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Standard Callendar - Van Dusen

The relationship between resistance (R) and temperature (t) is generated from the Callendar-van Dusen equations.

For the temperature range -200° to 0°C;

  •      W(t90) = R(t90)/R(0) = { 1 + At90 + Bt290 + Ct390(t90 - 100)} ...(1)

For the temperature range 0° to 661°C:

  •      W(t90) = R(t90)/R(0) = { 1 + At90 + Bt290} ...(2)

The constants A, B, and C are determined by the properties of the platinum wire used in the construction of the detector types Pt100, F100, and D100. The wire is specially selected to give nominal values of the constants as in the table below. The listed values for Alpha, Delta, and Beta are also listed.

TYPICAL CALIBRATION COEFFICIENTS – International Temperature Scale 1990 (ITS-90)

Pt100 F100 D100
A (°C-1)3.90830 x 10-33.95834 x 10-33.97869 x 10-3
B (°C-2)-5.77500 x 10-7-5.83397 x 10-7-5.86863 x 10-7
C (°C-4)-4.18301 x 10-12-4.29000 x 10-12-4.16696 x 10-12
Alpha (°C-1)3.850 x 10-33.900 x 10-33.920 x 10-3
Delta (°C)1.499901.495891.4971
Beta (°C)0.108630.110000.10630

(NOTE: "Pt" Alpha value is 3.85055 x 10⁻-3 for calculation purposes)

The constants A, B, and C can be written:

  • A = Alpha x { 1+ (Delta/100)} °C-1
  • B = -Alpha x Delta x 10-4 °C-2
  • C = -Alpha X Beta x 10-8 °C-4

Alpha (α) is the temperature coefficient of resistance obtained by measuring the detector resistance at both 0° & 100°C and is defined as:

  • Alpha = (R100 - R0)/(100 x R0)

Delta(δ) is obtained by calibration at a high temperature, for example, the Freezing Point of Indium, Tin, Zinc, or Aluminum (156.5985°, 231.928°, 419.527°, and 660.323°C respectively).

Beta (β) is obtained by calibration at a negative temperature, for example, Triple Point of Mercury and Argon (-38.8344° and -189.3442°C respectively) or Liquid Nitrogen (approximately -196°C).

Choosing the high and low temperature point which best suites your application range improves the R vs. T correlation when applying the formulas.

Using Alpha, Delta, and Beta, the Callendar-van Dusen equation can alternately be written:

W(t90) = R(t90)/R(0) = { 1 + α{t90 - δ(t90/100)(t90/100 – 1) – β(t90/100)3(t90/100 – 1)]}
(β is equal to 0 when t90 is greater than zero)