Work out how far lead resistance shifts a Pt100 or Pt1000 reading for 2-wire, 3-wire and 4-wire connections, from the cable or the measured lead resistance.
Reading error, high
8.982°C
Check the values to see a result.
Both leads add to the sensor resistance, so the reading is high.
2-wire ΔT = 2 × Rlead ÷ S3-wire ΔT = ΔRmismatch ÷ S4-wire ΔT ≈ 0
A 2-wire Pt100 with 3.448 Ω of lead loop reads 8.982 °C high.
Tip: On a 2-wire Pt100 every ohm of lead loop reads about 2.6 °C high. Three wires cancel most of it; four remove it.
An RTD measures temperature by its resistance, so the resistance of the wires to it adds to the reading. On a 2-wire Pt100, every ohm of lead resistance reads about 2.6 °C high. Twenty metres of 0.5 mm² copper, out and back, adds 1.379 Ω and a 3.55 °C error at room temperature.
ΔT = 2 × Rlead ÷ S
Both leads are in series with the sensor. S is the sensor’s sensitivity: about 0.385 Ω/°C for a Pt100 and 3.85 Ω/°C for a Pt1000 near room temperature, from the IEC 60751 curve. The error is always high.
ΔT = ΔRmismatch ÷ S
The third wire lets the instrument measure one lead and subtract it. Equal leads cancel; only the difference between them remains, from length, joints or terminal resistance.
ΔT ≈ 0
Two wires carry the current and two separate wires sense the voltage at the sensor, so lead resistance drops out of the measurement.
Lead resistance for copper is its resistivity, 0.01724 Ω·mm²/m at 20 °C, times the length, divided by the cross-section. It rises about 0.4% per degree with the cable’s own temperature, which is one reason a 2-wire error drifts with the weather.
Each 20 m lead of 0.5 mm² copper is 0.6896 Ω, so the loop is 1.379 Ω. At a sensitivity of 0.3885 Ω/°C that reads 3.55 °C high, more than ten times the Class A tolerance at 20 °C.
Reading error, high 3.55 °C Open in the calculator
A Pt1000 has ten times the sensitivity, so the same 1.379 Ω reads only 0.355 °C high. That is why 2-wire connections are usually made with Pt1000 sensors.
Reading error, high 0.355 °C Open in the calculator
On a 50 m run the leads are 1.724 Ω each, but only the 0.1 Ω difference between them affects a 3-wire reading: 0.1 ÷ 0.3839 = 0.2605 °C. A loose terminal can add more than that, so check connections at commissioning.
Reading error 0.2605 °C Open in the calculator
Reading error in °C at 20 °C for 2-wire connections on copper cable, leads out and back.
| Cable length (m) | Pt100, 0.5 mm² (°C) | Pt100, 1.5 mm² (°C) | Pt1000, 0.5 mm² (°C) |
|---|---|---|---|
| 1 | 0.1775 | 0.05917 | 0.01775 |
| 2 | 0.355 | 0.1183 | 0.0355 |
| 5 | 0.8875 | 0.2958 | 0.08875 |
| 10 | 1.775 | 0.5917 | 0.1775 |
| 20 | 3.55 | 1.183 | 0.355 |
| 50 | 8.875 | 2.958 | 0.8875 |
| 100 | 17.75 | 5.917 | 1.775 |
4-wire is the most accurate, 3-wire is the usual industrial compromise and 2-wire suits short runs or Pt1000 sensors. The instrument decides which it supports.
The same lead resistance is ten times smaller relative to the sensor, so lead and connection errors shrink by ten. The trade-off is slightly more susceptibility to leakage and noise at the higher resistance.
Only for the lead resistance at the temperature you measured it. The cable’s resistance changes with its own temperature, so a fixed offset is right on the day and drifts afterwards.
TES sensors use 10 kΩ NTC thermistor probes with the cable fitted at the factory. At 10 kΩ, the resistance of the probe cable is a negligible share of the reading.
