plot(data,char,size,clr)

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Part: 6

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Reconciliate Pt100 calculator

eit90 - 273.15 . . . 961.78 °C

]]> plot(data,char,size,clr)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

eit90 273.15 - 0.00006230541 268.935 - 0.000155487 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.5689173 660.323 3.3760086 961.78 4.28642053 1064.43 4.57255961 1084.5 4.62715523 162 mat :

sub eit90 16 range 21 range el : up eit90 614 range 21 range el : 21 sys

x sub 1 0.00006230541 x ≤ (x 0.21585975 ≤ (& cases : x up 1 0.21585975 x ≤ (x 4.28642053 ≤ (& cases : up up . 12 black plot : sub sub . 12 black plot : 41 sys

°C 1 :

Ω 1 :

<= user units

... exact eit90 @ Thiele support points 'up' [-189.3442 ... 961.78 °C] x J189 7659976110000 / - 241815.0333 x 32.7767646 - 1.2867874 x 7.19133 - 0.007997 x 0.20056 - 0.0315216 x 2.570662 - / - / + / - / - :

0.21585975 J189 4.28642053 J189 21 mat 189.3442 - 961.78 21 mat

Smath al_nleqsolve λ 4.582374490 0.689736236 - 4.153686384 - 50.944725014 - 41 mat :

... exact eit90 inverse in the subCryo  [-259.3467...-189.3442] x λ subCryo λ 1 el x λ 3 el - (λ 2 el x *^(* 1 x ln + x λ 3 el - (- exp + λ 4 el + (* :

Ω cryo 0.00006230541 Ω ≤ (Ω 0.21585975 ≤ (& : Ω high 0.21585975 Ω ≤ (: (Ω 4.28642053 ≤ (& 21 sys

Ω °C_eit90 Ω λ subCryo Ω cryo Ω J189 Ω high * cases :

Extrapolated subCryo =>

Conformity @ suupport points eit90 * δ T eit90 114 range 12 range el : X T 2 col : Y T 1 col : 12 mat i 1 T rows range Δ i el Y i el X i el °C_eit90 - 4 round eval : for t X Y Δ augment : Header Ω °C Δ°C 13 mat : Header t stack 61 line :

δ Ω °C Δ°C 0.00006230541 273.15 - 0 0.000155487 268.935 - 0 0.00119007 259.3467 - 0 0.00844974 248.5939 - 0 0.09171804 218.7916 - 0 0.21585975 189.3442 - 0 0.84414211 38.8344 - 01 0.01 0 1.11813889 29.7646 0 1.60980185 156.5985 0 1.89279768 231.928 0 2.5689173 419.527 0 3.3760086 660.323 0 4.28642053 961.78 0153 mat

calibrate the XTR low high 12 mat 200 - 40012 mat :

min Ω λ subCryo low - 0 ≡ Ω 0.1 0.2 solve : max Ω J189 high - 0 ≡ Ω 2 2.6 solve : 21 sys

min Ω XTR
max Ω XTR min max 21 sys Ω 0.16804473 2.50033034 21 sys

Calibrate Pt100 . . .

1. bath test measure Wr @ 0.01 °C

2. multiply XTR [min/max] by 1/Wr measured

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on-line °C from reading Ω 1.23456789 °C_eit90 0.123456789 °C_eit90 21 mat °C 59.356 210.6392 - 21 mat

subcryo range from the eit90 inverse subCryo(x,λ)

x λ subCryo x sub * x J189 x up * sub 0.00006230541 273.15 - + 20 red 1 5 mat 4 1 sys

low/up from Thiele wrt range support points

up x J189 x up * 2 1 sys

..... more Pt100 user segments .....

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Mathcad  Minerr LM μ 1015.59658242 0.05304418 1.32997985 - 2.19590058 - 41 mat :

... exact eit90 inverse mid range[-189.3442  ... 156.5985 x μ Φ μ 1 el x μ 3 el - (μ 2 el x *^(* 1 x 2 + ln + x μ 3 el - (- exp + μ 4 el + (* :

max balistic error 1.89279768 μ Φ 231.928 - °C 0.024

38.8344 - 0.01 29.7646 156.5985 231.928 51 mat

ρ 997.46316714 0.05214427 1.18339077 - 2.15115758 - 41 mat :

...exact eit90 mid range [-38.8344 ... 231.928] ± 0.0000 x ρ mid ρ 1 el x ρ 3 el - (ρ 2 el x *^(* 1 x 1.825 + ln + x ρ 3 el - (- exp + ρ 4 el + (* :

Mathcad Minerr LM ζ 795.75522816 0.05179366 0.39683701 1.58191684 - 41 mat :

231.928 419.527 660.323 961.78 41 mat

...exact eit90 inverse upper range [231.928 ... 961.78] x ζ Extrapol ζ 1 el x ζ 3 el - (ζ 2 el x *^(* 1 x ln + x ζ 3 el - (- exp + ζ 4 el + (* :

..... Pt100 primary model XFR .....

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data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Pt100 XFR x β f β 1 el β 2 el 1 β 4 el β 3 el β 4 el - (/ x 259.3467 + (- β 4 el β 2 el * / exp * + β 3 el β 3 el β 4 el - (/ x 259.3467 + (- β 3 el β 2 el * / exp * - (* + :

eit90 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.56891730 660.323 3.37600860 961.78 4.28642053 122 mat :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

MCD osculatrice β 0.0009996 12.4435128 228.330346 1.7276022 41 mat :

L 259.3467 - : H 961.78 : N 1221 : vx L H N xd : 41 line

X eit90 1 col : Y eit90 2 col : data eit90 o 5 black plot : 31 line

FIT i 1 vx rows range vy i el vx i el β f eval : for vx vy augment 21 line :

Δwr i 1 eit90 rows range u i el X i el β f eval : for Y u - augment 21 line :

Pt100 ... XFR primary model

data FIT 2 1 sys

The osculatrice coefficients is "exact" @ end points and center 0.01. Despite the 8 decimals in Wr, it does not prove they are true, considering they were constructed from two polynomial segments. In short: leave it as is.

Wr conformity
     wrt eit90 Δwr 0.000 0.003 - 0.006 - 0.001 0.002 0.000 0.001 - 0.004 - 0.004 - 0.002 - 0.003 0.000 121 mat

data FIT 2 1 sys

..... Pt100 Thiele XFR .....

continuous inverse interpolation

[-259.3467 ... 961.78 °C]

over the 12 support points

]]> Cfr(K,X,x)

Thiele on length of support points 'j' K U x Cfr j 12 : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x U jj el - c jj el / + : 21 line for a 1 el 61 line :

The continued fraction ... Optimiz => NONE K U x Cfr K 1 el x U 1 el - K 2 el x U 2 el - K 3 el x U 3 el - K 4 el x U 4 el - K 5 el x U 5 el - K 6 el x U 6 el - K 7 el x U 7 el - K 8 el x U 8 el - K 9 el x U 9 el - K 10 el x U 10 el - K 11 el x U 11 el - K 12 el / + / + / + / + / + / + / + / + / + / + / +

Wr(K,X,x)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

K X x Wr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el - K 11 el x X 11 el - K 12 el / + / + / + / + / + / + / + / + / + / + / + :

K 0.00119007 1481.16925424985 0.028845074566 - 1311.68667916945 - 2.758880829033 87.121262673755 33.319386171553 27.672759469917 - 11.033135031489 - 329.084599654368 - 2.244251954285 179.627799615139 121 mat :

eit90 273.15 - 0.00006230541 268.935 - 0.000155487 259.3467 - 0.00119007 248.5939 - 0.00844974 218.7916 - 0.09171804 189.3442 - 0.21585975 38.8344 - 0.84414211 0.01 1 29.7646 1.11813889 156.5985 1.60980185 231.928 1.89279768 419.527 2.5689173 660.323 3.3760086 961.78 4.28642053 1064.43 4.57255961 1084.5 4.62715523 162 mat :

eit90 eit90 314 range 12 range el : X eit90 1 col : Y eit90 2 col : 12 mat data eit90 . 12 black plot : x c 1 259.3467 - x ≤ (x 1200 ≤ (& cases : 41 line

sanity check K X 218.7916 - Wr K X 231.928 Wr 21 mat 0.09171804 1.89279768 21 mat

calibrate XTR low high 21 mat 200 - 40021 mat :

min [Wr]XTR
max [Wr]XTR K X low Wr K X high Wr 21 mat 0.17005657 2.500453 21 mat

K X x Wr x c * data 259.3467 - 0.00119007 + 40 blue 1 5 mat 961.78 4.28642053 + 40 blue 1 5 mat 5 1 sys

273.15 - 268.935 - 259.3467 - 248.5939 - 218.7916 - 189.3442 - 38.8344 - 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 1064.43 1084.5 161 mat_NBP Helium TP Hydrogen TP Neon TP Oxygen TP Argon TP Mercury TP Water MP Gallium FP Indium FP Tin FP Zinc FP Aluminum FP Silver FP Gold FP Copper 161 mat 12 mat

°C Ω K X °C Wr :

200 - Ω 400 Ω 21 mat Ω 0.17005657 2.500453 21 mat

Calibrate/correct XTR . . .

1. bath test Pt100 c/w extension wiring

. . . at the triple point 0.01 °C

2. add/subtract to min/max XTR the

differential ΔWr =[1-measured Wr triple]

3. add if ΔWr [-] ... subtract if ΔWr [+]

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jmGiraud: 20190209

About this Pt100 CALCULATOR document . . .

1. Supersedes: Callendar-Van Dusen, CIPM polynomials.

2. Applies to most demanding projects [Scientific, High quality loops].

3. eit90 tracable to ITS_90

4. Applicable modules/parameters tracable to this document.

5. Auxilliairy Thiele tracable to Inst_Type Pt100 XFR Thiele.sm

6. Applies for specifying Pt100 linearization data logging/loop control.

7. Range XTR from Ω(°C) ... calibrate @ triple point 0.01 °C

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Carlos algorithm: 2018-05-10
Thiele table of inverse differences i 1 Y rows range k i 1 el Y i el : for j 2 Y rows range i j Y rows range k i j el X j 1 - el X i el - k j 1 - j 1 - el k i j 1 - el - / : iter j : 21 line break try for for 21 line

i 1 iter range Thiele i el k i i el 12 round : for

plug-in Wr(K,X,x)

Thiele 0.00119007 1481.16925424985 0.028845074566 - 1311.68667916945 - 2.758880829033 87.121262673755 33.319386171553 27.672759469917 - 11.033135031489 - 329.084599654368 - 2.244251954285 179.627799615139 121 mat

k 0.0012 00000 0.0084 1481.1693 0000 0.0917 447.9842 0.0288 - 000 0.2159 326.094 0.0513 - 1311.6867 - 00 0.8441 261.5953 0.172 - 1257.132 - 2.7589 01 259.6657 0.2035 - 1252.6011 - 3.2047 87.1213 1.1181 258.8402 0.2277 - 1249.7616 - 3.5383 88.0143 1.6098 258.574 0.3314 - 1240.6521 - 4.8701 92.5705 1.8928 259.7128 0.3934 - 1236.3532 - 5.5921 95.567 2.5689 264.387 0.5491 - 1226.9619 - 7.1865 103.5242 3.376 272.5094 0.752 - 1215.6591 - 8.8482 114.8177 4.2864 284.9617 1.0118 - 1200.9913 - 10.399 130.9681 126 mat