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APPLICATION NOTE 4875
HighAccuracy Temperature Measurements Call for Platinum Resistance Temperature Detectors (PRTDs) and Precision DeltaSigma ADCs
Abstract: Advanced industrial and medical applications require temperature measurements with accuracies of ±1°C to ±0.1°C or better, performed with reasonable cost over a wide range of temperature, and often with low power consumption. The temperature ranges common in these applications (200°C to +1750°C) generally require the use of thermocouples and platinum resistance temperature (RT) detectors, or PRTDs.
A similar version of this article appeared in the August 25, 2011 issue of EDN magazine.
Introduction
When absolute accuracy and repeatability are critical over temperature ranges of 200°C to +800°C, the best choice for precision industrial and medical applications is the platinum resistance temperature (RT) detector, or PRTD. Platinum is very stable and not affected by corrosion or oxidation. Nickel, copper, and other metals can also be used for RTDs, but those materials are less popular because they are not as stable or repeatable as platinum.
The development of modern PRTD standards such as the European IEC 60751 and the American ASTM 1137 allow substantial interchangeability of sensors between systems, based on the sensors' specified tolerance and temperature coefficients. These standards make it easy to replace a sensor with one from the same or a different manufacturer, while ensuring rated performance with minimal redesign or recalibration of the system.
PRTD Basics
Three common PRTDs are the PT100, PT500, and PT1000, which exhibit resistance values of 100Ω, 500Ω, and 1000Ω, respectively, at 0°C. Higherresistance devices such as the PT10000 are available at slightly higher cost. PT100s were more popular historically, but today the trend is toward higherresistance values that provide higher sensitivity and resolution at little or no extra cost. Typical of these is the PT1000, whose 0°C resistance is 1kΩ.
Manufacturers like Vishay® and JUMO Process Control now offer PRTDs in the standard SMD sizes (very similar to surfacemount resistor packages) with typical prices in the low singledollar range, depending on the value, size, and tolerance. Such devices reduce the sensor cost substantially and provide designers with the flexibility to place PRTDs on any type of printed circuit board (PCB). The example below includes the popular and costeffective PTS1206, a 1000Ω PRTD manufactured by Vishay Beyschlag.¹ Traditional methods for PRTD measurement using currentsource excitation are shown in Figure 1.²
Figure 1. A PRTD can sense temperature using an interface of four wires (a), three wires (b), or two wires (c). Each design delivers a differential signal to the ADC, here the MAX1403.
For measurements at a distance and with dissimilar lead wires, the 4wire approach of Figure 1a (Kelvin connection) gives the most accurate results. In this approach the currentcarrying wires are separated from the measurement wires; OUT1 provides a 200µA source for the PRTD and OUT2 remains floating in this configuration. For most industrial applications in which the RTD element is not mounted close to the ADC, fewer wires are preferred because each wire adds to the system cost and reliability concerns.
The 3wire temperaturesensing technique of Figure 1b is more economical and provides accurate readings, if the lead wires are similar. This is why it is the most popular design. The two matched current sources of the MAX1403 ADC cancel the IR errors due to lead wire resistance. OUT1 and OUT2 both source a 200µA current.
The 2wire technique of Figure 1c is the most economical and is used only when the parasitic wire resistance is known and unchanging. The IR errors of the wires are normally compensated by computation within the microcontroller or DSP. Because the higher resistance in a PT1000 PRTD makes it less sensitive to leadwire resistance while lowering its selfheating error, it can be connected to the ADC directly, even in a 2wire configuration.
The MAX11200 ADC is suitable for sampling various types of PRTDs. Some important characteristics of this ADC are listed in Table 1.
Table 1. 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 (max, ppm)  ±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} (max, µA)  300  Highest resolutionperunit power in the industry; ideal for portable applications 
GPIOs  Allows external device control, including local multiplexer control.  
Input range  0 to V_{REF}, ±V_{REF}  Wide input ranges 
Package  16pin QSOP, 10pin µMAX® (15mm²)  10pin µMAX offers very small size for spaceconstrained designs. 
As an alternative to current excitation, you can excite the PRTD with a precision voltage source. Voltage excitation is more desirable for higherresistance PRTDs, and the same voltage reference that biases the ADC can be used to bias the PRTD. A PRTD can be connected directly to the ADC, and the ADC reference provides PRTD bias current with a single precision resistor (Figure 2). The ADC then measures temperature accurately and ratiometrically.
Figure 2. The sensing technique in this circuit is based on voltage excitation, which works best with highervalue PRTDs.
Assuming that the lead wire resistances are orders of magnitude lower than R_{A} and R_{T}, the following formula applies:
Where R_{A} is the currentlimiting resistor; R_{T} is the PRTD resistance at t°C; V_{RTD} is the PRTD voltage; and V_{REF} is the ADC reference voltage. At the same time:
V_{RTD} = V_{REF} × (R_{T}/(R_{A} + R_{T})) (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). Combining Equations 1 and 2:
V_{RTD} = V_{REF} × (A_{ADC}/FS) (Eq. 2)
R_{T} = R_{A} × (A_{ADC}/(FS  A_{ADC})) (Eq. 3)
From Equation 3, it is clear that R_{A} must meet certain precision requirements dictated by the R_{T} specification.
PRTD Selection and Error Analysis
Error Due to LeadWire Resistance
Because the PRTD is a resistive sensor, any resistance introduced by connecting copper extension wires between it and the control instrument adds error, as shown in Figure 3.
Figure 3. IR drops in the wires of a 2wire sensing technique can produce errors at the ADC.
To estimate the errors in a 2wire circuit, multiply the total length of the extension leads times the resistance per foot for American wire gages (AWG) copper wire, as shown in the Table 2.
Table 2. Wire Gage Resistance Values
Copper Lead Wire (AWG)  Ω/Foot (+25°C) 
16  0.0041 
18  0.0065 
20  0.0103 
22  0.0161 
24  0.0257 
26  0.0418 
28  0.0649 
As an example, assume that you connected two 3foot lengths of AWG 22 wire to a PRTD. The lead wire resistance R_{W} is:
R_{W} = 2 × (3ft.) × (0.0161Ω/ft.) = 0.1Ω (Eq. 4)
The error in temperature reading due to the lead wires is T_{WER}, where T_{WER} = R_{W}/S, and S is the average PRTD sensitivity.
For a PT100 (PTS 1206, 100Ω) device,¹ the average sensitivity is S = 0.385Ω/°C, so:
For a PT1000 (PTS 1206, 1000Ω) device,¹ the average sensitivity is S = 3.85Ω/°C, so:
T_{WER} = R_{W}/0.385 = 0.26°C (Eq. 5)
T_{WER} = R_{W}/3.85 = 0.026°C (Eq. 6)
According to the IEC 60751 standard, T_{WER} = 0.026°C for the PT1000 is one order of magnitude below the CLASS F0.3 tolerance of ±0.30°C. This means that a 3foot, 2wire configuration can be used directly with the PT1000 without any method of wire compensation. A T_{WER} of 0.26°C for the PT100, however, is comparable with the ±0.30°C tolerance and, therefore, represents an unacceptable level of error for most precision applications. This example demonstrates the advantage of higherresistance PRTDs in a 2wire circuit.
Error Due to PRTD SelfHeating
Another source of error for PRTDs is selfheating of the RTD element itself, as excitation current flows through it. Excitation current flowing through the RTD resistance produces the voltage to be measured. This current should be as high as practical to ensure that the output voltage remains above the ADC's voltage noise level. At the same time, excitation current generates a power loss that warms the temperature sensor, thereby increasing the RTD resistance above the level that it would otherwise assume due to the temperature being measured. This thermal error from RTD power dissipation can be calculated from the package thermal resistance provided in the manufacturer's data sheet. The thermal error from self heating (T_{TERR} in °C) can be calculated using the formula:
T_{TERR} = I_{EXT}² × R_{T} × K_{TPACK} (Eq. 7)
Where I_{EXT} is the excitation current through the resistive sensing element; R_{T} is the PRTD resistance at the current temperature T_{°C}; and K_{TPACK} is the selfheating error coefficient (0.7°C/mW).¹
In Figure 2, an optimal value of the currentlimiting resistor, R_{A}, is determined using Equation 7 for T_{ERR}, plus a reference value used in the measurement system (V_{REF} = 3V). Examples of such R_{A} values for the 100Ω PTS 1206 and the 1000Ω PTS 1206 are shown in Table 3.
Table 3. Thermal Error Calculation Budget
V_{REF}  K_{TPACK}  T°C  R_{T}100  R_{T}1000  R_{A}100  R_{A}1000  T_{ERR}100  T_{ERR}1000  I_{EXT}100  I_{EXT}1000  VR_{T}100  VR_{T}1000 
(V)  (C/mW)  (°C)  (Ω)  (Ω)  (Ω)  (Ω)  (°C)  (°C)  (µA)  (µA)  (mV)  (mV) 
3  0.7  55  78.3  783.2  8200  27000  0.015  0.013  362.4  108.0  28.4  84.6 
3  0.7  0  100.0  1000.0  8200  27000  0.019  0.016  361.4  107.1  36.1  107.1 
3  0.7  20  107.8  1077.9  8200  27000  0.020  0.018  361.1  106.8  38.9  115.2 
3  0.7  155  159.2  1591.9  8200  27000  0.029  0.025  358.9  104.9  57.1  167.0 
Using R_{A} = 8.2kΩ for the 100Ω PTS 1206 and R_{A} = 27.0kΩ for the 1000Ω PTS 1206, the maximum thermal error, T_{ERR}, is between 0.025°C and 0.029°C in both cases, which is one order of magnitude below the CLASS F0.3 tolerance of ±0.30°C. It is evident that the average excitation currents, I_{EXT}100 and I_{EXT}1000, are very stable and predictable over the temperature ranges indicated in Table 3.
One other conclusion from Table 3 is that the maximum excitation currents are dramatically different from those of the R_{T}100 and R_{T}1000 models: I_{EXT}1000 = 108µA, and I_{EXT}100 = 362.4µA. Thus, an R_{T}1000 is preferable to an R_{T}100 for lowpower (portable) instrumentation, because its excitation current is less than onethird of the R_{T}100 current. R_{A} resistors should be the metalfilm type with ±0.1% or better tolerances, at least 1/4W power rating, and a low temperature coefficient. To ensure that R_{A} resistors deliver the desired characteristics, they should be acquired from a reputable source.
Linearity Error of PRTD
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:
R(t) ≈ R(0)(1 + T × a) (Eq. 8)
R(t) is the PRTD resistance at t°C; R(0) is the PRTD resistance at 0°C; T is the PRTD temperature in °C; and the constant, a, is 0.00385Ω/Ω/°C according to IEC 60751. (In this case a = 0.00385Ω/Ω/°C is actually defined as a mean temperature coefficient between 0°C and 100°C.)¹
PRTD calculations based on Equation 8 are shown in Table 4.
Table 4. PRTD Calculations for the Range 20°C to +100°C
a  Temp  R_{RTD}1000 Lin  R_{RTD}1000 Nom  R_{A}  V_{REF}  V_{RTD}  ADC Code  Err 
(Ω/Ω/°C)  (°C)  (Ω)  (Ω)  (Ω)  (V)  (V)  (LSB)  (%) 
3.85E03  20  923.00  921.60  27000  3  0.0991656  277286  0.15 
3.85E03  10  961.50  960.90  27000  3  0.1031597  288454  0.06 
3.85E03  0  1000.00  1000.00  27000  3  0.1071429  299592  0.00 
3.85E03  10  1038.50  1039.00  27000  3  0.1111151  310699  0.05 
3.85E03  20  1077.00  1077.90  27000  3  0.1150764  321776  0.08 
3.85E03  30  1115.50  1116.70  27000  3  0.1190269  332822  0.11 
3.85E03  40  1154.00  1155.40  27000  3  0.1229665  343838  0.12 
3.85E03  50  1192.50  1194.00  27000  3  0.1268955  354824  0.13 
3.85E03  60  1231.00  1232.40  27000  3  0.1308136  365780  0.11 
3.85E03  100  1385.00  1385.00  27000  3  0.1463801  409308  0.00 
In Table 4 the R_{RTD}1000 Lin column represents a linear approximation according to Equation 8. The R_{RTD}1000 Nom column lists the nominal PTS 1206Ω to 1000Ω values according to manufacturing specification EN 60751:2008. The values in the Linearization Error (Err) column for the stated temperature range are all within the range ±0.15%, which is better than the CLASS F0.3 tolerance (±0.30°C) for PTS 1206.
Practical measurements per Table 4 using the MAX11200 ADC (Figure 2) confirm that digital representations of the temperaturereading errors remain within the limits for CLASS F0.3 tolerance. For a wider range and higher accuracy, the temperaturemeasurement PRTD standard (EN 60751:2008) defines the behavior of platinum resistance vs. temperature by a nonlinear mathematical model called the CallendarVan Dusen equation.
For temperatures between 0°C to +859°C, the linearization equation requires two coefficients based on the following formula:
For temperatures in the range 200°C to 0°C:
R(t) = R(0)(1 + A × t + B × t²) (Eq. 9)
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. In Equations 9 and 10 A, B, and C are calibration coefficients derived from measurements by RTD manufacturers, as specified by IEC 60751:
R(t) = R(0)[1 + A × t + B × t² + (t  100)C × t³] (Eq. 10)
A = 3.9083 × 10  3°C^{1}
B =  5.775 × 10  7°C^{2}
C =  4.183 × 10  12°C^{4}
The use of Equation 8 shows that nonlinearity errors increase for temperatures outside the band of 0°C to +200°C (Figure 4, pink). Using Equation 9 (blue graph) reduces the error to negligible levels except at very low temperatures.
Figure 4. Linearity error vs. temperature for a PRTD, calculated with Equation 8 (pink) and Equation 9 (blue).
Figure 5 enlarges a portion of Figure 4 over a narrower temperature range. It shows that the errors within a smaller range (between 20°C and +100°C), when using Equation 8, are within ±0.15%. These errors become nearly negligible when we use Equation 9. Precision measurements over a wider temperature range (200°C to +800°C) require the implementation of these linearization algorithms using Equations 9 and 10. (These algorithms will be discussed in a future article.)
Figure 5. Amplified view from Figure 4, showing area where the two graphs intersect.
MAX11200 Measurement Resolution
The MAX11200 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 2 circuit using Equations 11 and 12:
R_{TLSB} = (V_{REF} × (T_{CMAX}  T_{CMIN}))/(FS × (V_{RTMAX}  V_{RTMIN})) (Eq. 11) R_{TNFR} = (V_{REF} × (T_{CMAX}  T_{CMIN}))/(NFR × (V_{RTMAX}  V_{RTMIN})) (Eq. 12)
Where R_{TLSB} is the PRTD resolution at 1 LSB; R_{TNFR} is the PRTD noisefree resolution (NFR); V_{REF} is the reference voltage; T_{°CMAX} is the maximum measurement temperature; T_{°CMIN} is the minimum measurement temperature; V_{RTMAX} is the PRTD voltage drop at maximum measurement temperature; V_{RTMIN} is the PRTD voltage drop at measurement temperature; FS is the ADC fullscale code for a MAX11200 in a singleended configuration (2^{23}1); and NFR is the ADC noisefree resolution for a MAX11200 in the singleended configuration (2^{20}1 at 10sps).
Table 5 lists calculations of the measurement resolution using Equations 11 and 12 for the PTS1206100Ω and PTS12061000Ω.
Table 5. TemperatureMeasurement Resolution
V_{REF}  T_{C}  R_{T}100  R_{T}1000  R_{A} (100)  R_{A} (1000)  R_{TLSB} (100)  R_{TLSB} (1000)  R_{TNFR} (100)  R_{TNFR} (1000) 
(V)  (°C)  (Ω)  (Ω)  (Ω)  (Ω)  (°C/LSB)  (°C/LSB)  (°C/NFR)  (°C/NFR) 
3  55  78.32  783.19  8200  27000  
3  0  100  1000  8200  27000  0.00317  0.000926  0.021  0.0073 
3  20  107.79  1077.9  8200  27000  
3  155  159.19  1591.91  8200  27000 
Table 5 provides the calculated values of °C/LSB error and °C/NFR error for a temperature range of 55°C to +155°C. Noisefree resolution (NFR) represents the minimum temperature value that can be differentiated by the ADC. An R_{TNFR}1000 value of 0.007°C/NFR easily allows a temperature resolution better than 0.05°C within the given range, which is more than sufficient for most industrial and medical applications.
Another way to consider the ADC requirement for this application is to look at the expected voltage levels for different temperature points, as shown in Table 6. The last row shows the range of differential voltage output for PRTD100 and PRTD1000 devices. The set of equations on the right calculates how many noisefree codes are produced by the MAX11200 ADC.
Table 6. Temperature Measurement Range for ADC in Figure 6

Noise free codes = (V_{MAX}  V_{MIN})/Input referred noise Noise free codes = 82.46mV/2.86µV_{PP} Noise free codes = 28,822 codes Temp (accy) = 210°C/28.82K Temp (accy) = 0.007°C 
Note that the total range of output signal in PRTD applications is about 82mV. The MAX11200 has an extremely low inputreferred noise of 570nV at 10sps, which gives the application a noisefree resolution of 0.007°C over a 210°C span.
Figure 6. Block diagram of the precision dataacquisition system (DAS) used for measurements in this article. Based on the MAX11200 ADC (Figure 3), the DAS includes a provision for simple calibration and computergenerated linearization.
As shown in Figure 6, the MAX11200's GPIO1 pin is set as an output to control the relay calibration switch, which selects either the fixed R_{CAL} resistor or the PRTD. This versatility improves the system precision and reduces the required calculations to those for the initial values of R_{A} and R_{T}.
Conclusion
In recent years the decline in price and package size for a PRTD has made these devices desirable for a variety of precision temperaturesensing applications. Such applications require a lownoise ADC (like the MAX11200) if the ADC and surfacemount 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.
High noisefree resolution, integrated buffers, and GPIO drivers allow the MAX11200 to interface directly with new highsensitivity 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, allowing the designer to implement a 2wire interface for distances up to 2 meters.
References
 PTS Series  PtSensors from Vishay Beyschlag, https://www.vishay.com/docs/28762/ptsserie.pdf.
 Maxim application note 3775, "Design Considerations for a LowCost Sensor and A/D Interface."
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APP 4875:
APPLICATION NOTE 4875, AN4875, AN 4875, APP4875, Appnote4875, Appnote 4875 
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