Calculating Self-Heat

Self-heating occurs when the power applied to the thermistor is greater than what the thermistor can dissipate. This causes the thermistor to "heat up" and change resistance. To calculate self-heat for a thermistor, you need the following information:

1. R vs. T curve for the thermistor you are using.

2. Dissipation constant (the amount of power it takes a thermistor to raise 1șC). Be sure to note whether the dissipation constant is for still air or stirred oil bath.

3. Applied voltage.

We will determine the self-heat for the circuit below. The thermistor, T, is a YSI 46006, 10k Ohms ±0.2șC (0 to 70șC), glass thermistor. We are operating over a temperature range of 0 to 100șC. The dissipation constant for this thermistor is 4mW/șC in still air. The divider resistor R is 10k Ohms and EIN is +5 volts.


The R vs. T curve for thermistor T is:
Temperature (șC)
Resistance (T, ohms)
0
29,940
25
10,000
40
5,592
70
1,990
100
816.8

First, we use Ohm's Law (E=I * R) to determine voltage drop across the thermistor.
Temperature (șC)
Resistance
(T, ohms)
Resistance
(Rt=T+R, ohms)
Current
(IT, amps)
Voltage drop
(ET, volts)
0
29,940
39,940
0.000127
3.734
25
10,000
20,000
0.000250
2.500
40
5,592
15,592
0.000321
1.793
70
1,990
11,990
0.000417
0.830
100
816.8
10,816.8
0.000462
0.378

Next, determine the power applied to the thermistor using equation, P=E2/R. At this point, we check to be sure that we are not exceeding the power rating for the thermistor. The YSI 46006 is rated for a maximum power of 50mW/șC derated to 2mW/șC @ 125șC.
Temperature (șC)
Resistance (T, ohms)
Voltage drop (ET, volts)
Power (PT, watts)
0
29,940
3.734
0.00047
25
10,000
2.500
0.00063
40
5,592
1.793
0.00058
70
1,990
0.830
0.00035
100
816.8
0.378
0.00017

Now that we know the power applied to the thermistor, PT, we can use the dissipation constant (DC) to figure self-heat:

Self-heat = PT / DC
Temperature (șC)
Resistance (T, ohms)
Self-Heat (still air, șC)
0
29,940
0.12
25
10,000
0.16
40
5,592
0.14
70
1,990
0.09
100
816.8
0.04

The maximum thermistor error is the tolerance plus self-heat error.
Temperature (șC)
Tolerance (șC)
Self-Heat (șC)
Total Error
0
0.2
0.12
0.32
25
0.2
0.16
0.36
40
0.2
0.14
0.34
70
0.2
0.09
0.29
100
0.2
0.04
0.34

Call YSI for help with your thermistor applications. The YSI Temperature call center is 800-747-5367 or 937-427-1231.

YSI Technical Note TP-TN017




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