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Ruthenium Oxide thermometer U02844

Wiring

The 4 leads from one side to the other: V+, V-, I-, I+. V leads and I leads are twisted pairs up in the fridge.

Extrapolation of RT curve

The thermometer is calibrated in the temperature range 43.8mK to 45K. The base temperature of K100 with a tower is around 25mK. It is inconvenient to guess the temperature of the detector when it is lower than the lower limit of the calibration range. So I did this fit and extrapolated the lower limit to 20mK.

RT curve and fit 
s = fitoptions('Method','NonlinearLeastSquares','Startpoint',[3.4 -0.5, 0.3, 0]);
f = fittype('a+b*x+c*x^2+d*x^3','options',s);
[c2,gof2] = fit(log10(tr(:,1)),log10(tr(:,2)),f)
 
General model:
       c2(x) = a+b*x+c*x^2+d*x^3
     Coefficients (with 95% confidence bounds):
       a =       3.378  (3.377, 3.38)
       b =     -0.5505  (-0.5531, -0.5478)
       c =      0.3124  (0.3108, 0.3139)
       d =    -0.06817  (-0.0699, -0.06643)

gof2 = 
           sse: 0.001213704088057
       rsquare: 0.999939625066065
           dfe: 73
    adjrsquare: 0.999937143904396
          rmse: 0.004077509460202

The equation used for fitting is

log10(R) = a + b*log10(T) + c*log102(T) + d*log103(T)

This is what I tried. And happily, Oxford Instruments uses a similar model to fit the RT curve in their applications.

The temperature points 20mK:2mK:40mK are added to the lookup table used in the Labview vi to convert resistance value to temperature. These points are 

Temperature             Resistance
(Kelvin)                (Ohms)

2.000000e-002	3.544690e+005
2.200000e-002	2.881067e+005
2.400000e-002	2.395061e+005
2.600000e-002	2.028288e+005
2.800000e-002	1.744483e+005
3.000000e-002	1.520182e+005
3.200000e-002	1.339669e+005
3.400000e-002	1.192102e+005
3.600000e-002	1.069806e+005
3.800000e-002	9.672271e+004
4.000000e-002	8.802626e+004

The original calibration file is 

Temperature             Resistance
(Kelvin)                (Ohms)

4.38046960000000E-02   7.59160000000000E+04
4.78349810000000E-02   6.49400000000000E+04
5.18431280000000E-02   5.66140000000000E+04
5.68250230000000E-02   4.88262000000000E+04
6.36521280000000E-02   4.05433000000000E+04
7.35613620000000E-02   3.17447000000000E+04
8.33089770000000E-02   2.59256000000000E+04
9.53904730000000E-02   2.11887000000000E+04
1.12093771000000E-01   1.70844000000000E+04
1.28251110000000E-01   1.43805000000000E+04
1.46150585000000E-01   1.22643000000000E+04
1.62456008000000E-01   1.08461000000000E+04
1.82254623000000E-01   9.51070000000000E+03
2.03781010000000E-01   8.41770000000000E+03
2.29497367000000E-01   7.44520000000000E+03
2.59700464000000E-01   6.58940000000000E+03
2.89953667000000E-01   5.94440000000000E+03
3.10389118000000E-01   5.59010000000000E+03
3.30237170000000E-01   5.29070000000000E+03
3.68009390000000E-01   4.82248000000000E+03
4.18039247000000E-01   4.34385000000000E+03
4.76044023000000E-01   3.92322000000000E+03
5.34744602000000E-01   3.59624000000000E+03
6.09769034000000E-01   3.27744000000000E+03
6.84203583000000E-01   3.03211000000000E+03
7.65314428000000E-01   2.82254000000000E+03
8.54406405000000E-01   2.64009000000000E+03
9.50692104000000E-01   2.48256000000000E+03
1.05095570039716E+00   2.34942000000000E+03
1.15028755335376E+00   2.24040000000000E+03
1.19962773083011E+00   2.19272000000000E+03
1.29929163689104E+00   2.10578527742315E+03
1.39908633330045E+00   2.03271846550891E+03
1.60012201267339E+00   1.91223359665648E+03
1.80013701175196E+00   1.81883755801600E+03
2.00160281730045E+00   1.74338769274531E+03
2.20163558188738E+00   1.68174064383733E+03
2.40023238738491E+00   1.63024564736497E+03
2.59994719646175E+00   1.58603497656574E+03
2.79829615776087E+00   1.54809053803973E+03
2.99670368669110E+00   1.51502692771822E+03
3.19776049400495E+00   1.48556173041211E+03
3.39541622260485E+00   1.45986238613052E+03
3.59106107230354E+00   1.43708071198947E+03
3.88871404906972E+00   1.40663744917702E+03
4.09294375218529E+00   1.38819487535905E+03
4.20581363365240E+00   1.37871557152302E+03
4.64071401045858E+00   1.34639122928049E+03
5.04256276698200E+00   1.32119022120470E+03
5.54672482460438E+00   1.29458038780479E+03
6.25109664293464E+00   1.26434524837764E+03
7.06180309114799E+00   1.23668154879416E+03
8.07590284949499E+00   1.20957215109907E+03
9.08526409791432E+00   1.18840565643880E+03
1.00988276318688E+01   1.17127293560055E+03
1.11183174681312E+01   1.15709084207785E+03
1.21284216182777E+01   1.14532751690714E+03
1.31369548385184E+01   1.13537970539598E+03
1.41410786811095E+01   1.12677213130088E+03
1.51285143976408E+01   1.11952086523702E+03
1.61185374965597E+01   1.11310758667982E+03
1.70992832555079E+01   1.10735465022853E+03
1.80825485155560E+01   1.10229342494940E+03
1.90620409338935E+01   1.09773977482489E+03
2.00457472812794E+01   1.09355180280870E+03
2.11307522151391E+01   1.08944845256726E+03
2.27137525569297E+01   1.08411121529227E+03
2.43106927189139E+01   1.07940760304155E+03
2.58945166839529E+01   1.07530643762068E+03
2.75068974403887E+01   1.07167284714376E+03
2.91195665753685E+01   1.06825123733792E+03
3.09418153980212E+01   1.06499228547192E+03
3.30517938036950E+01   1.06152397631841E+03
3.60530461306466E+01   1.05732751354981E+03
3.90426222281196E+01   1.05380105163921E+03
4.20421244330238E+01   1.05065175013304E+03
4.50390515692073E+01   1.04794406085150E+03