Questions on pt100 probes

[Yuu]

Hello all,

I'm going to put together a simple pt100 circuit with an ADS122C04 soon and I had some questions about pt100 probes.
What is the best way to program resistance interpretations? There's really three things I could do:
1. utilize 0.3850 ohm/C
2. utilize polynomial fit (1 but more complex)
3. use a lookup table

Downloading a pt100 csv table from fluke and comparing that to values obtained using 0.3850 ohm/C, I calculate at times an end temp difference of 0.38 C which is significant.
So if I want this to be as accurate as possible over my temp range (0 to 100C) then it's clear options 2/3 are more accurate.

Here's another thing I don't understand. They give these probes classifications and mine is a class A meaning
\( \pm 0.15 C \pm 0.002 |T_C|. \)
Does that uncertainty in temp assume the user is using the resistance measurements in one way or another? In other words, are they assuming you're using a linear fit or polynomial fit for ideal pt100 curve?

[mendip_discovery]

You might want to look up IEC 60751 which is the standard that defines them.

0.15 + (0.002 x Temp °C) = Tolerance
so
0.15 + (0.002 x 100 °C) = 0.35 °C

Classes are,
AA = ± (0.1 + 0.0017 x °C)
A = ± (0.15 + 0.002 x °C)
B = ± (0.3 + 0.005 x °C)
C = ± (0.6 + 0.01 x °C)

Formulas for the calculating,
For the range - 200 °C to  0 °C:
$$ R_{t} = R_{0}[1+At+Bt^{2}+C(t-100 °C)t^{3} $$
For the range of 0 °C to 850 °C:
$$ R_{t} = R_{0}(1+At+Bt^{2}) $$
where
\$ R_{t} \$ is the resistance at the temperature \$ t \$;
\$ R_{0} \$ is the resistance at \$ t = 0 °C\$

The constants in these equations are:
A = 3.9083 x 10^-3 °C^-1
B = -5.775 x 10^-7 °C^-2
C = -4.183 x 10^-12 °C^-4

EDIT: To clean up text and to fix errors.

[Yuu]

Ahh okay. So they make their table with the following polynomial fit for ideal pt100 curve:
\[ R_t = R_0 (1 + At + Bt^2)\]
and that's also how they "interact" with their tolerance for the 0 to 850 C range.

Meaning, given a measured resistance, you calculate temp using either a lookup table (generated from above) or via math. Then, for that calculated temp, the actual temperature should be \(\pm (0.15 + 0.002 \cdot |T|)\) for Class A. Where that uncertainty stems from the fact the probe isn't an ideal pt100 probe (e.g. may contain impurities) and its resistance curve may drift from the ideal curve.

[mendip_discovery]

I would think of it as the probe tolerance, much like a resistor rather than an uncertainty. However, it would make up a part of an uncertainty if you were to try and account for most of the errors in the system. Probe + reader etc.

[EC8010]

Exactly what I was going to say. It's a resistor. I had a couple of Farnell 219-1840 Class A PT100 probes measured for resistance at the triple point of water and whilst they were within 0.4% of 100 ohm, they weren't spot-on. That tolerance is probably the major player in the uncertainties.

Interestingly, the triple point of water is determined acoustically - at that temperature there are crackling noises. One day, that might be the deciding point in a pub quiz. Probably need to be a pub near a scientific establishment, though. 

[Yuu]

A = 3.9083 x 10^-3 °C^-1
B = 5.775 x 10^-7 °C^-2
C = 4.183 x 10^-12 °C^-4

I'm seeing negatives in front of B and C, see attachment.
Hehe, you know it sucks I can't access probably more up-to-date standards without paying for them for some reason. Who does that??? That's like me having to use "alternate methods" to access research papers because journals want to charge you even though you know they get enough fake money from universities anyway.

[mendip_discovery]

Oops, my mistake. I missed that bit when typing it up.

It's scary how expensive standards are, especially when you are just looking. I find pdf's while having a coffee.com handy for that. However, I usually end up buying them in the end as it is for work.

[Sensorcat]

I had a couple of Farnell 219-1840 Class A PT100 probes measured for resistance at the triple point of water and whilst they were within 0.4% of 100 ohm, they weren't spot-on. That tolerance is probably the major player in the uncertainties.

One thing to consider is that this measurement is not easy. For an accurate result, one has to:

• Reach the triple point.
• Maintain that point, at least for one integration interval.
• Make sure that the resistor grid is at the same temperaure of the water, even though there is a barrier between both, which has thermal resistance.
• Make sure that the resistor grid is at the same temperaure of the water, even though there is an electrical connection to the outside, which also conducts thermally.
• Take self-heating of the resistor into account.
• Preferably use Kelvin-connection, since the other constraints favor long electrical connections.

Since I don't know your work, I'm not saying that you did not achieve a very accurate measurement. But even the first condition alone is tricky: How do you make sure that your entire water reservoir is at triple point? How do you detect if slight variations in water temperature exist inside the reservoir? If you detect the triple point, how do you know which part of the water body has it? Did you have access to a proven triple-point cell for the measurement?

[mzzj]

Interestingly, the triple point of water is determined acoustically - at that temperature there are crackling noises. One day, that might be the deciding point in a pub quiz. Probably need to be a pub near a scientific establishment, though. 

temperature is not determined acoustically, only the physical integrity or level of vacuum in the triple point cell.
Triple point cell makes nerve-wracking  cracks and clicks if you "slosh" the water inside it but it happens also at room temperature.

Once triple point conditions have formed inside the cell and the ice is annealed it sits quietly without making any noise.

[mzzj]

One thing to consider is that this measurement is not easy. For an accurate result, one has to:

• Reach the triple point.
• Maintain that point, at least for one integration interval.
• Make sure that the resistor grid is at the same temperaure of the water, even though there is a barrier between both, which has thermal resistance.
• Make sure that the resistor grid is at the same temperaure of the water, even though there is an electrical connection to the outside, which also conducts thermally.
• Take self-heating of the resistor into account.
• Preferably use Kelvin-connection, since the other constraints favor long electrical connections.

Since I don't know your work, I'm not saying that you did not achieve a very accurate measurement. But even the first condition alone is tricky: How do you make sure that your entire water reservoir is at triple point? How do you detect if slight variations in water temperature exist inside the reservoir? If you detect the triple point, how do you know which part of the water body has it? Did you have access to a proven triple-point cell for the measurement?

No need to make it overly complicated if you don't work in primary laboratory with 10000 eur SPRT's
Properly prepared ice-water bath is easily better than 0,005 Cel accuracy and with some care 0,002Cel accuracy is quite possible. All you need is 10 eur thermos flask and 1 eur worth of distilled water. (ok, also some means to freeze the water but most of us have freezer)

[Sensorcat]

Properly prepared ice-water bath is easily better than 0,005 Cel accuracy and with some care 0,002Cel accuracy is quite possible. All you need is 10 eur thermos flask and 1 eur worth of distilled water. (ok, also some means to freeze the water but most of us have freezer)

I have measured 1°C temperature differences in an ice-water bath, perhaps more. It's a myth that an ice-water bath as such has uniform temperature. There's gravity and convection, and there is a surface and a bottom, wich means that an open bath has no thermal symmetry. How do you prepare your bath to get this surprising accuracy? And how do you verify that? Now irony intended, if you have a way to reach that accuracy with simple means, and proper verification, I would like to learn how. Please note that I view this from an industrial perspective, which means you have to put your claims into a data sheet, and if it's wrong, an unsatisfied customer is the minimum consequence.

[mendip_discovery]

Properly prepared ice-water bath is easily better than 0,005 Cel accuracy and with some care 0,002Cel accuracy is quite possible. All you need is 10 eur thermos flask and 1 eur worth of distilled water. (ok, also some means to freeze the water but most of us have freezer)

I have measured 1°C temperature differences in an ice-water bath, perhaps more. It's a myth that an ice-water bath as such has uniform temperature. There's gravity and convection, and there is a surface and a bottom, wich means that an open bath has no thermal symmetry. How do you prepare your bath to get this surprising accuracy? And how do you verify that? Now irony intended, if you have a way to reach that accuracy with simple means, and proper verification, I would like to learn how. Please note that I view this from an industrial perspective, which means you have to put your claims into a data sheet, and if it's wrong, an unsatisfied customer is the minimum consequence.

I know a lab near to me that has 17025 for temp and they use the ice in a thermos perfectly fine for 0.035 °C k=2 at 0 °C. I don't have 17025 yet but I have an IsoTech Venus with the ability to do -55 °C to 140°C. Its my project for the next year, when I am not onsite.

[mzzj]

Properly prepared ice-water bath is easily better than 0,005 Cel accuracy and with some care 0,002Cel accuracy is quite possible. All you need is 10 eur thermos flask and 1 eur worth of distilled water. (ok, also some means to freeze the water but most of us have freezer)

I have measured 1°C temperature differences in an ice-water bath, perhaps more. It's a myth that an ice-water bath as such has uniform temperature. There's gravity and convection, and there is a surface and a bottom, wich means that an open bath has no thermal symmetry. How do you prepare your bath to get this surprising accuracy? And how do you verify that? Now irony intended, if you have a way to reach that accuracy with simple means, and proper verification, I would like to learn how. Please note that I view this from an industrial perspective, which means you have to put your claims into a data sheet, and if it's wrong, an unsatisfied customer is the minimum consequence.

Easy, fill the whole container with crushed ice and some water, making sure that ice is not floating on top of water. Or if there is water layer in the bottom don't insert your thermometer so deep that it reaches water-only part of the bath.
(Alternatively use circulating mixer)
NIST, BIPM and NZ national standards labs have some good guides:
https://www.measurement.govt.nz/resources/#collapse-control-1-5
https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1411.pdf
https://www.bipm.org/documents/20126/41773843/Specialized-FPs-above-0C.pdf/10265617-c79f-0ea5-8da9-8d359e21c6be

If I needed to verify the ice bath I have 3 resistance bridges, 5 triple point cells and close to dozen SPRT's at my disposal.
But if the ice bath is prepped according to above guides I'd suspect anything else before the ice bath. Haven't seen ice bath deviate more than 0.003C in my career if it is prepped properly.

[mzzj]

"The melting point of water is a very simple, effective and inexpensive temperature
reference. As shown in Figure 12, the melting point of pure water at atmospheric
pressure of 101325 Pa is near 0.0024 C. However, this is not the ice point as it is used
as a temperature reference. The practical ice point is the equilibrium temperature of ice
and air-saturated water, which occurs at a pressure of 101.325 kPa at the lower
temperature of 0.0 C almost exactly. The 0.0024 C difference is caused by dissolved
air in the water and ice.
Historically the ice point was the defining point for many temperature scales until
the more precise water triple-point cells were developed. It still has a major role in
thermometry since it is a fixed point that can be readily achieved by almost any
laboratory with a minimal cost. The main advantage of the ice point is that it can be
made very simply and cheaply and, so long as the basic principles are followed [ASTM
2002, Nicholas and White 2001], it is relatively easy to achieve uncertainties of 10 mK,
and with a little care it can be realised with an uncertainty of 1 mK, and with great care
with an uncertainty of about 100 K [Harvey et al. 2012]."

[Yuu]

NIST, BIPM and NZ national standards labs have some good guides:
https://www.measurement.govt.nz/resources/#collapse-control-1-5
https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1411.pdf
https://www.bipm.org/documents/20126/41773843/Specialized-FPs-above-0C.pdf/10265617-c79f-0ea5-8da9-8d359e21c6be

If I needed to verify the ice bath I have 3 resistance bridges, 5 triple point cells and close to dozen SPRT's at my disposal.
But if the ice bath is prepped according to above guides I'd suspect anything else before the ice bath. Haven't seen ice bath deviate more than 0.003C in my career if it is prepped properly.

Thank you for posting these.

[Sensorcat]

Properly prepared ice-water bath is easily better than 0,005 Cel accuracy and with some care 0,002Cel accuracy is quite possible. All you need is 10 eur thermos flask and 1 eur worth of distilled water.

Some quotes from the third document you linked:

However, for steel-sheathed thermometers, such as industrial platinum resistance thermometers, fine ice is essential if uncertainties below 0.01°C are to be achieved. The ice maybe shaved using commercial ice shavers ...

... care should be taken not to contaminate the ice adjacent to the thermometer. Errors due to contamination of the ice can easily be several tens of millikelvin.

For steel-sheathed resistance thermometers, it may be necessary to compress the ice quite firmly to achieve an uncertainty below 0.01 °C.

Yeah, easy. 11€. If we get to know what compressing quite firmly is, we can do that on the kitchen table, and guarantee not to exceed 5mK error. Just that we don't know what we have, unless we can practice with a proven standard, which exceeds the BOM of 11€ quite a bit.

[mzzj]

YMMV.  Opinions and experiences wary from your 1000mK to 0.1mK

In my experience ice bath compaction or fine ice is not that critical if you have enough immersion depth. 30xD or 40xD usually takes care of that.
And we use "Slush method" mentioned in next chapter that is not so picky about ice fineness or compaction.   

Contamination and water purity is critical point but easily taken care by using distilled water and not washing your face with the ice bath.
Typical tap water around here has ~5mK lower freezing point due to dissolved salts.   

[mendip_discovery]

Also worth reading is,
Euromet Guides - No. 13 | Guidelines on the Calibration of Temperature Block Calibrators | TC-T | Version 4.0, 09/2017
https://www.euramet.org/publications-media-centre/calibration-guidelines

While it is easy to do the maths to go from Temp to Ohms, doing the ohm to temp is another issue. I like maths but I don't know it well enough to work out the best way to do it, and of course any documentation I find is always assuming I understand coding and maths to a level beyond my comprehension.

[EC8010]

OK. Two posters have queried a couple of my comments. Fair enough. I had my two PT100 sensors calibrated at water triple point in a calibration laboratory. I know they had in-calibration 3458A available (and almost certainly used) but I didn't make a note of the water bath apparatus used (which I was shown). In discussion with the head of the laboratory, he mentioned the crackling. Perhaps I misinterpreted his comment, but I took it to mean that the crackling was an indication that the triple point had been achieved. I know for sure that the PT100 connection was a Kelvin connection since I provided that. I assume that (as a calibration laboratory) that they knew that considerable time is required to achieve stability. Hope that helps.

I shall read the ice bath preparations - then I can do a calibration good enough for my needs at home.

The various comments made have reaffirmed my conviction that it's quite difficult to measure temperature accurately. I glue small PT100 sensors to whatever I want to measure and make an effort to keep the glue film as thin as possible because of the temoperature drop across it. I also insulate the outside of the sensor to maximise thermal resistance to the environment to minimise the thermal potential divider effect. But in doing so, I must slightly change the cooling of the measurand. Like I said, measuring temperature is tricky. But whilst my measurements may not have perfect accuracy, they do reveal small changes repeatably, and that's often more important.

[nfmax]

Also worth reading is,
Euromet Guides - No. 13 | Guidelines on the Calibration of Temperature Block Calibrators | TC-T | Version 4.0, 09/2017
https://www.euramet.org/publications-media-centre/calibration-guidelines

While it is easy to do the maths to go from Temp to Ohms, doing the ohm to temp is another issue. I like maths but I don't know it well enough to work out the best way to do it, and of course any documentation I find is always assuming I understand coding and maths to a level beyond my comprehension.

A recommended way to do this is given in Nicholas & White on page 242. They use a recursive technique: an initial approximate solution is improved by repeated application of a 'polishing' function.

Given a measured resistance ratio W(t), i.e. the ratio of the measured resistance to the resistance at 0˚C (nominally 100Ω, but you can use a measured calibration value) and the PRT100 formula constants A, B, and C, calculate an initial temperature estimate t0 (in ˚C) using the quadratic formula on the equation:

W(t) = 1 + A*t0 + B* t0^2

Then use the calculated t0 to calculate t1:

t1 = (W(t) - 1)/(A + B*t0 + C*t0^2*(t0 - 100))

(the C term is only required if t0 > 0 ˚C)

For 'normal' temperatures, one application of the iteration is 'good enough', but you can repeat it to claculate t2 in terms of 1, etc.

This is simple enough to set up in Excel: then you can play with it and compare the results with published PRT tables, to convince yourself it works!

[mendip_discovery]

Well I have got the maths working, it's not neat but it does the job. I just did a loop until it gets the same value as the resistance. I am sure there is a better way to do it but meh.

@Yuu I will post the maths to github as I used python to do it and you can use what you need to do what you need. I am still playing with it at the moment so I will post later.

My motivations is partly due to the MD at work telling me that he would like me to get 17025 accreditation for temperature so I am interested in the maths as well.

[mzzj]

Also worth reading is,
Euromet Guides - No. 13 | Guidelines on the Calibration of Temperature Block Calibrators | TC-T | Version 4.0, 09/2017
https://www.euramet.org/publications-media-centre/calibration-guidelines

While it is easy to do the maths to go from Temp to Ohms, doing the ohm to temp is another issue. I like maths but I don't know it well enough to work out the best way to do it, and of course any documentation I find is always assuming I understand coding and maths to a level beyond my comprehension.

I have used approximate inverse function of the reference function. Was fairly straightforward task to do even with excel and the 6th degree function I have been using is accurate to 0,003mK mOhm.
For some reason there is no commonly used or "approved" inverse polynomial function for IEC60751.  (ITS-90 SPRT's and thermocouples have published reference functions and their inverse polynomials)
Not the best way to do it on small microcontroller but even slowly 8 bit AVR can crank the 6-th degree polynomial probably in 10-20milliseconds.

[Yuu]

Well I have got the maths working, it's not neat but it does the job. I just did a loop until it gets the same value as the resistance. I am sure there is a better way to do it but meh.

@Yuu I will post the maths to github as I used python to do it and you can use what you need to do what you need. I am still playing with it at the moment so I will post later.

My motivations is partly due to the MD at work telling me that he would like me to get 17025 accreditation for temperature so I am interested in the maths as well.

Oh cool. Thanks. It'll probably be a week or two until I get the pcbs, get them soldered, etc... etc.. but I'll let you know what I end up doing when programming the calculations. I'm pretty good at math so hopefully it'll turn out nice hehe.

[TUMEMBER]

 Sensorcat
You know, you made a trivial mistake then. The ice is supposed to be moist/moistened and not swim in "cold water". Water has the highest density at 4 degrees Celsius. This causes ice to "dribble to the bottom of the vessel", while ice has a lower density at approximately 0 degrees Celsius, so it "floats". This is one of the reasons why fish survive in lakes in winter. The ice in the thermos must be constantly "drained" of excess water - this is NECESSARY in such an implementation. The sensor is not meant to be "pushed to the very bottom of the vessel". The sensor is to be in the "middle part of the snow block" - pressed.
There is a very nice pdf explaining how to do this on the New Zeland National Laboratory website.

[mendip_discovery]

For those that are interested,
https://github.com/mendip-defender/conversion_calculators/

It is not perfect, but its better than nothing.

I need to learn how to make interactive Jyputer Notebooks that way people can play with it a little more.

Note: Already updated to correct a small error > to a >=