## Thermocouple Design

### Objective:

Design a 3V temperature measurement system using a K type TC at 125°C with an accuracy of 2.5°C

### Solution:

• Understand there are multiple contributing components to the accuracy of a TC measurement system. This includes the accuracy of the TC itself, the accuracy of the temp sensor used for measuring reference junction temperature and the accuracy/resolution of the analog to digital converter.
• ADS1118IDGST is the ideal Low power Solution for Thermocouples with reference junction compensation. It has an internal Temperature Sensor whose absolute accuracy is 0.5C at 25C. The integrated Programmable Gain Amplifier improves resolution.

Thermocouple measurement: Estimate of Accuracy/Resolution

• Estimate of Accuracy using the Total Unadjusted Error Calculation Approach:
• Example using K-type TC at 150°C Using FS +/- 0.256V;

Thermocouple Voltage at 150°C = 6.138mV

• Estimate of ADC voltage conversion absolute accuracy at 150°C :

Total Error = [(offset)2 + (gain error)2 + (INL)2]1/2

• Offset Error = +/- (2 LSB)*(0.256V*2) /( 216 -1)= +/-15.63µV
• INL Error = (1 LSB)*(0.256V*2) / (216-1) =+/-7.81µV
• Gain Error = +/-0.15%*6.138 =+/-9.207µV
• This yields an accuracy error = +/-19.75µV or +/- (19.75µV/ 40µV/°C) = +/-0.494°C

Total Accuracy Error= [(IC Temp Sensor)2 + (ADC Error)2 +(Thermocouple Error)2]1/2

Total Accuracy Error= [(0.5 °C)2 + (0.494°C)2 +(2.2°C)2]1/2

Total Accuracy Error =  +/-2.3095°C @ 150°C

• Estimate of Accuracy using the Total Unadjusted Error Calculation Approach:
• Example using K-type TC at -40°C Using FS +/- 0.256V;

Thermocouple Voltage at -40°C = -1.527mV

• Estimate of ADC voltage conversion absolute accuracy at 150°C :

Total Error = [(offset)2 + (gain error)2 + (INL)2 ]1/2

• Offset Error = +/- (2 LSB)*(0.256V*2) /( 216 -1)= +/-15.63µV
• INL Error = (1 LSB)*(0.256V*2) / (216-1) =+/-7.81µV
• Gain Error = +/-0.15%*1.527mV =+/-2.29µV
• This yields an accuracy error = +/-17.62µV or +/- (17.62µV/ 40µV/°C) = +/-0.441°C

Total Accuracy Error= [(IC Temp Sensor)2 + (ADC Error)2 +(Thermocouple Error)2]1/2

Total Accuracy Error= [(0.5 °C)2 + (0.441°C)2 +(2.2°C)2]1/2

Total Accuracy Error =  +/-2.298°C @ -40°C

• Example using K-type TC

Using FS +/- 0.256V

• Calculation of ADC Resolution:

Noise = ~8µV p-p; at +/-0.256 scale 128SPS
SNR (dB) = 20*log10(Noise / Full-Scale)
SNR (dB)  = +20*log10(8 µV/(0.256*2 V)) = -96.12dB
SNR (dB)= 6.02 N + 1.761 where  N = Noise Free Bits
Noise Free Bits = ( 96.12 – 1.76)/6.02 = 15.67
Resolution (Volts) = 0.256 V *2 / (215.67 -1)= 24.35µV
Assuming Seebeck Coefficient of 40µV/°C for K-type
Resolution = 24.35µV/ 40 µV/°C = 0.244 °C/bit; (Noise Free)

NOTE:  Total error in accuracy of temperature measurement is dominated by the +/- 2.2°C  rated K-type Thermocouple on this Example.  Higher accuracies can be obtained by using special grade K-type or other types of Thermocouples.