
Keywords: platinum resistance temperature detector, PRTD, data acquisition system, DAS, temperaturemeasurement PRTD standard, EN60751, ADC, MAX11200, MAXQ2000 processor
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Modern PRTD Temperature Sensors and HighResolution DeltaSigma ADCs Enable Wide Range HighAccuracy Temperature Measurements
By: 
Sohail Mirza, Applications Engineer Manager 

Joseph Shtargot, Strategic Applications Engineer 

Mohammad Qazi, Applications Engineer 

Abstract: Many modern industrial, medical, and commercial applications require temperature measurements in the extended temperature range with accuracies of ±0.3°C or better, performed with reasonable cost and often with low power consumption. This article explains how platinum resistance temperature detectors (PRTDs) can perform measurements over wide temperature ranges of 200°C to +850°C, with absolute accuracy and repeatability better than ±0.3°C, when used with modern processors capable of resolving nonlinear mathematical equation quickly and cost effectively. This article is the second installment of a series on PRTDs. For the first installment, please read application note 4875, "HighAccuracy Temperature Measurements Call for Platinum Resistance Temperature Detectors (PRTDs) and Precision DeltaSigma ADCs."
A similar version of this article appeared in the June 21, 2012 issue of
EDN magazine.
Introduction
This article explains how to achieve highperformance precision, widerange temperature measurement for platinum resistance temperature detectors (PRTDs), using a dataacquisition system (DAS) comprised of a deltasigma analogtodigital converter (ADC) and a modern processor. This DAS offers high performance, yet is cost effective.
The development DAS presented here resolves design and mathematical challenges quickly and achieves precision temperature measurement in the PRTD's maximum range (200°C to +850°C).
Platinum resistance temperature detectors, or PRTDs, are absolute temperaturesensing devices that can assure repeatable measurements over temperature ranges of 200°C to +850°C. Platinum, moreover, is very stable and not affected by corrosion or oxidation. PRTDs thus provide optimal performance for precision industrial and medical applications that require precise temperature measurements.^{1}
PRTDs are nearly linear devices. Depending on the temperature range and other criteria, you can make a linear approximation by calculating the PRTD resistance change over a temperature range of 20°C to +100°C.^{1} For a wider temperature range (200°C to +850°C) and for higher accuracy, however, the temperaturemeasurement PRTD standard (EN 60751:2008) defines the behavior of platinum resistance versus temperature by a nonlinear mathematical model called the CallendarVan Dusen equation.
Years ago, implementation of such algorithms could present both technical and cost constraints in DAS design. Today's modern processors like the
MAXQ2000 and affordable PCs can resolve these challenges quickly and cost effectively, while providing the user with a friendly graphical display.
The CallendarVan Dusen equation can be used in such a modern DAS to reduce errors to negligible levels for the wide 200°C to +850°C dynamic range. Accuracy will be ±0.3°C or better can be achieved.
Designing an Example DAS
The DAS discussed in this article provides a highresolution, lownoise measurement in the PRTD linear temperature range from 20°C to +100°C. Its accuracy is ±0.15% without implementation of the CallendarVan Dusen equation. By using a PRTD1000 (PTS12061000Ω), a very common platinum RTD that is both size and cost effective, then temperature resolution better than ±0.05°C is achievable within the given range.^{1}
This simple DAS uses a
MAX11200 24bit deltasigma ADC for data conversion and a lowpower, costefficient MAXQ2000 processor
^{2} for data acquisition. The DAS implements the linearization algorithm in a PC. Any other capable processor, controller, or DSP could also be used.
PRTD devices like the PTS12061000Ω are an attractive choice for temperature ranges from 55°C to +155°C because they are available in standard surfacemount device (SMD) sizes, which are very similar to surfacemount resistor packages and priced in the low singledollar range. For temperature ranges between 50°C and +500°C, thinfilm PRTDs represent a costeffective practical choice.^{3} Thinfilm PRTDs consist of thinfilm platinum deposited on a ceramic substrate with a glasscoated platinum element. Resistance and temperature deviation can be controlled to within ±0.06% and ±0.15°C, a tolerance that corresponds to Class A per EN 60751. For hightemperature measurements in liquid or corrosive environments, thinfilm PRTDs are often placed inside a protective probe.
Figure 1 is a simplified schematic showing the precision DAS developed for this article. It uses the evaluation (EV) kit for the MAX11200 ADC. The MAX11200's GPIO1 pin is set as an output to control the relay calibration switch, which selects either the fixed RCAL resistor or the PRTD. This versatility improves the system precision, reduces the required calculations to those for the initial values of RA and RT, and provides excellent system diagnostics at the same time.
Figure 1. Block diagram of the DAS used for measurements in this article. The DAS includes a provision for system calibration/diagnostics and the MAXQ2000 processor for ADC initialization and data collection with subsequent computergenerated linearization. The DAS dynamically selects either the PRTD measurement or calibration measurement and transmits data though a USB port to the PC.
Equation 1 is used to calculate R(t) from the ADC's output code:

(Eq. 1) 
Where A_{ADC} is the ADC's output code and FS is the ADC's fullscale code (i.e., 2^{23}  1 for the MAX11200 in a singleended configuration).
According to EN 60751, the PRTD range 200°C to +850°C is divided in two nonlinear temperature zones with different mathematical models. For temperatures between 0°C and +850°C, the linearization equation requires two coefficients based on the following formula:
R(t) = R(0) × (1 + A × t + B × t^{2}) 
(Eq. 2) 
For temperatures from 200°C to 0°C:
R(t) = R(0)[1 + A × t + B × t^{2} + (t  100)C × t^{3}] 
(Eq. 3) 
Where R(t) is the PRTD resistance at t°C; R(0) is the PRTD resistance at 0°C; and t is the PRTD temperature in °C.
Using Equations 2 and 3, then A, B, and C are calibration coefficients derived from measurements by RTD manufacturers, as specified by IEC 60751:
A = 3.9083 × 10^{3}°C^{1}
B = 5.775 × 10^{7}°C^{2}
C = 4.183 × 10^{12}°C^{4}
Note that Equation 2 for temperatures between 0°C to +850°C is a quadratic and, therefore, allows a direct mathematical solution:
t_{+800} = [R(0) × A + ((R(0) × A)^{2}  4 × R(0) × B × (R(0)  R(t))^{1/2}]/2 × R(0) × B 
(Eq. 4) 
Where R(t) is the PRTD resistance at t°C calculated using Equation 1; R(0) is the PRTD resistance at 0°C; and T is the PRTD temperature in °C.
Referring back to Part 1 of this article,^{1} the firstorder linear equation for R(t) shows large nonlinearity errors for temperatures outside the 20°C to +100°C range. Using Equation 2 for R(t) reduces the error to negligible levels.
Figure 2. Data show that nonlinearity errors increase for temperatures outside 20°C to +100°C (purple curve). The errors decrease to negligible levels, except at very low temperatures (blue curve).
Table 1 shows that calculations based on Equation 4 provide measurement errors below 0.25°C which, in turn, match the nominal PRTD resistance tables for EN 60751 in the 100°C to +850°C range.
Table 1. Detailed Temperature Calculations and Absolute Errors 
Nominal Temperature (°C) 
Calibration Coefficients Specified by IEC 60751 
Nominal PRTD Resistance by EN 60751 (Ω) 
Calculated Temperature Using Eq 2 (°C) 
Absolute Errors (°C) 
A 
B 
200.0 
3.91E03 
5.78E07 
185.2 
202.425 
2.42 
100.0 
3.91E03 
5.78E07 
602.56 
100.208 
0.21 
70.0 
3.91E03 
5.78E07 
723.35 
70.060 
0.06 
20.0 
3.91E03 
5.78E07 
921.6 
20.001 
0.00 
0.0 
3.91E03 
5.78E07 
1000 
0.000 
0.00 
20.0 
3.91E03 
5.78E07 
921.6 
20.001 
0.00 
100.0 
3.91E03 
5.78E07 
1385.06 
100.001 
0.00 
250.0 
3.91E03 
5.78E07 
1940.98 
250.000 
0.00 
350.0 
3.91E03 
5.78E07 
2297.16 
350.000 
0.00 
600.0 
3.91E03 
5.78E07 
3137.08 
600.000 
0.00 
850 
3.91E03 
5.78E07 
3904.81 
850 
0 
Temperature measurements with errors below 0.25°C across the 100°C to +850°C range are more than sufficient for most industrial and medical applications. The precision provided by this development DAS is better than the Class A measurement precision prescribed by EN 60751. The ability to arrive at a direct solution (Equation 4) makes this DAS even more attractive because it substantially reduces calculation effort and complexity.
Finally, some last thoughts on Equation 3. While allowing a precision solution for temperatures between 200°C to 100°C, Equation 3 is actually a fourthorder polynomial equation that can be resolved only using computer math tools. Those tools will find the bestfit polynomial approximation expressions for the inverse transfer function or use successive approximation methods.
Processing the Data
The firmware on the MAXQ2000RAX microcontroller manages the following major functions, which are charted in Figure 3:
 Initializes the MAX11200 ADC
 Collects and processes the ADC's output data
 Maintains the USB interface with the PC
During initialization, the MAX11200 ADC goes through the selfcalibration process, sets the optimal sampling rate (10sps or 15sps), and enables the input signal buffers.
Selection of the sampling rate is very important for temperature measurement in industrial and medical applications. This DAS allows reasonably fast data acquisition with excellent (100dB or better) power line 50Hz/60Hz rejection. The recommended external clock for 60Hz linefrequency rejection is 2.4576MHz, which is effective for data rates of 1, 2.5, 5, 10, and 15sps. For 50Hz linefrequency rejection, the recommended external clock is 2.048MHz, which is effective for data rates of 0.83, 2.08, 4.17, 8.33, and 12.5sps.
Use of input signal buffers increases the input impedance to the highmegaohms range. This improves measurement precision because it practically eliminates the shunting effect of the input dynamic current.
The firmware also uses the
MAX3420E USB interface and, thus, does not require driver software on the PC side. Once the DAS is connected to a PC through USB, the MAX3420E USB module is initialized and the ADC temperature conversion is ready to be transmitted.
The software implements algorithms based on Equations 2 and 4. Raw measurement data is processed inside the PC. The processing sequence is also shown in Figure 2. Visuals of the results are shown in Figure 4.
Figure 3. Chart outlines the toplevel actions of the DAS firmware and software.
Figure 4. DAS software collects the data generated by the evaluation (EV) kit for the MAX11200 ADC. The PC processes this data using Equation 4 and supplies temperature output in °C or °F. Complementary scope outputs conveniently provide PRTD voltage and code that is useful for system analyses and further engineering development.
Verification of Results
To verify the accuracy of the DAS, we use the Fluke®724 calibrator. Used as a temperature simulator, the calibrator provides precision equivalent resistance that corresponds to the output of the PRTD1000O over the 200°C to +600°C range. The DAS dynamically selects either the PRTD measurement or calibration measurement (1.0kΩ, 0.1% resistor) and transmits data though a USB port to the PC. The setup is shown in Figure 5.
Table 2 shows that the DAS achieves better than ±0.3°C precision over the 100°C to +600°C temperature range. This performance is overall much better than Class A for EN 60751.
Figure 5. The development system for the DAS. This system features a certified precision calibrator, Fluke724, used as a temperature simulator to replace a hightemperature PRTD probe.
Table 2. Temperature Measurement from the DAS Development System 
Temperature by Calibrator Fluke724 (°C) 
Temperature Measured by DAS (Fig. 4) (°C) 
Absolute Error (°C) 
PRTD Class by IEC 60751 
200.0 
202.48 
2.48 
N/A 
100.0 
100.26 
0.26 
A 
70.0 
70.11 
0.11 
A 
20.0 
20.05 
0.05 
A 
0.0 
0.06 
0.06 
A 
20.0 
19.94 
0.06 
A 
100.0 
99.95 
0.05 
A 
250.0 
249.93 
0.07 
A 
350.0 
349.90 
0.10 
A 
600.0 
599.89 
0.11 
A 
Conclusion
In recent years, PRTDs became desirable devices for a variety of precision temperaturesensing applications where absolute accuracy and repeatability are critical over temperature ranges of 200°C to +850°C. Those applications require a lownoise ADC if the ADC and PRTD are to be connected directly. Together, the PRTD and ADC provide a temperaturemeasurement system that is ideal for portable sensing applications. This combination offers high performance, yet is cost effective.
To accurately measure temperatures in the maximum PRTD range (200°C to +850°C), nonlinear mathematical algorithms called the CallendarVan Dusen equations (EN 60751:2008) must be implemented. But just a few years ago implementing those algorithms presented both technical and cost constrains in DAS system design. Today's modern processors like the MAXQ2000 in conjunction with an affordable PC can resolve these challenges quickly and cost effectively.
References
Fluke is a registered trademark of Fluke Corporation.
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© Aug 01, 2012, Maxim Integrated Products, Inc.

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APP 5244: Aug 01, 2012
REFERENCE SCHEMATIC 5244,
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APP5244,
Appnote5244,
Appnote 5244
