side quest: temperature measurement

A project log for automated gardening - reservoir infrastructure

Building Reservoirs and Weighing Water for level gauging and flow metering.

helgehelge 08/12/2018 at 12:280 Comments

I must confess I haven't spent much time looking at NTC curves before. My prior knowledge was that they are somewhat ill-defined and can only deliver reliable measurements when calibrated individually.


The temperature characteristics of NTCs can be fitted using the Steinhart-Hart (S-H) equation to a practical degree of precision:

As it turns out, I seem to have bought 10k NTCs of the K164 type and I don't know their R/T number. Apparently they're made by EPCOS / TDK and offered in a whole array of curve shapes / coefficients.

At first glance, 1014, 2903 and 2904 characteristics seem to match the quick&dirty calibration values:

Mouser only seems to stock B57164K0103K052 which is listed as having the 2904 characteristics (from EPCOS/TDK datasheet above), and the datasheet only states 2904 for the 10k type.

The Steinhart-Hart-coefficients can be fitted after some OCR gore as follows:

Final set of parameters            Asymptotic Standard Error
=======================            ==========================
a0              = 0.00130396       +/- 2.557e-006   (0.1961%)
a1              = 0.000214209      +/- 4.56e-007    (0.2129%)
a3              = 9.80175e-008     +/- 1.801e-009   (1.837%)

correlation matrix of the fit parameters:
                a0     a1     a3
a0              1.000
a1             -0.991  1.000
a3              0.935 -0.968  1.000

note that the S-H equation needs absolute resistance in Ohm.

There was also an error in prior graph formulas... but now the temperature calculation looks much better:

I could in principle take one of the NTCs to work and properly characterize it over its temperature range against a known PT100 element but for the sake of brevity I'm inclined to trust the datasheet values to within 2 Kelvin.