Napier:
Excellent questions.
First of all, there’s no set formula to absolutely predict how much an RTD (or any instrument or sensor, for that matter) will drift between calibrations. This is because it depends on a number of environmental variables. The “enemies” of an RTD are:
- Excessive vibration
- Shock
- High temperature
- Thermal shock
- Over-excitation (over-current)
Minimizing shock & vibration is extremely critical when it comes to an SPRT, since the platinum element is wound in a strain-free fashion. An IPRT is wound in a “semi strain-free” fashion, and is thus a little more forgiving of shock & vibration. But you “pay” for this in terms of inferior repeatability and hysteresis specs.
So since there are many factors that determine how much an RTD drifts, it is impossible to predict drift with 100% certainty. The only way to know for sure is to perform a thorough calibration once per year and see – afterwards - how much it has drifted. But this data is still valuable, since it will give you an idea (within certain confidence limits) how much the RTD will drift between the current calibration and the next calibration.
But what about the very first calibration? What kind of tolerance should you assign it? That’s a good question, and unfortunately there’s not a good answer. The only thing you can do for the first calibration is go on engineering judgment & the drift history of similar RTDs.
Are you curious what kind of drift I’ve found with IPRTs? We have an IPRT that we’ve used for about 5 years as a calibration standard. You can think of it as a “poor man’s SPRT.” I’m at home right now, so I don’t have the calibration data in front of me. I’ll look it up when I get to work tomorrow, and post the data. I’ll provide drift info on R[sub]0[/sub], A, and B. (I think I assign a calibration tolerance of 0.06 °C to it.)
Now some words about calibration:
An RTD should undergo a thorough calibration at least once per year. You’ll need to take at least 3 data points in order to calculate R[sub]0[/sub], A, and B. (That’s a minimum; if you can afford more, take more.) The lowest calibration temperature will be the lowest traceable range for the IPRT; the highest calibration temperature will be the highest traceable range for the IPRT. Most IPRT calibrations are done by comparing it to an SPRT in a stirred bath. Now you may be asking, “I know what range I want the IPRT calibrated over. So what calibration temperatures should I specify?” There are two schools of thought on this:
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Spread the calibration temperatures evenly throughout the range. This is true even if you’re only calibrating the IPRT at three temperatures (low, middle, high). This will allow the quadratic or curve fitting software to “sample” the temperature-resistance curve in a more uniform fashion. As an example, if you wanted to calibrate an IPRT at three points between 0.01 °C and 500 °C, you would calibrate the IPRT at 0.01 °C, 250 °C, and 500 °C.
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Calibrate the IPRT at temperatures where the SPRT has the lowest uncertainty. Since the SPRT is calibrated using fixed-point cells, it makes sense that the SPRT’s linearization error (which is systematic) will be lowest at these temperatures. So to continue our example, let’s say you wanted to calibrate an IPRT at three points between 0.01 °C and 500 °C. 0.01 °C would definitely be one of the points (TP of water). 231.928 °C (FP of tin) would be the “middle” point. For the “high” point, you would choose 419.527 °C (FP of zinc) or 660.323 °C (FP of aluminum). But keep in mind that the SPRT may not have been calibrated at all of these fixed points. Always examine the SPRT’s calibration certificate to find out what temperatures it was calibrated at.
The current calibration data will allow you to calculate new values for R[sub]0[/sub], A, and B. But before you do that, you should also take the current calibration data and plug it into the quadratic using the previous values for R[sub]0[/sub], A, and B, just to make sure it isn’t out-of-spec. Once you’re satisfied that the current calibration data is “within spec” when using the previous values for R[sub]0[/sub], A, and B, you can go ahead and calculate new values for R[sub]0[/sub], A, and B.
One more thing: The Callendar Van Dusen equation specifies resistance as a function of temperature. For T > 0 °C the equation is a 2nd-order polynomial, and thus the inverse (T vs. R) is simple to derive using the quadratic equation. But I calibrate our IPRTs at T < 0 °C, which turns the Callendar Van Dusen into a 4th-order polynomial. While there are published inverse equations that purport to accurately fit the Callendar Van Dusen equation for T < 0 °C, I don’t trust them. So I actually solved the 4th-order polynomial using equations I found in the CRC Handbook. It was a bitch.
Note that I’m just touching the tip of the iceberg here. If you really want to get anal about the whole thing, you’ll need to do come up with an uncertainty budget or perform an uncertainty analysis. This will allow you to quantitatively justify a tolerance for the IPRT. It combines all errors such as drift, hysteresis, linearization error, stem loss, self heating, signal conditioning and instrumentation (i.e. IPRT readout) error, uncertainty of the SPRT, and uncertainty of the calibration bath.
If you like, I can email you some documents that I’ve written. Drop me a note.
magcraft@main-net.com
