If you create a thermal gradient, in the E-W direction, just affix the copper joints along a N-S line. The thermal gradient can be steered, too, with strategic routed slots.
It can't be hard to measure the terminal block - in a box of electronics with not a lot of self heating, the sensor 1cm away from the terminal block, with a 4 layer PCB with copper inside it...
Ought to do it. But those coefficients come with a health warning. You have to evaluate them carefully to get the right answer!
Only if you are prepared to sacrifice accuracy at the two extremes which happen to be very important in cryogenic and furnace applications.
I thought it might be amusing to take a look at the official N=10 coefficients and I have to say I really don't like what I see.
It is an overfit with the terms d4 and beyond being largely determined by rounding in the numerical algorithm used to do the fitting! This is particularly worrying in the series for low temperatures where the magnitudes of the individual higher terms when T=-270 are all of O(1) !
The series is not absolutely convergent and so the order in which you sum the terms matters. If you were to add them up in the summation notation used in the article then cancellation errors dominate.
A good sanity check on a calibration polynomial is that the higher order corrections should tend to get smaller over the entire valid range. IOW for d[n] evaluate individual terms d[n]*270^n get smaller with n.
They don't! This is rather disturbing.
I tried splicing the two series together in Excel and allowed its charting to do a quick and dirty polynomial fit across the entire range.
It came up with:
y = -0.0000000004055574x3 + 0.0000192958020498x2 + 0.0385860759819436x +
0.0186901808972161y(-270) = -8.984903778 I have no confidence that any of these numbers are good to anything better than 4 sig fig. Note the systematic error at T=0.
If I force it through the origin then it gives:
y = -0.0000000005079249x3 + 0.0000194397323253x2 + 0.0385748719682873x
y(-270) = -8.988061459
There are a couple of problems with this wide range polynomial fit.
It is wrong by about 60mK at -270C and by 25mK at 1250C.
More importantly the gradient (and zero crossing if allowed to optimally fit all parameters) isn't quite right at T=0 which means that a lot of commonly measured temperatures would have a systematic error.
I have no idea what the Gaussian bump at T=126.9686 is but I suspect it might be an ad hoc fix to hit an out of position calibration point!
I am not aware of any phase transitions around that temperature.
BTW note to the OP. Do not assume that your ADC is truly linear across its entire range if maximum accuracy deliverable really matters to you.
-- Regards, Martin Brown
This is really interesting.
I too noticed that the last coefficients, around E-30, are bound to be just silly. You would need to use double floats for them and almost anything done with that is defying physical reality :)
The accuracy requirement for thermocouples is perhaps 0.2C and for RTD perhaps 0.1C. I am not doing a calibration-grade box. I am using the ADS1118 whose smallest range is 256mV. I am amplifying the four lowest output TCs by 7.5 with an external instrumentation amp (four 0.1% resistors around a TLV2333) whose low input terminal is at a constant
+20mV (because I don't have a negative rail in this application; long story).So getting hold of the nine polynomials (8xTC, 1xRTD) would be brilliant. The TC ones have to go both ways, for the CJC calculation.
Another reason for discarding the higher terms is that the simplified version of the equation (the multi-nested one which doesn't involve calculating the powers) gets really unwieldy if you are doing it for
10 terms - AFAICT; maths is not my strong point :) We do have a 32F ARM at 150MHz with hardware 32-bit floats but still calculating 20 x^y powers for each reading might well be a bit much...The higher order terms should definitely make progressively smaller contributions.
Mart>>> >>
He has a point in this instance though. There is little evidence that the N=10 solutions used by the ITS-1990 are any better than N=3 or N=4.
Evaluate the individual terms for T=-270 in the low range polynomial to see what I mean. I am old school where polynomials are concerned I like to see nice well behaved convergence towards a solution.
Put another way you should be worried when d[n]/d[n+1] < 270
I reckon d[n] for n>5 are not improving things in any meaningful sense but have to be included because of the way the fitting was done.
FWIW Excel charting can get plausible looking fits out to N=6 (which is as far as it permits users to go). That is in the sense that they have coefficients d[n] that tend towards zero faster than (1/270)^n.
I am mystified how they managed to calibrate this at all when there are so few well behaved triple points available for precision spot checks.
-- Regards, Martin Brown
The choice appears to have been made to splice at 0C so that both scales have very good precision at commonly measured temperatures.
It is possible to fit a polynomial across the entire temperature range but it will be less accurate at both extremes as a result.
-- Regards, Martin Brown
Yes, it can be hard.
Why heat a block, and control its temperature, and try to keep all the tc-to-copper junctions at that temp, when you could just leave the block at ambient and measure it?
I have seen forced ref junction boxes, but they are rare and expensive. The thermocouple leads are at ambient temp outside of the ref junction box, so conduct heat in or out, so mess up their own transition temps. If the ref junction is at natural ambient temp, such heat conduction is steady-state zero.
This box keeps all the terminal blocks approximately at ambient, and gives the wires some distance to settle down to box interior temp. It senses that with a good platinum RTD. It has no steady-state gradients.
Being different metals, the two wires in a thermocouple pair have different thermal conductivities. Type T is copper+constantan, about as bad as it gets. Any temp gradient from outside to the reference junctions is double bad news.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
The joke here is that you can't measure the resistance of a platinum resistance thermometer without dissipating some heat in it's resistance. It shouldn't be much - 1mA in 100R is 0.1mW - but it is finite.
So why don't you tell you customers to put a blob of soft potting compound on top of the pairs of wires at the terminal block?
It's a lot more thermally conductive than air ...
-- Bill Sloman, Sydney
Silly they may be but when multiplied by ~1000^9 they are not ignorable. Some of those coefficient numbers don't look at all sane to me.
It is one reason why I prefer Chebyshev polynomials for such fitting. They necessarily converge on any reasonable dataset and you can truncate to Nth order and get a nice solution with well defined error ripple.
If you wanted to truncate then you would have to remap the existing polynomial into an equivalent Chebyshev series and then decide where to cut it off and recompute the corresponding polynomial. I doubt if there is anything of physical significance in the coefficients beyond N=5.
Unfortunately in some of the examples they do not. Try T=-270 cryo for example or T= 1200 in the high temperature model.
You have to evaluate the terms carefully in an expression of the form
N=9; sum = 0; for (i=N;i>=0;i--) sum = sum*x + d[i];
But some of those coefficients give divergent results :(
-- Regards, Martin Brown
snipped-for-privacy@highlandsniptechnology.com wrote
I was not suggesting heating the block. I was saying that I can't see why its temperature should be far different from that of a sensor say
1cm away from it.Obviously the overall accuracy will be only as good as that of the CJC sensor, which needs to be either a PT100 also, or something lesser (like the +/-0.5C one in the ADS1118) and calibrate it in production.
A friend has pointed out that the fact that the equations are split around 0C is actually not an issue.
For RTD, a resistance above/below 100R selects the equation. Simple!
For a TC, a voltage above/below zero selects the equation. Simple!
So no iteration is required.
One thing which still worries me a bit is whether I got this right:
For a TC, the process is in three steps:
1) Measure the CJ - the terminal block - (thermistor, PT100, etc) and convert it to an equivalent TC voltage (which will be negative if the CJ is below 0C)2) Measure the TC voltage at the terminal block and add the above voltage to it
3) Convert the resulting voltage to T (selecting the equation according to whether the voltage is positive or negative)
Sorry, that was suggested a couple of posts above.
The t/c terminations and the reference sensor can indeed be kept isothermal to millikelvins, but it takes some care.
I use 1K thinfilm platinum RTDs in my box. 1206 surface-mount, 4-layer PC board, hunky die-cast aluminum box.
Commercial thermocouples are usually specified for 0.5 to 5 C accuracy. Numbers like +-2C +-0.75% are typical. Ref junction sensing and amplifier errors add to that. We're dealing with microvolts.
In real life, reasonably close to room temp, they are usually a lot better than their specs.
Table lookup and interpolation is easy. The numbers are available in tables.
Because an uninsulated block might be subject to thermal gradients from any and all exterior sources. Uncontrolled variables, like that, are what the design is intended to eliminate or minimize.
Once it's insulated, heating is inexpensive.
tc-to-copper doesn't need to be controlled temperature, just paired with the copper-to-tc return in proximity/equal temperature.
You mean triple-point references? You get what you pay for. I've seen ovenized crystals with almost NO expense taken, that could have been replicated with bottle caps and fluff from a dead water heater.
The cheap fix is to make a two-inch thermocouple connection with ten inches of wire, zig-zagging a lot. I put an extra foot of wire into a tube furnace thermal sensor; worked fine.
You know that:
But it controls only the gradients, not the absolute temperature, which means a secondary measure of temperature is a variable to be first measured, then calculated away, Repeatedly. Those aren't a feature shown in that picture.
That can be designed out, in favor of a constant in the calibration table.
Not if you have to heat the whole world to the same temperature, which is what you'll need to do to eliminate gradients and heat flow along the wires.
More common was heated boxes as ref junctions.
I'd rather not pay for heaters or coolers or massive layers of insulation.
How can you keep the interior of the box at a constant temperature without a sensor? What's the advantage of then adding heaters and power supplies and power amps, other than avoiding a little math?
A microprocessor doesn't mind doing math "repeatedly."
-- John Larkin Highland Technology, Inc lunatic fringe electronics
That is probably why no-one has noticed that some of the N=10 fitted polynomial coefficients in that standards document are complete crap.
Do you happen to have a table for type K? I'd be interested in doing a proper polynomial fit to what the correct result ought to look like.
-- Regards, Martin Brown
Martin Brown wrote
Those last coefficients are not even computable using 32 bit floats. They must be crap in the physical sense, but they *are* significant because of what they are being multiplied by.
It almost seems easier to just interpolate the table. Even storing the whole table for all eight TCs and RTD, in 1C increments, in floats, is
40kbytes. Linear interpolation would be perfect. One could do a lot better by storing every few degrees and fitting a curve.
You insulate so you do NOT heat the whole world, that's why you use insulation. It has insulating properties. This never 'eliminates' heat flow, just limits it to within your tolerances. Gradients on the wire are why you actively heat, of course. So, that's solved already.
Few if any boxes with ADC capabilities are lacking in power supplies, and the heater requirements are so crude, you could even use AC. No 'added' power supply. Every semiconductor junction is a sensor, and it only takes an error amplifier, and one calibration trial, to find the thermal setpoint.
The advantage would be lessened computation and conversion requirements.
Or any other unnecessary task. Angry Birds doesn't annoy a cellphone.
The older CRC handbooks had thermocouple tables. (not sure about newer editions) George H.
Here's a type T table, voltage to temperature. The NMR people like T because it covers their range well. I derived this from the NIST polynomials with a PowerBasic program, generating a file for a 68K cross assembler.
I probably have a type K somewhere. We've done every known type.
I recall doing the RTD tables by typing the numbers from an Omega handbook. There aren't many points for the ref junction correction.
-- John Larkin Highland Technology, Inc lunatic fringe electronics
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