Temperature Sensors - Self Heating Phenomena

        Temperature sensors can exhibit a phenomenon known as self-heating.  When a temperature sensor is self heated, the sensor itself contributes heat to raise its' own temperature.  In this short note, we want to examine that possibility.  We'll look at it in the worst case scenario, one with a thermistor.  Here's a voltage divider with a thermistor.  Let's examine what happens here.

        In this circuit, the voltage source, Vin, acts to produce a current in the resistor, Ra, and the thermistor temperature sensor, represented by Rt.  The current that flows in the circuit (through every device) is given by:

Notice that the resistance of the thermistor comes into play when you compute the current through the series combination of resistors.  Now imagine the following sequence of events.
  1. The voltage source is turned on, producing a current through the series combination of resistors, Rt and Ra.
  2. The current flowing through the thermistor generates some heat because the thermistor dissipates electrical power.
  3. The heat causes a temperature rise in the thermistor.
  4. The temperature rise in the thermistor causes the resistance of the thermistor to decrease.
  5. The decrease in resistance causes and increase in current through the thermistor.
  6. The increased current through the thermistor generates more heat.
  7. The additional heat raises the temperature even higher.
  8. Go back to step 4.  Ad infinitum!
        The only real question here is whether this ever stops.  If the voltage is low enough the process should stop.  However, even if the process stops, the thermistor is at a temperature higher than its' surroundings.  That means that the temperature it measures is not the surrounding temperature (which is what you want it to be), but one that is higher.  When this happens the measured temperature is higher than the temperature you wanted to measure.  This phenomenon is called self heating.         Self heating is not the worst thing that can happen.  If the voltage is high enough, and if the series resistor, Ra, is low enough, the entire process can accelerate with the result being thermal runaway.  When you have thermal runaway, the thermistor just keeps getting warmer at a faster rate.  The end result is a very hot, damaged, and unusable thermistor.  It's not going to give you a good temperature reading.  Not now, and not in the future!