# Type B Thermocouple Calibration

Convert type B thermocouple voltages to temperatures efficiently using rational polynomial function calibration equations.

If you use Mosaic's Thermocouple Wildcard, thermocouple voltage measurements are automatically converted to temperatures for you by the included software drivers, and with high accuracy.

But for those of you not using the Mosaic Thermocouple Wildcard, and looking for accurate equations for thermocouple measurement, we hope the thermocouple calibration coefficients on this page are helpful.

Equations for voltage to temperature conversion usually are based on high-order polynomials. In fact, the National Institute of Standards and Technology (NIST database of thermocouple values) provides a high order polynomial formula along with coefficients curve fitted to thermocouple data they also provide.

However, even very high order polynomials are often not very accurate – they produce systematic errors as the polynomial functions oscillate around the desired data, as shown in curve fits to Type K thermocouple data.

But there is a better way – you can use rational polynomial functions. This page shows you how to convert thermocouple voltage to temperature with rational polynomial functions more accurately and more efficiently than you can with the more commonly used higher order polynomials.

The rational polynomial coefficients provided here produce an order of magnitude lower errors than the NIST ITS-90 thermocouple coefficients for direct and inverse polynomials.

## Properties type B thermocouple wire

Type B thermocouple wire has the following properties:

Type B Thermocouple Wire Characteristics
Composition Sensitivity Temperature range
(+) Platinum - 30% Rhodium
(–) Platinum - 6% Rhodium
5 to 10 µV/°C +250 to +1820 °C

The noble metal alloys of B type thermocouple wire are not very sensitive to temperature – they are only 1/4 as sensitive as Type K wire – but they do allow it to be used for measuring high temperatures in hostile environments.

The voltage of Type B thermocouples increases monotonically with temperature, but not very linearly – there is a significant curvature to the increase. Unfortunately, the degree of curvature varies over the temperature range, making fitting the data with simple functions difficult.

The following graph shows the variation of thermocouple voltage with temperature – the data is taken from the NIST database.

## Type B calibration equation

A rational polynomial function approximation for Type B thermocouples is used for computing temperature from measured thermocouple potential. The calibration equation uses a ratio of two smaller order polynomials rather than one large order polynomial. Using a least squares curve fitting procedure we fit the National Institute of Standards and Technology (NIST) type B thermocouple data with a rational function of the following form,

` `

where T is the thermocouple temperature (in °C), V is the thermocouple voltage (in millivolts), and To, Vo, and the pi and qi are coefficients. The function uses a ratio of two polynomials, P/Q, in this case a fourth order to a third order polynomial. The second form of the equation emphasizes the most efficient order of operations.

The coefficients, To, Vo, pi and qi were found by performing a least squares curve fit to the NIST data for type B thermocouples. The full temperature range is broken into several sub-ranges, and a different set of coefficients used for each. The coefficients, fitted data and charts of residual errors may be found in this Excel spreadsheet of Type B thermocouple data.

The following table contains calibration coefficients for Type B thermocouple wire.

 Range Voltage: 0.291 to 2.431 mV 2.431 to 13.820 mV 250 to 700 °C 700 to 1820 °C `5.0000000E+02` `1.2461474E+03` `1.2417900E+00` `7.2701221E+00` `1.9858097E+02` `9.4321033E+01` `2.4284248E+01` `7.3899296E+00` `-9.7271640E+01` `-1.5880987E-01` `-1.5701178E+01` `1.2681877E-02` `3.1009445E-01` `1.0113834E-01` `-5.0880251E-01` `-1.6145962E-03` `-1.6163342E-01` `-4.1086314E-06`

## Type B thermocouple accuracy and calibration error

The following graph shows the calibration error:

The graph shows residual errors after calibrating the thermocouple with a rational function of polynomials. Most of the residual error results from rounding of the NIST provided voltage values to the nearest microvolt. You can see the rounding errors as aliasing or Moiré patterns in the data.

The rational function approximation interpolates the data well so that computed values of temperature are more accurate than the residuals plots would indicate.

## Computing type B cold junction voltages

Your type B thermocouple may be terminated at a cold junction temperature other than 0°C. If so, you must measure the temperature of the cold junction using another sensor, perhaps a thermistor. You can then compute a cold junction voltage from that measured temperature, and use it to compensate the type B thermocouple voltage before converting the thermocouple voltage to a temperature.

In that case you need the inverse transform, that is, an equation for converting temperature into voltage. You don't need a valid equation for a wide temperature range as the cold junction is likely to be placed at ambient temperature. Usually a range of -20 to +70°C is sufficient.

To convert temperature to voltage, you can again use a rational function approximation of the form,

` `

where TCJ is the cold junction temperature, VCJ is the computed cold junction voltage, and the T0, V0, pi and qi are coefficients.

You can find the coefficients here:

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