to DIN IEC 751/DIN EN 60751 (1995) are:
As electrical resistance of PRT’s can become very small (e.g. 18.53 Ohm at 200°C for a Pt100 sensor) resistance of the wires used to cable the sensor may be significant. Another point to pay attention for is selfheating of the sensor due to a continuous measurement current.
EquationAs PRT’s are not completely linear polynomial approximation is required. In the range 200°C ≤ ϑ < 0°C electrical resistance at temperature t is calculated according to the polynomial:
In the range of 0°C ≤ ϑ ≤ 850°C coefficient c is set to zero and the polynomial becomes:
For conversion of electrical resistance to temperature the above equations can be used after solving for t: Polynomial coefficients for conversion of resistance to temperature, or vice versa, from platinum resistance thermometers according to IPTS68 and ITS90 scale.
AlgorithmThe above equations are implemented in two functions for temperatures on ITS90 scale. For IPTS68 coefficients need to be changed to the respective values tabulated in table (XYZ). It can be easily seen that conversion is senseless, if R_{0}=0. Thus both functions check for this case. The first function is temp_PRTResistanceValue. It calculates electrical resistance of a PRT of type R_{0} (Ω) at temperature aTemp (°C, ITS90). If aTemp is not within the defined range of 200°C to +850°C function returns FALSE and a resistance value of 0 in the variable Resistance. Otherwise electrical resistance will be calculated. Depending on the value in aTemp respective equation (XYZ) is chosen for aTemp values ≥0°C and equation (XYZ) for aTemp values <0°C. The second function is temp_PRTTemperatureValue. It calculates the temperature from a given electrical resistance aResistance for a PRT of the type defined in R_{0}. Function first calls twice temp_PRTResistanceValue for calculating lower and upper limits of electrical resistance for the respective PRT type with base value R_{0}. When aResistance is outer these limits function returns FALSE and a temperature value of 0 in the variable Temperature. Otherwise temperature is calculated from electrical resistance with respect to the PRT type R_{0} and returned in the variable Temperature.
SourceFunction temp_PRTResistanceValue (aTemp, R0 :Double; Var Resistance : Double) : Boolean;
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Last Updated on Friday, 18 March 2011 18:32 