Thermocouples & Cold-Junction Compensation
Thermocouples — Seebeck Effect and Cold-Junction Compensation
A thermocouple is a junction of two dissimilar metals that generates a small voltage proportional to the temperature difference between the junction and a reference. Discovered by Seebeck in 1821, the effect is the basis for the most widely used industrial temperature sensor in the world — robust, passive, self-generating, and good for ranges no other sensor can touch, from cryogenic work to molten-steel furnaces.
In the Webster / Pallàs-Areny framework, a thermocouple is a self-generating transducer: it needs no excitation. The price paid is a low output level (microvolts per degree) and the mandatory task of cold-junction compensation (CJC) so that the voltage represents only the measuring-junction temperature.
This lesson derives the Seebeck relation, tabulates the common thermocouple types, and walks through a software CJC calculation — the industry-standard approach in modern data loggers.
$$V_{AB}(T, T_{\text{ref}}) = \int_{T_{\text{ref}}}^{T} [S_A(T') - S_B(T')]\,dT'$$
where $S_A, S_B$ are the absolute Seebeck coefficients of the two metals. For most practical work we use polynomial tables defined by NIST and ITS-90.
| Type | Metals | Range (°C) | Sensitivity (µV/°C) |
|---|---|---|---|
| K | Chromel / Alumel | -200 to 1350 | ~41 |
| J | Iron / Constantan | -40 to 750 | ~52 |
| T | Copper / Constantan | -250 to 350 | ~43 |
| E | Chromel / Constantan | -200 to 900 | ~68 |
| R/S | Pt-Rh / Pt | 0 to 1600 | ~10 |
A Type-K thermocouple measures a furnace at $T = 500\,^\circ\text{C}$ with a cold junction at $T_{\text{ref}} = 25\,^\circ\text{C}$. Using the approximate sensitivity $S_K = 41\,\mu\text{V}/^\circ\text{C}$, estimate the raw output.
$V \approx S_K\cdot(T - T_{\text{ref}}) = 41\times10^{-6}\cdot 475 = 19.5\,\text{mV}$.
(Tables give 20.644 mV for 500 °C vs 0 °C; subtracting the 25 °C value of about 1.00 mV yields 19.6 mV — consistent.)
We measure $V_{\text{TC}} = 12.0\,\text{mV}$ at the instrument where the reference block sits at $T_{\text{ref}} = 30\,^\circ\text{C}$. Find the hot-junction temperature.
Step 1: Convert $T_{\text{ref}}$ to an equivalent 0 °C-referenced voltage using the K table:
$V(30) \approx 1.203\,\text{mV}$.
Step 2: Corrected voltage: $V_{\text{corr}} = 12.0 + 1.203 = 13.20\,\text{mV}$.
Step 3: Look up $V_{\text{corr}}$ in the K table: $T \approx 324\,^\circ\text{C}$.
(Without CJC the naive $T \approx V/S_K + T_{\text{ref}} = 293 + 30 = 323\,^\circ\text{C}$ — close but not table-accurate at large spans.)
A 30-metre run of Type-K extension cable sees a loop resistance of 10 Ω. The voltmeter has 10 MΩ input impedance. How much voltage is dropped across the wire?
$I = V/(R_{\text{wire}} + R_{\text{in}}) \approx 20\,\text{mV}/10^7 = 2\,\text{nA}$.
Drop across wire $= 2\,\text{nA}\cdot 10\,\Omega = 2\times10^{-8}\,\text{V} = 0.02\,\mu\text{V}$ — utterly negligible. This is why thermocouples can be run over long cables without resistance-induced error (unlike RTDs).
Practice Problems
Show Answer Key
1. $V = 52\times10^{-6}\cdot 175 = 9.1\,\text{mV}$.
2. The measured voltage depends on the temperature difference between the hot and reference junctions; without knowing $T_{\text{ref}}$, you cannot extract the hot-junction temperature.
3. $V(22) \approx 0.88\,\text{mV}$. Corrected $V = 8.98\,\text{mV}$. $T \approx 8980/41 = 219\,^\circ\text{C}$.
4. Platinum alloys remain stable and reproducible to 1600 °C where base-metal wires have oxidized or melted.
5. Extra metals inserted in a circuit add no net EMF as long as both ends of each inserted segment are at the same temperature.
6. Type-E (~68 µV/°C) is more sensitive than Type-T (~43 µV/°C).