Calibrating RTD Sensors
RTD devices depend on the fact that metals increase resistivity approximately in proportion to temperature. Their thermal characteristics are conventionally described by a base resistance value and a conversion characteristic that equals 1.0 exactly at 0 degrees C.
R = R0 ( 1.0 + ka * T + kb * T2 + ... )
At T = 0 degrees C, the measured value of R equals the base
Though inexpensive materials can be used for making RTDs, platinum RTDs have a response that is close to perfectly linear. A common approximation is to draw a "straight line curve," starting from the nominal normalized resistance 1.0 at temperature 0 degrees C, extending to the normalized resistance for the device at 100 degrees C.
The illustration above exaggerates the curvature so that there is something to see. For platinum RTD devices, the slope of the constructed line — the alpha parameter value — is 0.00385 per-unit resistance change per degree C. The difference between this straight-line approximation and the exact curve is about 0.4 degrees, with the maximum error occurring at roughly 50 degrees C. If this is already within an acceptable tolerance, there is no point in doing any additional calibration. This is what makes RTDs so popular.
For accurately modelling RTD response through its full temperature range of a few hundred degrees, a higher order polynomial is used. For platinum materials, a polynomial of order two is usually sufficient for full measurement accuracy. For less expensive but less linear RTD devices, you might need a polynomial order as high as six.
Unfortunately, a conventional RTD characteristic maps temperature to normalized resistance. This is usually the reverse of how you want to use it — to map the normalized resistance into a temperature. Inverting the curve equation is no problem for a first or second order polynomial, but for higher-order polynomials you must either use iterative methods or abandon the standard form.
The steps to determine the temperature of an RTD, using a calibrated characteristic curve in conventional form, are as follows:
Usually it is most efficient to compute RTD characteristic
curves directly. As with any sensor, it is possible to
select corner points at intervals along the
characteristic curve and represent the inverse curve
with a piece-wise linear approximation, and evaluate it
Operating over a wide temperature range, you will probably do well to measure the RTD resistance using a simple voltage divider network and unity amplifier gain.
Operating over a limited temperature range, you might want to consider a bridge configuration. If the bridge is reasonably well balanced, you can measure the differential voltage across the bridge with a gain amplifier to improve measurement resolution. A linear mapping from differential voltage to temperature will then yield an accurate conversion.
You can use the