Linearisation of TC & RTD

[Gaurav Gawade]

Hello,

As a novice, I'm not aware of how to linearise a thermocouple or RTD uisng 16-bit delta sigma ADC.

I'm trying to implement this using ATmega16 uC interfaced with ADC using I2C.

Please suggest me a simple algorithm for linearising the thermocouple and RTD using C language.

 

[Sabin]

For thermistors, use Hart and Steinhart Equation. RTDs are quite linear though may need to correct cold junction issues with proper resistors
 ……can use the following code –

1. #include <SPI.h>
2. #include "Adafruit_MAX31855.h"
3.  
4. #define DO 12
5. #define CS 11
6. #define CLK 10
7. Adafruit_MAX31855 thermocouple(CLK, CS, DO);
8.  
9. void setup() {
10. Serial.begin(9600);
11. Serial.println("MAX31855 test");
12. // wait for MAX chip to stabilize
13. delay(500);
14. }
15. void loop() {
16. // Initialize variables.
17. int i = 0; // Counter for arrays
18. double internalTemp = thermocouple.readInternal(); // Read the internal temperature of the MAX31855.
19. double rawTemp = thermocouple.readCelsius(); // Read the temperature of the thermocouple. This temp is compensated for cold junction temperature.
20. double thermocoupleVoltage= 0;
21. double internalVoltage = 0;
22. double correctedTemp = 0;
23.  
24. // Check to make sure thermocouple is working correctly.
25. if (isnan(rawTemp)) {
26. Serial.println("Something wrong with thermocouple!");
27. }
28. else {
29. // Steps 1 & 2. Subtract cold junction temperature from the raw thermocouple temperature.
30. thermocoupleVoltage = (rawTemp – internalTemp)*0.041276; // C * mv/C = mV
31.  
32. // Step 3. Calculate the cold junction equivalent thermocouple voltage.
33.  
34. if (internalTemp >= 0) { // For positive temperatures use appropriate NIST coefficients
35. // Coefficients and equations available from http://srdata.nist.gov/its90/download/type_k.tab
36.  
37. double c[] = {-0.176004136860E-01, 0.389212049750E-01, 0.185587700320E-04, –0.994575928740E-07, 0.318409457190E-09, –0.560728448890E-12, 0.560750590590E-15, –0.320207200030E-18, 0.971511471520E-22, –0.121047212750E-25};
38.  
39. // Count the the number of coefficients. There are 10 coefficients for positive temperatures (plus three exponential coefficients),
40. // but there are 11 coefficients for negative temperatures.
41. int cLength = sizeof(c) / sizeof(c[0]);
42.  
43. // Exponential coefficients. Only used for positive temperatures.
44. double a0 = 0.118597600000E+00;
45. double a1 = –0.118343200000E-03;
46. double a2 = 0.126968600000E+03;
47.  
48.  
49. // From NIST: E = sum(i=0 to n) c_i t^i + a0 exp(a1 (t – a2)^2), where E is the thermocouple voltage in mV and t is the temperature in degrees C.
50. // In this case, E is the cold junction equivalent thermocouple voltage.
51. // Alternative form: C0 + C1*internalTemp + C2*internalTemp^2 + C3*internalTemp^3 + … + C10*internaltemp^10 + A0*e^(A1*(internalTemp – A2)^2)
52. // This loop sums up the c_i t^i components.
53. for (i = 0; i < cLength; i++) {
54. internalVoltage += c[i] * pow(internalTemp, i);
55. }
56. // This section adds the a0 exp(a1 (t – a2)^2) components.
57. internalVoltage += a0 * exp(a1 * pow((internalTemp – a2), 2));
58. }
59. else if (internalTemp < 0) { // for negative temperatures
60. double c[] = {0.000000000000E+00, 0.394501280250E-01, 0.236223735980E-04, –0.328589067840E-06, –0.499048287770E-08, –0.675090591730E-10, –0.574103274280E-12, –0.310888728940E-14, –0.104516093650E-16, –0.198892668780E-19, –0.163226974860E-22};
61. // Count the number of coefficients.
62. int cLength = sizeof(c) / sizeof(c[0]);
63.  
64. // Below 0 degrees Celsius, the NIST formula is simpler and has no exponential components: E = sum(i=0 to n) c_i t^i
65. for (i = 0; i < cLength; i++) {
66. internalVoltage += c[i] * pow(internalTemp, i) ;
67. }
68. }
69.  
70. // Step 4. Add the cold junction equivalent thermocouple voltage calculated in step 3 to the thermocouple voltage calculated in step 2.
71. double totalVoltage = thermocoupleVoltage + internalVoltage;
72.  
73. // Step 5. Use the result of step 4 and the NIST voltage-to-temperature (inverse) coefficients to calculate the cold junction compensated, linearized temperature value.
74. // The equation is in the form correctedTemp = d_0 + d_1*E + d_2*E^2 + … + d_n*E^n, where E is the totalVoltage in mV and correctedTemp is in degrees C.
75. // NIST uses different coefficients for different temperature subranges: (-200 to 0C), (0 to 500C) and (500 to 1372C).
76. if (totalVoltage < 0) { // Temperature is between -200 and 0C.
77. double d[] = {0.0000000E+00, 2.5173462E+01, –1.1662878E+00, –1.0833638E+00, –8.9773540E-01, –3.7342377E-01, –8.6632643E-02, –1.0450598E-02, –5.1920577E-04, 0.0000000E+00};
78.  
79. int dLength = sizeof(d) / sizeof(d[0]);
80. for (i = 0; i < dLength; i++) {
81. correctedTemp += d[i] * pow(totalVoltage, i);
82. }
83. }
84. else if (totalVoltage < 20.644) { // Temperature is between 0C and 500C.
85. double d[] = {0.000000E+00, 2.508355E+01, 7.860106E-02, –2.503131E-01, 8.315270E-02, –1.228034E-02, 9.804036E-04, –4.413030E-05, 1.057734E-06, –1.052755E-08};
86. int dLength = sizeof(d) / sizeof(d[0]);
87. for (i = 0; i < dLength; i++) {
88. correctedTemp += d[i] * pow(totalVoltage, i);
89. }
90. }
91. else if (totalVoltage < 54.886 ) { // Temperature is between 500C and 1372C.
92. double d[] = {-1.318058E+02, 4.830222E+01, –1.646031E+00, 5.464731E-02, –9.650715E-04, 8.802193E-06, –3.110810E-08, 0.000000E+00, 0.000000E+00, 0.000000E+00};
93. int dLength = sizeof(d) / sizeof(d[0]);
94. for (i = 0; i < dLength; i++) {
95. correctedTemp += d[i] * pow(totalVoltage, i);
96. }
97. } else { // NIST only has data for K-type thermocouples from -200C to +1372C. If the temperature is not in that range, set temp to impossible value.
98. // Error handling should be improved.
99. Serial.print("Temperature is out of range. This should never happen.");
100. correctedTemp = NAN;
101. }
102.  
103. Serial.print("Corrected Temp = ");
104. Serial.println(correctedTemp, 5);
105. Serial.println("");
106.  
107. }
108.  
109. delay(1000);
110.  
111. }

[Amerdas D K]

RTD is quite linear, for thermocouple use cold junction and a resistor of appropriate value

[Author]

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