= Thermocouple reference function
{title2=$F(T)=E(T,0)$}
A <thermocouple reference function> gives the nominal thermoelectric <electromotive force> versus <temperature> for a specified material pair and reference <temperature>, conventionally $0\,{}^\circ\mathrm C$. Real <Seebeck coefficients> vary with <temperature>, so
$$
F'(T)=S_A(T)-S_B(T)
$$
is generally nonconstant. A lookup calibration can use <interpolation> between tabulated values; a fitted calibration can use <polynomials> over stated intervals. Use the correct material type, units, reference and validity interval in both the forward and inverse conversions. The FP-TC-120 manual specifically requires the channel's <thermocouple> type to be configured and describes its use of NIST-175 reference characteristics.<FP-TC-120 and cFP-TC-120 Operating Instructions by National Instruments>[p. 6, Connecting Thermocouple Input Signals: channel type and NIST-175 linearization]{ref} A nominal reference curve is not evidence that an aged or inhomogeneous wire still follows it.
A local error estimate explains why the reference <thermometer> matters. If $\delta V$ is an additive voltage error and $\delta T_c$ is the error in the supplied reference <temperature>, <differentiation> of the compensation equation gives, for $F'(T_h)\ne0$,
$$
\delta T_h\approx\frac{\delta V+F'(T_c)\,\delta T_c}{F'(T_h)}.
$$
A small <slope> $F'(T_h)$ magnifies voltage errors. In the stipulated $40\,\mu\mathrm{V/K}$ model, a $40\,\mu\mathrm V$ offset gives a $1\,\mathrm K$ inferred-<temperature> error, and a $1\,\mathrm K$ reference error gives a $1\,\mathrm K$ inferred-<temperature> error. These are sensitivities of the chosen model, not universal performance figures for real sensors.
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