Modern thermocouples and a high-resolution delta-sigma ADC enable high-precision temperature measurement: A reference design for a precision DAS

Joseph Shtargot, Strategic Applications Engineer, Mohammad Qazi, Applications Engineer, Maxim Integrated -October 18, 2013


This article presents the design of a cost-effective, portable, high-resolution data acquisition system (DAS) based on a precision delta-sigma ADC. This presentation is based on a prior article that reviewed the history of thermocouple technology and the principal of the operation. It described a thermocouple interface with the MAX11200 ADC evaluation (EV) kit.1              


Here we present a dedicated reference design (RD) in which the MAX11200 ADC interfaces with a thermocouple and platinum resistance temperature detector (PRTD) using a simple multiplexor. No additional instrumentation amplifiers, low-noise references, and optical isolation are needed for precise temperature measurement. The new RD is cost effective, compact, and low power. We will also describe the high-resolution thermocouple’s DAS and the software required to achieve accuracies of ±1°C, or better, using standardized linearization calculation algorithms.


Thermocouple Calculation Overview      

In our earlier article2 we explained that thermocouples generate a voltage/charge (VOUT) and do not require any voltage or current excitation. Readers familiar with the technology can jump to the next section below.


VOUT is the function of the temperature differential, – (TJUNC – TCOLD), produced by two dissimilar metals. The differential is due to the different electric potentials for the Metal 1 and Metal 2 and the temperature gradient applied to them.3 The NIST ITS-90 Thermocouple Database4 defines this VOUT function for most practical Metal 1 and Metal 2 combinations and enables the calculation of relative temperature TJUNC based on the VOUT measurements. It is important to emphasize that TJUNC is only a relative temperature in relation to the cold junction (TCOLD). To find the absolute temperature (in °C, °F, or K), TCOLD temperature must be independently measured:


    Tabs = TJUNC + TCOLD                                                                      (Eq. 1)



Tabs is the absolute temperature of the hot junction;

TJUNC is the relative temperature of the hot junction versus the cold reference junction;

TCOLD is the absolute temperature of the reference cold junction.


Note that the TJUNC and TCOLD temperature measurements must be produced in the same units (i.e., in °C, °F, or K).


Equation 1 dictates that the thermocouple measurement requires VOUT precision measurements for the hot junction, as well as an accurate complimentary sensor5 for the cold-junction temperature measurements.


Accuracy and Resolution

Thermocouple temperature calculation can be done using simplified linearization algorithms. The approximate absolute temperature is calculated as:



E is the measured thermocouple output in mV;

Tabs are the absolute temperature of the thermocouples in °C;

Ecj is the cold-junction thermocouple equivalent output in mV, calculated by using the cold junction temperature, measured independently, and the ITS-90 Thermocouple Database tables;

k is the thermocouple average sensitivity.


While a linearization approach could substantially reduce the calculation volume and complexity, it can also produce large temperature-measurement errors. For example, in a K-type thermocouple linear approximation by Equation 2 allows only a 1°C to 4°C degree of precision in the narrower -50°C to +350°C temperature range. At +1000°C the calculation errors could reach around 7°C, while at -100°C the error would be around 13°C. (See Table 2.) The root cause of the large errors can be traced to nonlinearity, as shown in Figure 1.

Figure 1. K-type thermocouple nonlinearity. The data show the output voltage vs. temperature for a K-type thermocouple. The curve is reasonably linear in the range of -50°C to +350°C, and it clearly has significant deviations from absolute linearity at the “ends,” below -50°C and above +350°C.6


Output voltages from the most common thermocouples,7, 8  as a function of temperature, are highly nonlinear. This nonlinearity can produce large errors in the extended temperature ranges as shown in the K-type thermocouple example in Figure 1.


Errors in the extended temperature ranges are also common for application-specific ICs (ASICs) like the MAX31855 thermocouple-to-digital converter. For example, if an extended temperature range of -270°C to +1372°C is needed for K-type thermocouples, then the MAX31855 thermocouple’s overall accuracy will be ±6°C. A similar situation exists for the other popular thermocouples.


Consequently, Figure 1 and Equation 2 demonstrate that rather complex nonlinear compensation is needed to further improve the accuracy of a popular industrial thermocouple.


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