RTDs, Thermistors & Resistance Thermometry

An RTD or thermistor reports its own element temperature through resistance. The desired process temperature is inferred only if the element is thermally coupled to the process and electrical excitation does not heat it appreciably.

RTDs #

Near 0 °C a platinum RTD can be approximated by

$$R(T)\approx R_0(1+\alpha T).$$

For a Pt100 with $R_0=100\ \Omega$ and $\alpha\approx0.00385\ \mathrm{K^{-1}}$, sensitivity is about 0.385 Ω/K. At 1 mA, that becomes 0.385 mV/K and dissipates roughly 0.1 mW near 0 °C. Full-range precision requires the specified nonlinear conversion rather than indefinite use of the linear approximation.

Two-wire measurement includes both lead resistances. Three-wire compensation assumes matched leads and circuit symmetry. Four-wire Kelvin measurement separates excitation and sensing, so sense-lead current is negligible.

Thermistors #

NTC thermistors offer much larger resistance change over a narrower useful range. A common model is

$$R(T)=R(T_0)\exp\left[B\left(\frac{1}{T}-\frac{1}{T_0}\right)\right],$$

with absolute temperature in kelvin. Sensitivity and self-heating vary strongly with temperature, so a divider optimized at one point may use ADC range poorly elsewhere.

Thermal dynamics and self-heating #

Electrical power $P=I^2R$ raises element temperature approximately $\Delta T=P\theta$ in steady state, where $\theta$ is dissipation constant in K/W for the actual medium and mounting. Reducing current lowers self-heating quadratically but also lowers signal and worsens noise sensitivity.

The sensor time constant belongs to the probe, sheath, mounting, flow, and medium—not only the bead. A fast electronic filter cannot recover temperature information lost to slow thermal coupling.

Diagnostic checks #

• Substitute precision resistors at the connector to separate electronics from probe and wiring.
• Compare two excitation currents; a temperature shift suggests self-heating or leakage.
• Check 2/3/4-wire configuration and actual terminal mapping.
• Test response in the installed medium; air and stirred liquid give different time constants.
• Treat open/short detection as explicit fault states, never valid endpoint temperatures.