PT100 & PT1000 RTD Callendar-Van Dusen Calculator

Platinum RTD Physics & Callendar-Van Dusen Linearization

Resistance Temperature Detectors (RTDs) made from pure platinum ((\text{Pt})) provide the most accurate and stable temperature measurements between -200°C and +850°C. Their resistance-temperature relationship is internationally standardized by IEC 60751.

1. Callendar-Van Dusen Equations

For temperatures above 0°C ((T \ge 0^\circ\text{C})), the relationship is a second-order quadratic:

$$R(T) = R_0 \left(1 + A \cdot T + B \cdot T^2\right)$$

For sub-zero temperatures ((-200^\circ\text{C} \le T < 0^\circ\text{C})), a fourth-order term is introduced:

$$R(T) = R_0 \left[1 + A \cdot T + B \cdot T^2 + C \cdot (T - 100) \cdot T^3\right]$$

Standard DIN constants: (A = 3.9083 \times 10^{-3}), (B = -5.7750 \times 10^{-7}), (C = -4.1830 \times 10^{-12}).

2. The Lead Wire Resistance Trap (2-Wire vs 3-Wire vs 4-Wire)

In a standard PT100 sensor, sensitivity near room temperature is only +0.385 Ω per °C. A 15-meter run of standard 24 AWG copper wire adds 2.5 Ω of round-trip lead resistance, creating a catastrophic +6.5°C false error in a 2-wire setup:

• 2-Wire: Lead wire resistance adds directly to the RTD reading. Suitable only for short connections (<1 meter) or high-resistance PT1000 sensors.
• 3-Wire: Uses a third sense wire in a Wheatstone bridge or dual matched current sources to cancel out symmetrical lead resistance.
• 4-Wire (Kelvin): Forces excitation current through two outer leads while a high-impedance ADC measures voltage across two inner sense leads. Completely immune to lead wire length and contact resistance.

3. Preventing Self-Heating Error

Excitation current (I_{\text{ex}}) dissipates electrical power (P = I_{\text{ex}}^2 R(T)). For PT100, keep current below 1.0 mA; for PT1000, keep current below 100 μA to maintain self-heating below 0.05°C.