Error components in Temperature Measurement System

In principle, when calculating the overall measurement uncertainty of a temperature measurement system, all the individual components, from the evaluation electronics, indication, cable, sensor, must be included.
The sensor provides a temperature-dependent signal that is fed via the cable to the evaluation electronics, where it is ultimately converted to a temperature indication or to a current signal (for example, 0 - 20 mA). The error sources of all three components have to be included in the consideration of measurement uncertainty. This means that additional measurement uncertainty components are introduced once again, when transmitters are used during the conversion into a temperature indication. So, every component from the temperature measurement system generates error, and in order to provide precise formula for the measured temperature every single error component must be included in this formula. The precise formula for the output signal of the temperature measurement system will look like this:

Ix = Tm + σMF** + σMD + σMA + σME** + σMTh** + σMRI** - CS x σt0S* + σVLX* + σRAL** + σV + σtM + σtW + σB + σLZ

Here, the Ix is the output signal from the measurement system, actually this is the indicated temperature or the temperature equivalent (for example, the current signal). The Tm is temperature at the measurement point. The rest of the components included in the formula depends on the system used for measurement. The components that are marked with * are included only when thermocouples are used, and the components marked with ** are included only when resistance thermometers are used.


Measurement uncertainties at the sensor and in the cables:

>> σMF - measurement signal deviation caused by the heat conduction error of the thermometer;
>> σMD - measurement signal deviation caused by the deviation of the sensor as per EN 60 751 (resistance thermometer) or as per EN 60 584 (thermocouple);
>> σMA - measurement signal deviation caused by insufficient stabilization;
>> σME - measurement signal deviation caused by the self-heating of the sensor (only with resistance thermometer);
>> σMTh - measurement signal deviation caused by thermoelectric emfs (resistance thermometer);
>> σMRI - measurement signal deviation caused by inadequate insulation resistance (resistance thermometer);
>> CS - sensitivity of the sensor, e.g. in °C/µV (thermocouple);
>> σt0S - temperature deviation caused by the reference temperature deviating from the assumed value;
>> σVLX - voltage deviation caused by the compensating cables (thermocouples);
>> σRAL - variation in the lead resistance (resistance thermometer);

Measurement uncertainties at the transmitter and indication:

>> σV - deviation of the evaluation electronics caused by supply variations (effect of voltage);
>> σtM - deviation caused by fluctuating ambient temperature (effect of temperature);
>> σtW - processing and linearization errors in the evaluation electronics;
>> σB - indication deviation caused by the influence of the input resistance (effect of burden);
>> σLZ - long-term stability of the evaluation electronics (deviation caused by component ageing);