Sensor to Transmitter Matching (Calendar-van Dusen equation)

Rosemount offers improvement in accuracy of temperature measurement by RTD. It can be attained using a temperature sensor that is matched to a temperature transmitter.

This process involves identifying the relationship between resistance and temperature for a specific RTD sensor. This relationship, approximated by the Callendar-van Dusen equation, is described as:

Rt = Ro + Roα[t – δ(0.01t – 1)(0.01t) – β(0.01t – 1)(0.01t)³],

Where

Rt = Resistance (ohms) at Temperature t (°C)

Ro = Sensor-Specific Constant (Resistance at t = 0 °C)

α =Sensor-Specific Constant

δ =Sensor-Specific Constant

β =Sensor-Specific Constant (0 at t > 0 °C)

 

The exact values for the Callendar-van Dusen constants (Ro, α, δ, β) are specific to each RTD sensor and are established by testing each individual sensor at various temperatures.

Series 65 RTD sensors can be ordered with the Calibration Option codes V10 or V11, where the values of all four sensor-specific constants are supplied with each sensor. So the transmitter can be programmed with these constants to improve the accuracy.

 

Below the example of improvement by this approaching.

 

Standard 65 sensor

Rosemount 3144P    : + 0.1 ^oC

Standard Series 65    : + 1.05 ^oC

Total system        : 1.05 ^oC

 

65 sensor with V10 option

Rosemount 3144P    : + 0.1 ^oC

Standard Series 65    : + 0.18 ^oC

Total system        : 0.21 ^oC

 

IEC 751 Interpretation

There is similar approaching from IEC to describe the relation between resistance and temperature. The IEC 752 R vs T relationship standard uses the following equation:

R_t = Ro[1 + At + Bt² + C (t-100)t³]

 

Either methodology yields the same result in any sensor-to-transmitter matching scenario, since one equation is a simple mathematical interpretation of the other.

 

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Source : Rosemount