# Calculating Thermocouple Measurement Error in DMM/Switch Temperature Measurement Systems

Updated Sep 9, 2020

## Environment

### Hardware

• DMM Probe
• PXI-407X
• PXI-2527
• TB-2627
One of the best ways to take high-accuracy thermocouple measurements is with a digital multimeter (DMM) and a switch. You can use the NI 407x series of DMMs along with the NI PXI-2527 32-channel multiplexer and the NI TB-2627 terminal block to measure thermocouples and maximize the total accuracy of the system. With this basic set of equipment, it’s possible to easily create a high-accuracy thermocouple system with hundreds or even thousands of measurement channels.

To assist in programming such a system, software from NI (such as NI LabVIEW or NI LabWindows/CVI) can convert a thermocouple voltage to the actual thermocouple temperature. For example, code demonstrating DMM/switch programming and thermocouple temperature conversion, visit the Developer Zone.

When measuring thermocouples, be sure to account for error in your measurements. For the case of the NI 4070 DMM and the NI PXI-2527 multiplexer, the total error is the sum of the system error (determined by the thermal EMF of the NI PXI-2527 and the cold-junction compensation (CJC) sensor temperature of the NI TB-2627) and the thermocouple error itself (determined by the type of thermocouple used). For a closer look at these numbers, the following document provides step-by-step instructions for calculating the error when using the NI PXI-2527 and TB-2627.

For product information on NI digital multimeters and switches please see:
NI Digital Multimeter (DMM) and LCR Meter
NI Switches

### Determining the System Error of the Switch System

To determine the system error for the NI PXI-2527/TB-2627 (or any other switch), first, calculate the error due to thermal EMF of the NI PXI-2527 using the following equation. • EEMF = error due to thermal EMF of the NI PXI-2527
• T = temperature being measured, in degrees Celsius
• T+1 = T + 1 °C
• V= voltage that corresponds to T
• V+1 = voltage that corresponds to T+1
• VEMF = thermal EMF of the NI PXI-2527

* In thermocouple reference tables, T and T+1 are known values used to calculate the slope of the thermocouple Temperature vs. Voltage graph. Refer to a thermocouple reference table to determine the values of V and V+1 that correspond to T and T+1,, respectively.

The thermal EMF of the NI PXI-2527 is specified in two different ways: a typical value and a maximum value. The typical value for the PXI-2527 is 2.5 µV, and the maximum value is < 12 µV. For optimal thermocouple performance (VEMF = 2.5 µV), it is necessary to power down the latching relays of the NI PXI-2527. For more information on powering down latching relays, refer to the “Power Down Latching Relays After Debounce” property in the NI-SWITCH driver documentation or the “Power Down Latching Relays After Settling” property in the NI-DAQmx driver documentation. The maximum thermal EMF property is reflective of power active to the latching relays over the full temperature range of the switch module (0-55 °C).

After you have determined the error due to thermal EMF, calculate the system error using the following equation. • ES = system error of the NI PXI-2527/TB-2627
• EEMF = error due to thermal EMF of the NI PXI-2527
• ECJC = error due to CJC temperature sensor of the NI TB-2627**

** From 15 °C to 35 °C, the NI TB-2627 CJC has an accuracy of ±0.5 °C. From 0 °C to 15 °C and 35 °C to 55 °C, the NI TB-2627 has an accuracy of ±1.0 °C. For more information about temperature sensor accuracy, refer to the NI TB-2627 Installation Instructions.

Note: For extremely high accuracy requirements, it is possible to use an external CJC sensor with even higher-accuracy capability (often as low as 0.1 °C). The manufacturers listed below provide external references that could be used with the PXI-2527 to lower the CJC component of the total system error.

### Example - Error Contributed by the PXI-2527/TB-2627

Measuring a K-type thermocouple at 200 °C with a CJC temperature of 25 °C, the system error of the NI PXI-2527/TB-2627 is calculated below.†

Assuming typical thermal EMF (2.5 µV), first calculate the error due to thermal EMF using Equation 1. To determine the system error, add the error due to thermal EMF to the error due to the CJC temperature sensor using Equation 2. † In this example, the values of V and V+1 are found in the thermocouple reference tables of Omega Engineering’s The Temperature Handbook. Vol. 29. Stamford, CT: Omega Engineering Inc, 1995.

This answer provides the key value for the error introduced by the switching system. In a thermocouple measurement system, though, this error is only a portion of the total error. We must also take into account the error introduced by the thermocouple itself - a value that is usually much larger than the switch error.

### Example - Error Contributed by the Thermocouple

Independent of the NI PXI-2527/TB-2627 system, thermocouple error is the greater of the following values: ± a temperature range or ± a percentage of the measurement.

In this example, a standard grade K-type thermocouple is used to measure 200 °C. The error for a standard grade K-type thermocouple is ±2.2 °C or ±0.75% of the measurement temperature.‡ Because ±0.75% of 200 °C (±1.5 °C) is less than ±2.2 °C, the error of a standard grade K-type thermocouple is ±2.2 °C. ‡ Omega Engineering. The Temperature Handbook. Vol. 29. Stamford, CT: Omega Engineering Inc, 1995.

### Determining the Total Error

The total error in thermocouple measurement is the sum of the system error and the thermocouple error. Use the following equation to determine the total error in thermocouple measurement. • ET = total error in thermocouple measurement
• ES = system error
• ETh = thermocouple error

To determine the total error for the thermocouple measurement in this example, add the thermocouple error to the system error using Equation 3, as illustrated below. Assuming typical thermal EMF, the total error in thermocouple measurement at 200 °C for the NI PXI-2527/TB-2627 with a K-type thermocouple is ±2.76 °C. It is important to note how large a role the thermocouple error plays in the total error. While it is possible to buy a highly-optimized switching system with ultra-low EMF and a highly-accurate CJC, the error associated with the thermocouple will often negate the additional resources spent on those components.

he combination of a DMM and a multiplexer can create a high-accuracy temperature measurement system with the potential to handle very high channel counts. When developing such a system, though, it is important to understand the accuracy implications of using not only the switch but also the particular type of thermocouple chosen. The system error for a DMM/switch system is dependent on the accuracy of the CJC sensor, the thermal offset of the switch itself, and the accuracy of the thermocouple being used.