Notices and measurement accuracy

FM33xx operating principle

The picture below shows the thermocouple circuit starting from inside the FM33xx electronic board out to the point of temperature measurement T4:

On the left side there is the A/D converter board inside the plug, then we have two thermo element wires going to the male connector (the connector consisting of male and female part is assumed as yellow/golden rectangular block in the drawing), then the two wires exit the female connector part of the mating TC plug and join at the measurement point. The indexes “l” and “k” are used to mark the different materials of the thermolement wires.

The temperatures

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T1 is the temperature at the A/D-converter board in the TC plug,

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T2 is the temperature at the point where the thermo element wires enter the male part of the gold plated connector,

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T3 is the temperature at the point where the thermo element wire exits the female gold plated connector

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T4 is the target point where the actual temperature is measured

The thermocouple principle is based on the Seebeck-effect: if one heats one end of a conductor and cools the other end then one can observe a small voltage difference between the two ends. The voltage is assumed proportional to the temperature difference with the Seebeck-coefficient in-between:

U = α. ΔT

Taking this simple equation, and assuming two different materials (Index “k” and index “l”) and the goldplated mating connector (male+female, Index “G”) in-between and put the voltage arrows across the circuit, the Kirchhoff voltage law across a closed loop results in:

Each individual voltage is a function of its individual temperature difference at the end-points of the respective conductor following the Seebeck equation.

U_M is ultimately the voltage measured by the AD-converter in the TC plug. This voltage is translated to a corresponding temperature T4 by using internal conversion tables specific to the thermocouple material (e.g. type J is FE / CU-NI ).

TC plug measurement accuracy

In the factory, the FM33xx-B110 modules are calibrated to an accuracy of

±0.5 °C at 546.19 °C with a max. temperature difference ΔT ≤ 0.5 °C across all thermocouple channels

However, when measuring target temperature in real circumstances, there are several factors which will introduce an error. Here is a short explanation of the most important ones, together with their corresponding error range.

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a.) Translation table inaccuracy at different temperatures ±0.1 °C (internal software algorithm based on segmented temp/voltage table)

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b.) Self-heating or external heat to plug: ±0.4 °C (for ambient temperature +10°C to +55°C)

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c.) Electronic ageing / burn-in ±0.5 °C (based on statistic experience)

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d.) Temperature drop in plug mating section ±0.5 °C (typical, but depends on mounting direction, external heat/cooling in vicinity, …)

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e.) Quality of thermocouple wires ±2.5 °C ( or ±1.5 °C, if higher quality tc material is used )

As shown, a large error budget is introduced by the quality of thermocouple wire material.

Here is a deeper explanation for d):

An installation of TC plug at the machine consists of the plug himself and a receptacle part, typically fastened to the body of the machine. The cold junction compensation for the thermo-measurement is implemented on the controller board in the vicinity of the where the internal tc wiring is soldered to the analog printed circuit board. In theory we would need to measure the cold junction temperature at point T3, but this is not possible because this is across the mating section of the installation.

In the above equation (fig. 1), the voltage U_G disappears, no matter of its magnitude and this is one potential source for inaccurate measurement. If we would assume T3 = T2, then we have no issue, measurement is correct. If T3 is different of T2, the associated Seebeck-voltage UG will still disappear in the closed loop voltage equation and the delta temperature T3-T2 will be a direct constant fault value in the measurement of T4.

As a consequence, U_M is a function of ΔT₂₁ and ΔT₄₃, but is not a function of ΔT₃₂. The temperature difference between T3 and T2 influences the measurement: it simply needs to be added to what the plug thinks it measures as a final temperature. The assumption is, that the temperature difference between T2 and T3 is not very high, because the metal parts of male and female connector will go into a steady and balanced thermal state with minimum temperature difference. This should be taken into account when choosing where to install the plug and it´s receptacle.