### AN-1087: Thermocouple Linearization When Using the AD8495/AD8496/AD8497 (Rev. 0) PDF

```AN-1087
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
by Reem Malik
INTRODUCTION
provide a simple, low cost solution for measuring thermocouple
temperatures. These amplifiers simplify many of the difficulties
of measuring thermocouples. A fixed-gain instrumentation amplifier amplifies the small thermocouple voltage, and an integrated
temperature sensor performs cold junction compensation.
The AD849x is optimized to measure and amplify J and K type
thermocouple signals for a linear 5 mV/°C response such that
VOUT = (TMJ × 5 mV/°C) + VREF
Whether a thermocouple measurement needs linearization
depends on the type of thermocouple chosen, the required
system accuracy, and the temperature range being measured.
The nonlinearity of thermocouple signals is well studied and
is constant for a specific thermocouple type. Therefore, the
measurement system can compensate for it.
COMPENSATION
where TMJ is the temperature at the measurement junction of
the thermocouple.
The AD849x output is accurate to within 2°C across the entire
range of measurement and ambient temperatures listed in Table 1.
This application note describes ways to achieve even greater
accuracy when operating at or measuring temperatures outside
the specified ranges using the AD849x.
THERMOCOUPLE NONLINEARITY
The voltage generated by a thermocouple is inherently nonlinear.
For example, a J type thermocouple changes by 52 μV/°C at 25°C
and by 55 μV/°C at 150°C. K type thermocouples tend to be much
more linear, staying fairly near 41 μV/°C when temperatures are
above 0°C. The voltage response of a thermocouple to a temperature gradient can be described by a greater than sixth-order
polynomial (see Figure 1).
100
80
Although the AD849x does not actively correct thermocouple
nonlinearity, the amplifiers are precision trimmed to match the
transfer characteristics of J type and K type thermocouples. This
means that the AD849x compensates for nonlinearity by choosing
a specific section of the thermocouple curve and performing a
linear best fit to this section to create a 5 mV°/C output.
Table 1 shows the temperature ranges chosen, resulting in
an error from thermocouple nonlinearity of less than ±2°C.
Figure 2 shows the nonlinearity error graphically.
Table 1. AD849x ±2°C Accuracy Temperature Ranges
Thermocouple
Type
J
K
J
K
Part
Max
Error
±2°C
±2°C
±2°C
±2°C
Ambient
Temperature
Range
0°C to 50°C
0°C to 50°C
25°C to 100°C
25°C to 100°C
Measurement
Temperature
Range
−35°C to +95°C
−25°C to +400°C
+55°C to +565°C
−25°C to +295°C
E
2.0
J
T
60
1.5
–1.0
Rev. 0 | Page 1 of 4
MEASUREMENT JUNCTION TEMPERATURE (°C)
Figure 2. AD849x Output Error due to Thermocouple Nonlinearity
09282-001
–2.0
600
The AD849x linearly amplifies the (cold junction compensated)
thermocouple signal. This means that the output signal is as
nonlinear as the input signal from the thermocouple.
650
–1.5
550
Figure 1. Seebeck Coefficient of Thermocouple vs. Temperature
500
1400
450
1200
400
1000
350
800
300
600
250
400
TEMPERATURE (°C)
200
200
150
0
100
–200
–0.5
0
0
–400
0
50
20
0.5
–50
K
OUTPUT ERROR (°C)
1.0
40
09282-002
SEEBECK COEFFICIENT (µV/°C)
An application may require better nonlinearity (meaning greater
accuracy) than is provided directly by the thermocouple in that
temperature range. In such cases, linearization, or correction, of
the thermocouple measurement is required.
AN-1087
Application Note
Each part in the AD849x family is precision trimmed to optimize
a linear operating range for a specific thermocouple type and
for specific measurement and ambient temperature ranges. The
following three parameters are trimmed to achieve a 5 mV/°C
output with minimal errors:
•
•
•
Gain of the amplifier
Offset of the amplifier (error voltage at 0°C to achieve
125 mV at 25°C)
Scale factor of the temperature sensor/cold junction
compensator
VTC = fNIST (TMJ − 0) − fNIST (TRJ − 0)
Output values for intermediate temperatures can be interpolated
or calculated using the AD849x output equations and the NIST
thermoelectric voltage tables referred to 0°C.
For the AD8494, the equation is as follows:
VTC ‫ ן‬TMJ – TRJ = (TMJ − 0) − (TRJ − 0)
TMJ = fNIST ((VOUT − VREF)/96.7)
The following transfer function should be used to determine
the actual thermocouple voltages being measured by the
AD849x (see Table 2 for specific values for each part).
For the AD8495, the equation is as follows:
TMJ = fNIST ((VOUT − VREF − 1.25 mV)/122.4)
VOUT − (TRJ × CJC ) − VOFFSET − VREF
For the AD8496, the equation is as follows:
Gain
TMJ = fNIST ((VOUT − VREF − 20.2 mV)/90.35)
where:
CJC is the cold junction compensation scale factor.
VOFFSET is the error voltage at 0°C to achieve 125 mV at 25°C.
VREF is the user input voltage.
Gain is the gain of the amplifier.
For the AD8497, the equation is as follows:
TMJ = fNIST ((VOUT − VREF + 0.98 mV)/122.4)
Table 2. Transfer Function Values for the AD8494, AD8495,
Part
The second method is to use the following equations, where TMJ
is the temperature at the thermocouple measurement junction,
and fNIST is a millivolt-to-temperature function based on the
standard lookup tables or on equations published by the
National Institute of Standards and Technology (thermocouple
databases can be found at http://srdata.nist.gov/its90/main).
Recall that VTC ‫ ן‬TMJ − TRJ, such that
The thermocouple voltage, VTC, is a function of the thermocouple type, the measurement junction temperature (TMJ),
and the reference junction temperature (TRJ).
VTC =
NIST Thermoelectric Voltage Lookup Tables
Gain
96.7
122.4
90.35
122.4
CJC Factor (mV/°C)
5
4.95
4.8
5.0392
Offset (mV)
0
1.25
20.2
−0.98
LINEARITY CORRECTION ALGORITHMS
Using the same example as for the first method (an AD8495 at
room temperature with a grounded reference pin connected to
a K type thermocouple that reads 1 V), the correction procedure
is as follows:
TMJ = fNIST ((1 V − 1.25 mV)/122.4) = fNIST (8.158 mV)
1.
2.
Thermocouple nonlinearity is typically corrected with a
microcontroller in the digital domain. One of two correction
algorithms can be used.
AD849x Output Lookup Table
The first method is to use Table 3, which lists the ideal AD849x
output voltages as a function of the temperature for J type and
K type thermocouples with the specified junction temperatures.
For example, an AD8495 at room temperature (25°C) with a
grounded reference pin connected to a K type thermocouple
outputs 1 V. Using the 5 mV/°C transfer function, 1 V represents
200°C. For greater accuracy, the user must calculate the temperature that corresponds to the 1 V output as follows:
1.
2.
Table 3 indicates that at a measurement junction temperature of 200°C, the actual AD8495 output is 0.999 V, and at a
measurement junction temperature of 220°C, it is 1.097 V.
Linear extrapolation between these two points yields an
answer of 200.2°C at 1 V.
Rev. 0 | Page 2 of 4
Consulting a standard K type thermocouple table indicates
that at a measurement junction temperature of 200°C, the
thermoelectric voltage of the thermocouple is 8.138 mV,
and at a measurement junction temperature of 201°C, the
thermoelectric voltage is 8.178 mV.
Linear extrapolation yields a final answer of 200.5°C.
Application Note
AN-1087
Table 3. Actual AD849x Results Reflecting Thermocouple Nonlinearity
Measurement
Junction
Temperature (°C)
−260
−240
−220
−200
−180
−160
−140
−120
−100
−80
−60
−40
−20
0
20
25
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
520
540
560
580
600
620
640
660
680
AD8494/AD8495 Output, TA = TRJ = 25°C
Ideal Output (V)
Actual Output (V)
with J Type
with K Type
−1.3
−0.786
−1.2
−0.774
−1.1
−0.751
−1
−0.719
−0.9
−0.714
−0.677
−0.8
−0.658
−0.627
−0.7
−0.594
−0.569
−0.6
−0.523
−0.504
−0.5
−0.446
−0.432
−0.4
−0.365
−0.355
−0.3
−0.278
−0.272
−0.2
−0.188
−0.184
−0.1
−0.095
−0.093
0
0.002
0.003
0.1
0.100
0.100
0.125
0.125
0.125
0.2
0.201
0.200
0.3
0.303
0.301
0.4
0.406
0.402
0.5
0.511
0.504
0.6
0.617
0.605
0.7
0.723
0.705
0.8
0.829
0.803
0.9
0.937
0.901
1
1.044
0.999
1.1
1.151
1.097
1.2
1.259
1.196
1.3
1.366
1.295
1.4
1.473
1.396
1.5
1.580
1.497
1.6
1.687
1.599
1.7
1.794
1.701
1.8
1.901
1.803
1.9
2.008
1.906
2
2.114
2.010
2.1
2.221
2.113
2.2
2.328
2.217
2.3
2.435
2.321
2.4
2.542
2.425
2.5
2.650
2.529
2.6
2.759
2.634
2.7
2.868
2.738
2.8
2.979
2.843
2.9
3.090
2.947
3
3.203
3.051
3.1
3.316
3.155
3.2
3.431
3.259
3.3
3.548
3.362
3.4
3.666
3.465
Rev. 0 | Page 3 of 4
AD8496/AD8497 Output, TA = TRJ = 60°
Ideal Output (V)
Actual Output (V)
with J Type
with K Type
−1.3
−0.785
−1.2
−0.773
−1.1
−0.751
−1
−0.718
−0.9
−0.642
−0.676
−0.8
−0.590
−0.626
−0.7
−0.530
−0.568
−0.6
−0.464
−0.503
−0.5
−0.392
−0.432
−0.4
−0.315
−0.354
−0.3
−0.235
−0.271
−0.2
−0.150
−0.184
−0.1
−0.063
−0.092
0
0.027
0.003
0.1
0.119
0.101
0.125
0.142
0.126
0.2
0.213
0.200
0.3
0.308
0.301
0.4
0.405
0.403
0.5
0.503
0.505
0.6
0.601
0.605
0.7
0.701
0.705
0.8
0.800
0.804
0.9
0.900
0.902
1
1.001
0.999
1.1
1.101
1.097
1.2
1.201
1.196
1.3
1.302
1.296
1.4
1.402
1.396
1.5
1.502
1.498
1.6
1.602
1.599
1.7
1.702
1.701
1.8
1.801
1.804
1.9
1.901
1.907
2
2.001
2.010
2.1
2.100
2.114
2.2
2.200
2.218
2.3
2.300
2.322
2.4
2.401
2.426
2.5
2.502
2.530
2.6
2.603
2.634
2.7
2.705
2.739
2.8
2.808
2.843
2.9
2.912
2.948
3
3.017
3.052
3.1
3.124
3.156
3.2
3.231
3.259
3.3
3.340
3.363
3.4
3.451
3.466
AN-1087
Measurement
Junction
Temperature (°C)
700
720
740
760
780
800
820
840
860
880
900
920
940
960
980
1000
1020
1040
1060
1080
1100
1120
1140
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
1360
1380
Application Note
AD8494/AD8495 Output, TA = TRJ = 25°C
Ideal Output (V)
Actual Output (V)
with J Type
with K Type
3.5
3.786
3.568
3.6
3.906
3.670
3.7
4.029
3.772
3.8
4.152
3.874
3.9
4.276
3.975
4
4.401
4.076
4.1
4.526
4.176
4.2
4.650
4.275
4.3
4.774
4.374
4.4
4.897
4.473
4.5
5.018
4.571
4.6
5.138
4.669
4.7
5.257
4.766
4.8
5.374
4.863
4.9
5.490
4.959
5
5.606
5.055
5.1
5.720
5.150
5.2
5.833
5.245
5.3
5.946
5.339
5.4
6.058
5.432
5.5
6.170
5.525
5.6
6.282
5.617
5.7
6.394
5.709
5.8
6.505
5.800
5.9
6.616
5.891
6
6.727
5.980
6.1
6.069
6.2
6.158
6.3
6.245
6.4
6.332
6.5
6.418
6.6
6.503
6.7
6.587
6.8
6.671
6.9
6.754
registered trademarks are the property of their respective owners.
AN09282-0-8/10(0)
Rev. 0 | Page 4 of 4
AD8496/AD8497 Output, TA = TRJ = 60°
Ideal Output (V)
Actual Output (V)
with J Type
with K Type
3.5
3.562
3.569
3.6
3.675
3.671
3.7
3.789
3.773
3.8
3.904
3.874
3.9
4.020
3.976
4
4.137
4.076
4.1
4.254
4.176
4.2
4.370
4.276
4.3
4.486
4.375
4.4
4.600
4.474
4.5
4.714
4.572
4.6
4.826
4.670
4.7
4.937
4.767
4.8
5.047
4.863
4.9
5.155
4.960
5
5.263
5.055
5.1
5.369
5.151
5.2
5.475
5.245
5.3
5.581
5.339
5.4
5.686
5.433
5.5
5.790
5.526
5.6
5.895
5.618
5.7
5.999
5.710
5.8
6.103
5.801
5.9
6.207
5.891
6
6.311
5.981
6.1
6.070
6.2
6.158
6.3
6.246
6.4
6.332
6.5
6.418
6.6
6.503
6.7
6.588
6.8
6.671
6.9
6.754
```