Error Contributors in Temperature Calibration

From the moment a sensor is calibrated, any future measurements it makes are limited by the accuracy of that calibration – so it’s important that this calibration must be performed as accurately as possible. When calibrating a temperature sensor using a dry-block or heat bath; errors can be caused by temperature homogeneity, sensor geometry, age of the inserts used, and several other things. In this article, we take a look at the most common error contributors in temperature calibration and outline how to avoid the worst of them to minimize calibration uncertainty.

Temperature sensor calibrations often require the creation of an “uncertainty budget” (see example at the end of this article). This uncertainty budget represents the maximum possible calibration error of a sensor for a given application. The list of contributors to the total calibration uncertainty in temperature sensing is long, and includes the following:

• Spatial variation in temperature (axial and radial gradients)
• Thermal load in the calibration unit
• Resolution
• Thermal stability
• Hysteresis
• Type and age of the insert used
• Curve fit error

Let’s take a closer look at the biggest contributors to error.

Reducing Error Due to Thermal Load
Normally, the specifications of a given temperature calibrator are based on its performance when using only a low thermal load reference sensor. This means that the performance of the calibrator starts to vary from its specifications as soon as anything other than a reference sensor is used in the insert. This can lead to inaccuracies when calibrating large-diameter sensors or multiple sensors at the same time. For example, the thermal load of a 10 mm sensor in a typical dry-block calibrator can easily lead to errors over 0.15°C.

Fortunately, this source of error can be easily reduced by an order of magnitude or more by employing an external reference. By placing an additional reference sensor into the insert together with the unit under test, it can be used as a reference to indicate the accuracy and additionally be used as the controlling sensor. The external sensor can be an independent sensor connected to an external handheld thermometer, or preferably it can be connected directly to the calibrator.

Reducing Error Due to Axial Gradient
The laws of thermodynamics mean that even in a carefully controlled environment, the space around any heat source will contain a temperature gradient. Temperature calibration devices aim to minimize this spatial variation in temperature by any means possible, however, it is impossible to eliminate this. The best that can be achieved is to maximize the temperature homogeneity in the volume of space around the sensor being calibrated.

In an ideal world, heat sensors would be calibrated in heat baths containing rapidly stirred low-viscosity fluid to achieve a very high-temperature homogeneity around the sensor. However, the size of heat baths, the safety issues associated with hot oil, and the potential to pollute sensors with silicone oil mean that heat baths are often not a practical solution for many applications. For these reasons, a dry-block calibrator is often the chosen solution when performing on-site calibration.

Typically, temperature sensors have a relatively small radius compared to their length. For this reason, the error due to radial temperature gradient is normally very small, typically 0.01°C. The error due to axial gradient (i.e. the temperature gradient down the length of the sensor) is generally much higher and is additionally influenced by the effects of different loads and different temperatures.

Minimizing Axial Gradient Errors with Dynamic Load Compensation
The most effective way of minimizing errors due to axial gradient is to choose a calibrator with a dual-zone design with dynamic load compensation (DLC). Whereas many dry-block calibrators have only a single heating zone, dual-zone dry-block calibrators use two heating zones to compensate for heat loss. By embedding additional sensors within the insert along with the unit under test, the temperature difference between the two zones can be constantly measured, allow dynamic control over the thermal output of each heater, thus compensating for heat losses and minimizing the temperature gradient. 

The result is a dry-block system that can inform the user of the internal temperature distribution, and which behaves like a heat bath with regards to thermal homogeneity. The superior heat-distribution within DLC systems makes them perfectly suited to testing large-diameter sensors, and they can save time by enabling the calibration of multiple sensors simultaneously. Our tests show that the total uncertainty in sensor calibration (at a 95% confidence interval) can be reduced from 0.185°C to 0.034°C (see below uncertainty budget).

Uncertainty budget with and without gradient control: