
Keywords: data acquisition system, DAS, thermocouple, platinum resistance temperature detector, delta sigma ADCs, delta sigma, National Institute of Standards and Technology, NIST ITS90, sigma delta, temp measurement
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Modern Thermocouples and a HighResolution DeltaSigma ADC Enable HighPrecision Temperature Measurement
By: 
Joseph Shtargot, Strategic Applications Engineer 

Sohail Mirza, Applications Engineer Manager 

Abstract: Many industrial and medical applications require temperature measurements with accuracies of ±1°C or better, performed with reasonable cost over a wide range of temperatures (270°C to +1750°C), and often with low power consumption. Properly selected, standardized, modern thermocouples paired with highresolution ADC data acquisition systems (DASs) can cover this wide temperature range and ensure reproducible measurements, even in the harshest industrial environments.
A similar version of this article appeared in the June 22, 2011 issue of
EE Times magazine.
Introduction
Thermocouples are used in a wide range of temperaturesensing applications. Recent developments in thermocouple designs, as well new standards and algorisms, have greatly extended their temperature ranges and precision. Accuracies up to ±0.1°C are now possible over a very wide 270°C to +1750°C range. To utilize all the new thermocouple capabilities, highresolution thermocouple temperaturemeasurement systems are required. A lownoise, 24bit, deltasigma analogtodigital converter (ADC) with the ability to resolve very small voltages perfectly fits this task. When a data acquisition system (DAS) uses the evaluation (EV) kit for a 24bit ADC, thermocouple temperature measurements can be made across that wide temperature range. When the thermocouple, platinum resistance temperature detector (PRTD), and ADC are integrated in a circuit, they enable a highperformance temperaturemeasurement system. The ADCbased DAS can also be designed to operate at very reasonable cost and with low power consumption, making it ideal for portable sensing applications.
A Primer on Thermocouples
Thomas Seebeck discovered the principle of a thermocouple in 1822. A thermocouple is a simple temperaturemeasurement device consisting of a junction of two dissimilar metals, Metal 1 and Metal 2 (
Figure 1). Seebeck discovered that different metals will produce different electric potentials based on the temperature gradient applied to them. If these metals are welded together on the temperaturesensing junction (T
_{JUNC}, also known as the hot junction), the other differential unconnected junction (T
_{COLD}, which is kept at a constant reference temperature) will show a voltage, V
_{OUT}, that is directly proportional to the applied temperature at the welded junction. This makes thermocouples a voltage/charge generating device that does not require any voltage or current excitation.
Figure 1. Simplified thermocouple circuit.
V
_{OUT} is the function of the temperature differential (T
_{JUNC}  T
_{COLD}) and the types of metal in Metal 1 and Metal 2. This function is precisely defined in the National Institute of Standards and Technology (NIST) ITS90 Thermocouple Database [
1] for most practical Metal 1 and Metal 2 combinations. The database allows calculation of relative temperature, T
_{JUNC}, based on the V
_{OUT} measurements values. However, since the thermocouple measures T
_{JUNC} differentially, the absolute coldjunction temperature (in °C, °F, or K) must be known to determine the actual temperature measured at the hot junction. All modern thermocouplebased systems use additional absolute temperature sensors (PRTD, silicon sensors, and so forth) to accurately measure the temperature of cold junction end and mathematically compensate for the difference.
Temperature equation for the simplified thermocouple circuits shown at Figure 1 is:
Tabs = T_{JUNC} + T_{COLD} 
(Eq. 1) 
Where:
Tabs is the absolute temperature of the hot junction;
T
_{JUNC} is the relative temperature of the hot junction versus cold reference junction;
T
_{COLD} is the absolute temperature of the reference cold junction.
There are a dozen varieties of thermocouples, but some specific material pairs of dissimilar metals work better in certain industrial or medical conditions. These combinations of the metals and/or alloys were standardized by the NIST and the International Electrotechnical Commission (IEC), and are abbreviated with E, J, T, K, N, B, S, R, etc. The NIST and IEC provide thermocouple reference tables for the each of the popular thermocouple types. [
1]
The NIST and IEC also developed standard mathematical models for each type of thermocouple. These power series models use unique sets of coefficients which differ for different temperature segments within a given thermocouple type. [
1]
Examples of some common popular thermocouple types (J, K, E, and S) are shown in
Table 1.
Table 1. Typical Examples of Selected Popular Thermocouples
Thermocouple Type 
Positive Conductor 
Negative Conductor 
Temperature Range (°C) 
Seebeck Coefficient at +20°C 
J 
Chromel 
Constantan 
0 to 760 
51µV/°C 
K 
Chromel 
Alumel 
200 to +1370 
41µV/°C 
E 
Chromel 
Constantan 
100 to +1000 
62µV/°C 
S 
Platinum (10% Rhodium) 
Rhodium 
0 to 1750 
7µV/°C 
TypeJ thermocouples are widely used because of their relatively high Seebeck coefficient, high precision, and low cost. These thermocouples allow measurements with precision up to ±0.1°C, using a relatively simple linearization calculation algorithm.
TypeK thermocouples are very popular for industrial measurements covering a wide temperature range. These thermocouples offer a modestly high Seebeck coefficient, low cost, and good resistance to oxidation. Type K allows measurements with precision up to ±0.1°C.
TypeE thermocouples are less widespread than other thermocouples. However, the Seebeck coefficient is highest in this group. Measurements made by a TypeE thermocouple require less measurement resolution than other types. Type E allows measurements with precision up to ±0.5°C and requires a relatively complex linearization calculation algorithm.
TypeS thermocouples are comprised of platinum and rhodium, a combination that allows more stable and reproducible measurements at very high temperatures in oxidizing atmospheres. TypeS thermocouples have a low Seebeck coefficient and are relatively high cost. Type S allows measurements with precision up to ±1°C and requires a relatively complex linearization calculation algorithm.
Application Examples
The electronics interface to a thermocouple consists of a highresolution ADC with differential inputs and the ability to resolve small voltages; a stable and lowdrift reference; and some method of measuring the cold junction temperature accurately.
Figure 2 details a simplified schematic example. The
MX7705, a 16bit deltasigma ADC integrates an internal programmablegain amplifier (PGA), eliminates the need for an external precision amplifier, and resolves microvoltlevel voltages from thermocouples. Coldjunction temperature is measured using a
MAX6627 remote diode sensor and an external diodeconnected transistor located at the thermocouple connector. A limited range of the negative temperatures can be accommodated by the MX7705, whose input commonmode range extends 30mV below ground. [
2]
Figure 2. Thermocouple measurement circuit. The MX7705 measures the thermocouple output; the MAX6627 and external transistor measure the coldjunction temperature. The MAX6002 provides a 2.5V precision voltage reference to the MX7705.
Applicationspecific ICs are also available for thermocouple signal conditioning. These ICs integrate a local temperature sensor, precision amplifier, ADC, and voltage reference. For example, the
MAX31855 is coldjunctioncompensated thermocoupletodigital converter that digitizes the signal from a K, J, N, T, or E Type thermocouple. The MAX31855 measures thermocouple temperatures with 14bit (0.25°C) resolution (
Figure 3).
Figure 3. An ADC with integrated coldjunction compensation converts the thermocouple voltage without the need for external compensation.
Error Analysis
ColdJunction Compensation
Thermocouples are differential sensors in which the output voltage is generated by a temperature difference between hot and cold junctions. According to Equation 1 above, the absolute temperature of the hot junction (Tabs) can be found only if the absolute temperature of the reference cold junction (T
_{REF}) can be precisely measured.
A modern platinum RTD (PRTD) can be used for absolute temperature measurement of the reference cold junction. It offers the good performance across the wide temperature range with a small form factor, low power consumption, and very reasonable cost.
Figure 4 is a simplified schematic showing a precision DAS that uses the evaluation (EV) kit for the
MAX11200 24bit deltasigma ADC and allows thermocouple temperature measurements. Here, R1  PT1000 (PTS 1206, 1000Ω) is used for absolute temperature measurement of the cold junction. This solution allows the cold junction temperature to be measured with ±0.30°C accuracy, or better. [
3]
Figure 4. Simplified thermocouple DAS.
As shown in Figure 4, the MAX11200's GPIO is set to control the precision multiplexor, the
MAX4782, which selects either the thermocouple or the PRTD R1  PT1000. This approach allows dynamic thermocouple or PRTD measurements using a single ADC. The design improves the system precision and reduces the requirements for calibration.
Nonlinearity Errors
Thermocouples are voltagegenerating devices. But output voltages as a function of temperature from the most common thermocouples [
2,
4] are highly nonlinear.
Figure 4 and
Figure 5 demonstrate that without proper compensation, nonlinear errors for the popular industrial typeK thermocouples could exceed tens of °C.
Figure 5. The output voltage vs. temperature for a typeK thermocouple. The curve is reasonably linear in the range of 50°C to +350°C; it clearly has significant deviations from absolute linearity—below 50°C and above +350°C. [
1]
Figure 6. The deviation from a straightline approximation, assuming a linear output from 50°C to +350°C, for an average sensitivity of k = 41µV/°C. [
1]
Modern thermocouple standards, tables, and formulas such as the NIST ITS90 Thermocouple Database [
1] were adopted by the
IEC and currently represent the foundation for substantial interchange of thermocouple types among systems. These standards make it easy to replace thermocouples with one from the same or a different manufacturer, while ensuring rated performance with minimal redesign or recalibration of the system.
The NIST ITS90 Thermocouple Database provides detailed lookup tables. By using standardized polynomial coefficients [
1], it also allows the polynomial equation to be used to convert thermocouple voltage to temperature (°C) over a wide range of temperatures.
Polynomial coefficients, according to the NIST ITS90 Thermocouple Database, are:
T = d_{0} + d_{1}E + d_{2}E² + ... d_{N}E^{N} 
(Eq. 2) 
Where:
T – is the temperature in °C;
E is the V
_{OUT}  thermocouple output in mV;
d
_{N} is the polynomial coefficients unique to each thermocouple;
N = maximum order of the polynomial.
NIST (NBS) polynomial coefficients for a typeK thermocouple are shown
Table 2.
Table 2. TypeK Thermocouple Coefficients
TypeK Thermocouple Coefficients 
Temperature Range (°C) 
200 to 0 
0 to 500 
500 to 1372 
Voltage Range (mV) 
5.891 to 0 
0 to 20.644 
20.644 to 54.886 
Coefficients 

d0 
0.0000000E+00 
0.0000000E+00 
1.3180580E+02 
d1 
2.5173462E+01 
2.5083550E+01 
4.8302220E+01 
d2 
1.1662878E+00 
7.8601060E02 
1.6460310E+00 
d3 
1.0833638E+00 
2.5031310E01 
5.4647310E02 
d4 
8.9773540E01 
8.3152700E02 
9.6507150E04 
d5 
3.7342377E01 
1.2280340E02 
8.8021930E06 
d6 
8.6632643E02 
9.8040360E04 
3.1108100E08 
d7 
1.0450598E02 
4.4130300E05 
— 
d8 
5.1920577E04 
1.0577340E06 
— 
d9 
— 
1.0527550E08 
— 
Error Range (°C) 
0.02 to 0.04 
0.05 to 0.04 
0.05 to 0.06 
Table 2 shows that polynomial coefficients allow temperature, T, calculations with precision better than ±0.1°C for a 200°C to +1372°C temperature range. Similar tables with different unique coefficients are available for most popular thermocouples. [
1]
Contemporary NIST ITS90 coefficients that are provided for the temperature intervals 200°C to 0, 0 to +500°C, and +500°C to +1372°C allow temperatures to be calculated with much better accuracy (below ±0.1°C vs. ±0.7°C). This can be seen in the comparison with older "single" interval tables. [
2]
ADC Characteristics/Analysis
Table 3 shows the basic performance specifications of the MAX11200, featured in the circuit of Figure 4.
Table 3. MAX11200 Key Specifications

MAX11200 
Comments 
Sample Rate (sps) 
10 to 120 
The MAX11200's variable oversampling rate can be optimized for low noise and for 150dB linenoise rejection at 50Hz or 60Hz. 
Channels 
1 
GPIOs allow external multiplexer control for multichannel measurements. 
INL (ppm, max) 
±10 
Provides very good measurement linearity. 
Offset Error (µV) 
±1 
Provides almost zero offset measurements. 
NoiseFree Resolution (Bits) 
19.0 at 120sps; 19.5 at 60sps; 21.0 at 10sps 
Very high dynamic range with low power. 
V_{DD} (V) 
AVDD (2.7 to 3.6)
DVDD (1.7 to 3.6) 
AVDD and DVDD ranges cover the industry's popular powersupply ranges. 
I_{CC} (µA, max) 
300 
Highest resolution per unit power in the industry; ideal for portable applications. 
GPIOs 
Yes 
Allows external device control, including local multiplexer control. 
Input Range 
0 to V_{REF}, ±V_{REF} 
Wide input ranges 
Package 
16QSOP,
10µMAX® (15mm²) 
Some models like the MAX11202 are offered in a 10µMAX package—a very small size for spaceconstrained designs. 
The MAX11200 used in this article is a lowpower, 24bit deltasigma ADC suitable for lowpower applications that require a wide dynamic range and a high number of noisefree bits. Using this ADC, you can calculate the resolution in temperature for the Figure 3 circuit using Equations 3 and 4:

(Eq. 3) 

(Eq. 4) 
Where:
Rtlsb is the thermocouple resolution at 1 LSB;
Rtnfr is the thermocouple noisefree resolution (NFR);
V
_{REF} is the reference voltage;
Tcmax is the maximum thermocouple temperature in the measurement range;
Tcmin is the minimum thermocouple temperature in measurement range;
Vtmax is the maximum thermocouple voltage in the measurement range;
Vtmin is the minimum thermocouple voltage in the measurement range;
FS is the ADC fullscale code for a MAX11200 in a bipolar configuration (2
^{23}1);
NFR is the ADC noisefree resolution for a MAX11200 in the bipolar configuration (2
^{20}1) at 10 samples per second.
Table 4 lists the calculations of the measurement resolution using Equations 3 and 4 for the typeK thermocouples identified in Table 1.
Table 4. Measurement Resolution for TypeK Thermocouples Across Different Temperature Ranges
Temperature Range (°C) 
200 to 0 
0 to 500 
500 to 1372 
Voltage Range (mV) 
5.891 
20.644 
34.242 
Rtlsb Resolution (°C/LSB) 
0.0121 
0.0087 
0.0091 
Rtnfr Resolution (°C/NFR) 
0.0971 
0.0693 
0.0729 
Table 4 provides the calculated values of °C/LSB error and °C/NFR error for each temperature range. Noisefree resolution (NFR) represents the minimum temperature values that can be reliably differentiated by the ADC. For all temperature ranges, NFR values are below 0.1°C, which is more than sufficient for most thermocouples in industrial and medical applications.
Interfacing a Thermocouple with the MAX11200 EV Kit
The
MAX11200EVKIT offers a fully functional, highresolution DAS. The EV kit can help a design engineer expedite reallife developments, such as verification of the schematic solution suggested in Figure 4.
On the Figure 4 schematic, the popular typeK OMEGA thermocouple (KTSS116 [
5]) was connected to differential EV kit input A1. The absolute measurement of the cold junction temperature was done using the costeffective ratiometric method described in Maxim's application note 4875. [
3] Output of the R1 (PT1000) was connected to EV kit input A0. The MAX11200's GPIO was set to control the precision multiplexor, MAX4782, which dynamically selects either the thermocouple or the PRTD R1 outputs connected to the MAX11200's input.
The typeK thermocouple (Figures 3, 4) is reasonably linear across the 50°C to +350°C range. For some noncritical applications, linear approximation formulas (Equation 5) allow substantially reduced calculation volume and complexity.
Approximate absolute temperature could be calculated as:

(Eq. 5) 
Where:
E is the measured thermocouple output in mV;
Tabs is the absolute temperature of the typeK thermocouples in °C;
Tcj is the temperature of the cold junction of the thermocouples (°C) measured by PT1000; [3]
Ecj is the coldjunction thermocouple equivalent output in mV calculated by using Tcj.
Therefore:
k = 0.041mV/°C  average sensitivity from 50°C to +350°C
To make precision measurements in the wider temperature range (270°C to +1372°C), however, implementation of the polynomial formulas (Equation 2) and coefficients (according NIST ITS90) is strongly recommended:
Tabs = ƒ(E + Ecj) 
(Eq. 6) 
Where:
Tabs is the absolute temperature of the typeK thermocouples in °C;
E is the measured thermocouple output in mV;
Ecj is the coldjunction thermocouple equivalent output in mV calculated by using Tcj;
f is the polynomial function according equation 2;
T
_{COLD} is the temperature of the cold junction of the thermocouples (°C) measured by PT1000.
Figure 7 shows the development system for Figure 4. This system features a certified precision calibrator, Fluke®724, used like temperature simulator to replace the typeK OMEGA thermocouple.
More detailed image (PDF, 3.1MB)
Figure 7. The development system for Figure 4.
The Fluke724 calibrator is supplying precision voltage that corresponds to the TypeK thermocouple output in the 200°C to +1300°C range to the PT1000based coldjunction compensation module. The MAX11200based DAS dynamically selects either the thermocouple or the PRTD measurement and transmits data though a USB port to the laptop computer. Specially developed DAS software collects and processes data generated by the thermocouple and PT1000 outputs.
Table 5 lists measurement and calculations using Equations 5 and 6 for the 200°C to +1300°C temperature range.
Table 5. Measurement Calculations Across 200°C to +1300°C
Temperature (Fluke724) (°C) 
PT1000 Code Measured at "Cold Junction" (LSB) 
Thermocouple Code Adjusted to 0°C by PT1000 Measurements (LSB) 
Temperature Calculated by Equation 6 and Table 2 (°C) 
Temperature Error vs. Calibrator (°C) 
Temperature Calculated by "Linear" Equation 5 (°C) 
200 
326576 
16463 
199.72 
0.28 
143.60 
100 
326604 
9930 
99.92 
0.08 
86.62 
50 
326570 
5274 
50.28 
0.28 
46.01 
0 
326553 
6 
0.00 
0.00 
0.05 
20 
326590 
2257 
20.19 
0.19 
19.68 
100 
326583 
11460 
100.02 
0.02 
99.96 
200 
326486 
22779 
200.18 
0.18 
198.69 
500 
326414 
57747 
500.16 
0.16 
503.70 
1000 
326520 
115438 
1000.18 
0.18 
1006.92 
1300 
326544 
146562 
1300.09 
0.09 
1278.40 
As Table 5 shows, by using Equation 6 the MAX11200based DAS achieves in the order ±0.3°C precision over a very wide temperature range. Linear approximation by Equation 5 allows only a 1°C to 4°C degree of precision in the narrower 50°C to +350°C temperature range.
Note that using Equation 6 required relatively complex linearization calculation algorithms.
Around a decade ago implementation of such algorithms could present both technical and cost constrains in DAS system design. Today's modern processors resolve these challenges quickly and cost effectively.
Conclusion
In recent years costefficient, thermocouplebased temperaturesensing measurement has developed for a very wide temperature range in the order 270°C to +1750°C. Improvements in the temperature measurements and range have been accompanied by reasonable costs and often very low power consumption.
These thermocouplebased temperature measurement systems require a lownoise ADC (like the MAX11200), if the ADC and thermocouple are to be connected directly. When integrated in a circuit, the thermocouple, PRTD, and ADC provide a highperformance temperaturemeasurement system that is ideal for portable sensing applications.
High noisefree resolution, integrated buffers, and GPIO drivers allow the MAX11200 to interface directly with any traditional thermocouples and highresolution PRTDs like the PT1000 without the need for an additional instrumentation amplifier or dedicated current sources. Less wiring and lower thermal errors further reduce the system complexity and cost, thus allowing the designer to implement a simple DAS interface with a thermocouple and coldjunction compensation module.
References
[1] See the
NIST online databases.
[2] See application note 4679, "
Thermal Management Handbook."
[3] For more details about highaccuracy temperature measurements using a PRTD, see Maxim's application note 4875, "
HighAccuracy Temperature Measurements Call for Platinum Resistance Temperature Detectors (PRTDs) and Precision DeltaSigma ADCs."
[4]
Using Thermocouples  Thermocouple Introduction and Theory (PDF).
[5]
TypeK OMEGA thermocouple KTSS116 (PDF).
µMAX is a registered trademark of Maxim Integrated Products, Inc.
Fluke is a registered trademark of Fluke Corporation.
Related Parts 
MAX11200 
24Bit, SingleChannel, UltraLow Power, DeltaSigma ADCs with GPIO 
Free Samples

MAX11200EVKIT 
Evaluation Kits for the MAX11200, MAX11206, MAX11209, MAX11210, and MAX11213 

MAX31855 
ColdJunction Compensated ThermocoupletoDigital Converter 
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MAX6002 
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MAX6627 
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