# Accurate temperature measurement with advanced thermocouples and high-resolution delta-sigma ADC

Thermocouples are widely used for various temperature detection. Recent advances in thermocouple design, and the emergence of new standards and algorithms, have greatly expanded the operating temperature range and accuracy. Currently, temperature detection can achieve an accuracy of ±0.1°C over a wide range of -270°C to +1750°C. To take full advantage of the new thermocouple capabilities, a high-resolution thermocouple temperature measurement system is required. A low-noise, 24-bit, delta-sigma analog-to-digital converter (ADC) capable of resolving extremely small voltages is ideal for this task. The data acquisition system (DAS) uses a 24-bit ADC evaluation (EV) board with thermocouples capable of temperature measurement over a wide temperature range. Thermocouples, platinum resistance temperature detectors (PRTDs) and ADCs combine to form a high-performance temperature measurement system. DAS systems using low-cost, low-power ADCs are ideal for portable detection applications.

Getting Started with Thermocouples

Thomas Seebeck discovered the thermocouple principle in 1822. A thermocouple is a simple temperature measurement device consisting of two different metals (Metal 1 and Metal 2) (Figure 1). Seebeck found that different metals would generate different electrical potentials related to temperature gradients. If these metals are soldered together to form a temperature sensor junction (TJUNC, also known as a temperature junction), the differential junction (TCOLD, which acts as a constant temperature reference) that is not connected at the other end will present a voltage, VOUT, which is related to the temperature of the soldered junction. proportional. This allows the thermocouple to output a temperature-dependent voltage/charge without any voltage or current excitation.

The VOUT temperature difference (TJUNC – TCOLD) is a function of the metal type of Metal 1 and Metal 2. This function is rigorously defined in the National Institute of Standards and Technology (NIST) ITS-90 Thermocouple Database, covering the vast majority of practical metal 1 and metal 2 combinations. Using this database, the relative temperature TJUNC can be calculated from the VOUT measurement. However, since thermocouples measure TJUNC differentially, the absolute cold junction temperature (in °C, °C, or K) must be known in order to determine the measured temperature of the temperature junction. All modern thermocouple systems utilize another absolute temperature sensor (PRTD, silicon sensor, etc.) to precisely measure the cold junction temperature and compensate mathematically.

Figure 1 Simplified circuit of thermocouple

Tabs = T_{JUNC} + T_{COLD} (Formula 1)

where:

Tabs is the absolute temperature of the temperature junction.

T_{JUNC}is the relative temperature between the temperature junction and the reference cold junction.

T_{COLD}is the absolute temperature of the cold junction reference junction.

There are various types of thermocouples, but the most suitable dissimilar metal pair can be selected for a specific industrial or medical environment. These metal and/or alloy combinations are standardized by NIST and the International Electrotechnical Commission and are abbreviated as E, J, T, K, N, B, S, R, etc. NIST and IEC provide thermocouple reference tables for common thermocouple types.

NIST and IEC have also developed standard mathematical models for each thermocouple type. These power series models employ a unique combination of coefficients that are different for each thermocouple type and temperature range.

Table 1. Common Thermocouple Types

The J-type thermocouple has a relatively high Seebeck coefficient, high precision and low cost, and is widely used. These thermocouples can achieve a measurement accuracy of ±0.1°C using a relatively simple linearization algorithm.

Type K thermocouples cover a wide temperature range and are widely used in industrial measurement. These thermocouples have moderately high Seebeck coefficients, low cost, and good oxidation resistance. Type K thermocouples are accurate up to ±0.1°C.

The application of E-type thermocouples is not as popular as other types of thermocouples. However, this group of thermocouples has the highest Seebeck coefficient. Type E thermocouples require lower measurement resolution than other types. The measurement accuracy of the E-type thermocouple can reach ±0.5 °C, and the required linearization calculation method is relatively complex.

Type S thermocouples are composed of platinum and rhodium, a combination that enables stable, reproducible measurements in very high oxidizing environments. The Seebeck coefficient of the S-type thermocouple is low and the cost is relatively high. The measurement accuracy of the S-type thermocouple can reach ±1°C, and the required linearization algorithm is relatively complex.

Application example

Thermocouple circuit designs include a high-resolution ADC with differential inputs and the ability to resolve tiny voltages, a stable low-drift reference, and a method to accurately measure cold-junction temperature.

Figure 2 shows a simplified schematic. The MX7705 is a 16-bit, delta-sigma ADC with a built-in programmable gain amplifier (PGA) capable of resolving microvolt-level voltages from thermocouples without the need for an external precision amplifier. The cold junction temperature is measured using a MAX6627 remote diode sensor and a diode-connected transistor located at the thermocouple connector. The input common-mode range of the MX7705 extends to 30mV below ground, enabling a limited negative temperature range.

Figure 2 Thermocouple measurement circuit. The MX7705 measures the thermocouple output, and the MAX6627 and an external transistor measure the cold junction temperature. The MAX6002 provides a 2.5V precision voltage reference for the MX7705.

There are also ICs designed for specific applications for thermocouple signal conditioning. These ICs integrate local temperature sensors, precision amplifiers, ADCs, and voltage references. For example, the MAX31855 is a cold-junction-compensated thermocouple-to-digital converter that digitizes K, J, N, T, or E thermocouple signals. The MAX31855 measures thermocouple temperature with 14-bit (0.25°C) resolution (Figure 3).

Figure 3 ADC with integrated cold junction temperature compensation, no external compensation required when converting thermocouple voltages

Error Analysis

Cold Junction Compensation

Thermocouples are differential sensors that use the temperature difference between the temperature junction and the cold junction to generate an output voltage. According to Equation 1, the absolute temperature of the temperature junction (Tabs) can only be obtained when the absolute temperature of the cold junction (TREF) is accurately measured.

The cold junction absolute temperature can be measured with the new platinum RTD (PRTD). It offers good performance over a wide temperature range, small size, low power consumption, and very reasonable cost.

Figure 4 shows a simplified schematic of a precision DAS that uses the MAX11200 (24-bit, delta-sigma ADC) evaluation (EV) board for thermocouple temperature measurements. In this example, the absolute cold junction temperature is measured using R1 – PT1000 (PTS 1206, 1000Ω). This solution is capable of measuring cold junction temperature with ±0.30°C or higher accuracy.

Figure 4 Simplified diagram of thermocouple DAS

As shown in Figure 4, the MAX11200’s GPIOs are set to control the MAX4782 precision multiplexer, which selects the thermocouple or PRTD R1 – PT1000. This method enables dynamic measurements of thermocouples or PRTDs using a single ADC. Improves system accuracy and reduces calibration requirements.

nonlinear error

Thermocouples are voltage generating devices.However, most common thermocouples[2，4]The output voltage as a function of temperature exhibits very high nonlinearity.

As illustrated in Figures 4 and 5, the nonlinearity error of common industrial K-type thermocouples can exceed tens of degrees Celsius if not properly compensated.

Figure 5. The graph of the output voltage and temperature of the K-type thermocouple. The curve has good linearity in the range of -50℃ to +350℃; below -50℃ and above +350℃, there are obvious deviations from absolute linearity.

Modern thermocouple standardization, look-up tables and formula databases such as NIST ITS-90 adopted by IEC are the basis for the interchange of thermocouple types between current systems. With these standards, thermocouples can be easily replaced by other thermocouples of the same or different manufacturers, and performance specifications are assured with minimal system design updates or calibrations.

The NIST ITS-90 Thermocouple Database provides detailed lookup tables. Polynomials can also be used to convert thermocouple voltages to temperature (°C) over a very wide temperature range by using normalized polynomial coefficients.

According to the NIST ITS-90 Thermocouple Database, the polynomial coefficients are:

T = d0 + d1E + d2E² + … dNEN

(Formula 2)

where:

T is temperature, °C.

E is VOUT – thermocouple output, mV.

dN is a polynomial coefficient, and the coefficient of each thermocouple is unique.

N = maximum order of the polynomial.

Table 2 shows the NIST (NBS) polynomial coefficients for a Type K thermocouple.

Using the polynomial coefficients in Table 2, the temperature T can be calculated with an accuracy better than ±0.1°C over the -200°C to +1372°C temperature range. Different coefficient tables are available for most common thermocouples.

Table 2 K-type thermocouple coefficients

Similarly, similar NIST ITS-90 systems can be found in the -200°C to 0, 0 to +500°C, and +500°C to +1372°C temperature ranges, capable of higher accuracy (below ±0.1°C, relative to ± 0.7°C) to calculate the temperature. This can be seen by comparison with the original “single” interval table.

ADC Specifications/Analysis

Table 3 shows the basic specifications of the MAX11200, which has the circuit characteristics shown in Figure 4.

Table 3 Main Specifications of MAX11200

The MAX11200 used in this article is a low-power, 24-bit, delta-sigma ADC suitable for low-power applications requiring wide dynamic range and high resolution. Using this ADC, the temperature resolution of the circuit of Figure 3 can be calculated based on Equations 3 and 4.

(Formula 3)

(Formula 4)

where:

Rtlsb is the resolution of the thermocouple at 1 LSB.

Rtnfr is the noise free resolution (NFR) of the thermocouple.

VREF is the reference voltage.

Tcmax is the maximum temperature of the thermocouple within the measurement range.

Tcmin is the minimum temperature of the thermocouple within the measurement range.

Vtmax is the maximum voltage of the thermocouple in the measurement range.

Tcmax is the minimum thermocouple voltage within the measurement range.

FS is the ADC full-scale code, which is (223-1) for the MAX11200 in a bipolar configuration.

NFR is the noise-free resolution of the ADC, (220-1) for the MAX11200 in a bipolar configuration at 10Sa/s.

Table 4 lists the measurement resolutions of the K-type thermocouples in Table 1 calculated using Equations 3 and 4.

The °C/LSB error and °C/NFR error calculations are provided in Table 4 for each temperature range. Noise-Free Resolution (NFR) represents the smallest temperature value that the ADC can reliably distinguish. The NFR value is below 0.1°C over the entire temperature range, which is far sufficient for most thermocouples in industrial and medical applications.

Table 4 Measurement resolution of K-type thermocouples in different temperature ranges

Thermocouple Connections to the MAX11200 EV Kit

The MAX11200EVKIT provides a full-featured, high-resolution DAS. Evaluation boards help design engineers quickly complete project development, such as verifying the solution shown in Figure 4.

In the schematic shown in Figure 4, a common K-type OMEGA thermocouple (KTSS-116 ) is connected to the differential evaluation board input A1. Measure the absolute value of the cold junction temperature using the cost-effective ratiometric scheme described in Maxim Application Note 4875. The R1 (PT1000) output is connected to the EV kit input A0. The MAX11200’s GPIOs control the MAX4782 precision multiplexer, which dynamically selects to connect the thermocouple or PRTD R1 output to the MAX11200’s input.

Type K thermocouples (Figure 3, Figure 4) have adequate linearity over the range -50°C to +350°C. For some less stringent applications, the linear approximation formula (Equation 5) can greatly reduce the amount of computation and complexity.

The approximate absolute temperature can be calculated as:

(Formula 5)

where:

E is the measured thermocouple output, mV.

Tabs is the absolute temperature of K-type thermocouple, ℃.

Tcj is the temperature of the cold junction of the thermocouple measured by PT1000, °C.

Ecj is the equivalent output of the cold junction thermocouple calculated by Tcj, mV.

so:

k = 0.041mV/°C – Average sensitivity from -50°C to +350°C

However, for accurate measurements over a wider temperature range (-270°C to +1372°C), a polynomial (Equation 2) and coefficients (according to NIST ITS-90) are strongly recommended:

(Formula 6)

where:

Tabs is the absolute temperature of K-type thermocouple, ℃.

E is the measured thermocouple output, mV.

Ecj is the equivalent output of the cold junction thermocouple calculated by Tcj, mV.

f is the polynomial function in equation 2.

TCOLD is the cold junction temperature of the thermocouple measured by PT1000, °C.

Figure 7 shows the development system of Figure 4. The system includes a certified precision calibrator, Fluke®-724, as a temperature simulator in place of a Type K OMEGA thermocouple.

The Fluke-724 calibrator provides a precision voltage corresponding to the output of a K-type thermocouple in the range of -200°C to +1300°C to a PT1000 based cold junction compensation module. The MAX11200-based DAS dynamically selects thermocouple or PRTD measurements and sends the data to a notebook computer via the USB port. Specially developed DAS software acquires and processes the data generated by the thermocouple and PT1000 outputs.

Figure 6 Deviation from a linear approximation, assuming a linear output from -50°C to +350°C, with an average sensitivity of k = 41 μV/°C.

Figure 7 Figure 4 Development system

Table 5 lists the measured and calculated values over the temperature range of -200°C to +1300°C, using Equations 5 and 6.

Table 5 Measurement calculations for the range -200°C to +1300°C

As shown in Table 5, using Equation 6, a MAX11200-based DAS system can achieve an accuracy of the order of ±0.3°C over a very wide temperature range. The linear approximation in Equation 5 can only achieve an accuracy of 1°C to 4°C over a narrow range of -50°C to +350°C.

Note that Equation 6 requires a relatively complex linearization calculation algorithm.

About a decade ago, implementing such algorithms in DAS system designs was limited by technology and cost. Today’s modern processors are fast and cost-effective to address these challenges.

Summarize

In recent years, great progress has been made in cost-effective, thermocouple temperature detection technology suitable for the temperature range of -270°C to +1750°C. While improving temperature measurement and range, the cost is also more reasonable and the power consumption is lower.

These thermocouple-based temperature measurement systems require a low-noise ADC (such as the MAX11200) if the ADC and thermocouple are directly connected. Thermocouples, PRTDs, and ADCs, when integrated into a circuit, enable high-performance temperature measurement systems ideal for portable detection applications.

Featuring high noise-free resolution, integrated buffers, and GPIO drivers, the MAX11200 can interface directly with any conventional thermocouple and high-resolution PRTDs (such as the PT1000) without the need for additional instrumentation amplifiers or dedicated current sources. Less wiring and lower thermal errors further reduce system complexity and cost, enabling designers to implement simple interfacing of the DAS with thermocouple and cold junction compensation modules.

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