<p> 'c' normalised coefficients </p>

addfb55d-eb39-40cb-8ae0-2042e24f9623 46 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plotG k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

J 8.0957 - 210.002 - 7.7963 - 195.802 - 7.4807 - 182.962 - 3.7187 - 78.476 - 1.9063 - 38.862 - 00 1.3739 26.87 5.2677 100 6.4886 122.37 8.3743 156.634 12.5517 231.9681 14.7427 271.442 17.4928 321.108 17.8462 327.502 19.456 356.66 22.9259 419.58 24.3123 444.674 30.1095 548.23 34.9108 630.74 36.6933 660.37 55.669 961.93 61.716 1064.43 62.880 1084.5 232 mat :

Thiele support points [mV & k] mV_K 8.0957 - 210.002 - 3.7187 - 0.033279 1.3739 760.189605 5.2677 0.025269 8.3743 24629.820607 - 12.5517 0.000474 17.4928 17314.614489 22.9259 0.002681 - 30.1095 7282.328342 36.6933 0.009426 55.669 6453.527419 - 112 mat :

mV mV_K 1 col :

k mV_K 2 col :

x T k 1 el x mV 1 el - k 2 el x mV 2 el - k 3 el x mV 3 el - k 4 el x mV 4 el - k 5 el x mV 5 el - k 6 el x mV 6 el - k 7 el x mV 7 el - k 8 el x mV 8 el - k 9 el x mV 9 el - k 10 el x mV 10 el - k 11 el / + / + / + / + / + / + / + / + / + / + :

J°C t 8.1 - 63 7.9 - range : i 1 t rows range u i el t i el : v i el t i el T eval : 21 line for u v augment 31 line :

data List collects index list select 147810111316182021111 mat : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

ET J List :

ET 8.0957 - 210.002 - 3.7187 - 78.476 - 1.3739 26.87 5.2677 100 8.3743 156.634 12.5517 231.9681 17.4928 321.108 22.9259 419.58 30.1095 548.23 36.6933 660.37 55.669 961.93 112 mat

XY J . 10 black plotG : calib ET + 15 blue plotG : 21 line

Type "J" T/C ... °C temperature /millivolt[mV]

0 J XY calib 4 1 sys

Tpe 'J' T/C can be used up to the Copper FP 1084.5°C. In this upper range, 'J' calibration points are "uncertain from source", rarely used in practical applications. We have ignored these fixed points for the fit and satisfy ourself from the balistic extension. Try other selection in List(DATA) to fit better the upper range.

Calibrate the mV/I converter

XmV 100 - :

XmV °C ≡

mV 1 :

mV T XmV - mV 5 - 4 - solve mV 4.6309 -

Low range : -100°C => -4.6309 mV

4.6309 - T 100 -

XmV 200 :

XmV °C ≡

mV 1 :

mV T XmV - mV 020 solve mV 10.7768

High range : 200°C => 10.7768 mV

10.7768 T 200

Absolute accuracy of the fit

1. To avoid freaking the CF [Continued Fraction] we skip the 0 fixed point as in fact it is not 0 but rather the triple point 0.01 °C. 2. Several fixed points are 2 decimals, even if there would be only 1 point 2 decimals, we must round to 2 decimals. 3. From knowledge in CF, unlike polynomial fit that wiggle betweem points, CF don't wiggle ! This Thiele 'J' T/C is simply remarkable. 4. Finally, the in-situ accuracy will be the statistical combined accuracies of the T/C and the extension wiring and associated bridge.

Residual mV J°C 1 col : °C J°C 2 col : i 1 J°C rows range Δ i el mV i el T °C i el - 2 round : for mV °C Δ augment 41 line :

Testing an installation:

Residual 8.1 - 210.2113 - 0 7.9 - 200.897 - 0 7.7 - 192.3227 - 0 7.5 - 184.3434 - 0 7.3 - 176.8507 - 0 7.1 - 169.7618 - 0 6.9 - 163.0128 - 0 6.7 - 156.5529 - 0 6.5 - 150.3417 - 0 6.3 - 144.3464 - 0 6.1 - 138.54 - 0 5.9 - 132.9002 - 0 5.7 - 127.4084 - 0 5.5 - 122.0488 - 0 5.3 - 116.8079 - 0 5.1 - 111.6744 - 0 4.9 - 106.6382 - 0 4.7 - 101.6907 - 0 4.5 - 96.8245 - 0 4.3 - 92.0328 - 0 4.1 - 87.3098 - 0 3.9 - 82.6504 - 0 3.7 - 78.0498 - 0233 mat

1. Plunge the installed T/C in a testing bath set to the fixed point(s) 2. Read the mV output: mVtest 3. Plug mVtest in T(mVtet)= °C 4. Tabulate all the test results.

Latest eit90 [°C] eit90 259.3467 - 248.5939 - 218.7916 - 189.3442 - 38.8344 - 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 121 mat :

===== Ultimate fit from Mathcad =====

<p> 'c' normalised coefficients </p>

c 19.8518394369938 3.39708430077966 0.052276519294839 8.91649190043396 103 -^* - 9.92828185332406 105 -^* 8.38053206800752 106 -^* 3.1464248690302 107 -^* - 4.25243756863902 109 -^* 2.07174891774966 1011 -^* - 0.183112912617708 3.87083881009766 103 -^* 5.08713285834413 104 -^* - 2.26745307368593 106 -^* 6.6275111583499 107 -^* 2.21691344604783 108 -^* - 2.87497042511128 1010 -^* 1.36525976453514 1012 -^* - 171 mat :

x J1084 x c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + c 5 el x 4^* + c 6 el x 5^* + c 7 el x 6^* + c 8 el x 7^* + c 9 el x 8^* + 1 c 10 el x * + c 11 el x 2^* + c 12 el x 3^* + c 13 el x 4^* + c 14 el x 5^* + c 15 el x 6^* + c 16 el x 7^* + c 17 el x 8^* + / * :

X J 1 col : Y J 2 col : XY J . 12 black plotG : 31 line

J1084 mV 8.25 - 638 - range : i 1 mV rows range t i el mV i el J1084 eval : for mV t augment 31 line :

XY J1084 2 1 sys

ΔJ1084 X Y Y X J1084 - (vectorize augment :

ΔJ1084 8.096 - 210.002 - 0 7.796 - 195.802 - 0 7.481 - 182.962 - 0 3.719 - 78.476 - 0 1.906 - 38.862 - 0000 1.374 26.87 0 5.268 1000 6.489 122.37 0 8.374 156.634 0 12.552 231.968 0 14.743 271.442 0.001 17.493 321.108 0 17.846 327.502 0 19.456 356.66 0 22.926 419.58 0 24.312 444.674 0 30.11 548.23 0 34.911 630.74 0 36.693 660.37 0 55.669 961.93 0 61.716 1064.43 0 62.88 1084.5 0233 mat

submatrix ET356 J 115 range 12 range el :

The "Minerred" low cost "J356 companion" x J356 6271.432 - 2545758 x 401.6967 - 63.84713 x 15.21327 + 1.22019 x 9.517081 + / - / - / - :

ΔJ356 vx vy vy vx J356 - (vectorize augment : δ ΔJ356 1 col ΔJ356 3 col augment : 21 line

vx ET356 1 col : vy ET356 2 col : xy vx 0 vy * augment . 10 black plotG : 31 line

22.926 J356 420.0703

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

ΔJ356 8.1 - 210 - 0 7.8 - 195.8 - 0 7.48 - 182.96 - 0 3.72 - 78.48 - 0.01 1.91 - 38.86 - 0.01 - 000 1.37 26.87 0.01 5.27 100 0.01 6.49 122.37 0 8.37 156.63 0.01 - 12.55 231.97 0.02 - 14.74 271.44 0.01 17.49 321.11 0.02 17.85 327.5 0.02 19.46 356.66 0.03 - 153 mat

0 δ Error xy 3 1 sys

Minerred from Mathcad 11 x J356 6271.43239 - 2545758.47 x 401.696712 - 63.8471344 x 15.2132708 + 1.2201953 x 9.51708107 + / - / - / - :

Partial fraction from Mathcad 11 x ParfracJ356 6271.43239 - 903.116215 x 15.5679399 + / - 31.0089139 x 9.31550052 + / - 2544824.34 x 401.849801 - / - :

J356 mV 8.6 - 23 8.5 - range : i 1 mV rows range t i el mV i el J356 eval : for mV t augment 31 line :

J356 J1084 XY 3 1 sys

x y axes x y / - :

axes δ Error 2 1 sys