1. Calibration of a Thermistor Voltage Divider Portland State University Department of Mechanical Engineering ME 121: Engineering Problem Solving

2. A Voltage Divider for Thermistors The thermistor is located in the upper leg of a voltage divider 5V thermistor Analog input 10 kΩ Review: Why use the upper leg and not the lower leg? ME 121: Engineering Problem Solvingpage 1

3. Calibration Equipment The thermistor and a reference thermometer are placed in an insulated mug that is filled with a range of mixtures of hot and cold water. Thermistor probe Voltage divider for Arduino input Reference Thermometer Note:The fixed resistor in the voltage divider is an integral part of the thermistor calibration. Replacing the fixed resistor with another resistor, even one of the same nominal voltage, will change the calibration. +5V or digital output analog input Insulated Coffee mug ME 121: Engineering Problem Solvingpage 2

4. Calibration Equipment A digital kitchen thermometer provides the reference standard for calibration of the thermistor probe. ME 121: Engineering Problem Solvingpage 3

5. Calibration Procedure Once the equipment is assembled and ready to use, perform the following steps to obtain the calibration data. A source of hot water is provided in the laboratory. 1.Fill the coffee mug with water at a desired temperature. Mix hot and cold water as necessary. 2.Insert the reference thermometer and the thermistor probe through the hole in the lid of the mug. 3.Wait for the thermistor probe signal and the reading of the reference temperature to stabilize. 4.Record the temperature and the output of the Arduino analog input reading. Store a large sample of readings so that statistics can be computed. 5.Return to step 1 until you have collected calibration measurements at 8 to 10 temperatures. Ideally you should randomize the order of the temperatures, i.e., you should not take data only in order of increasing or decreasing temperature. ME 121: Engineering Problem Solvingpage 4

6. Calibration Procedure Use a table to record the nominal measurements along with any qualitative observations ME 121: Engineering Problem Solvingpage 5 T ( ◦ C)V(Volt)Comments

7. Calibration Procedure Suggestions for improving your results: Let your system come into equilibrium before taking readings.  The thermometer and your thermistor have thermal mass: you need to wait for them to come into thermal equilibrium (i.e., have the same temperature) with the water.  The insulated mug has more thermal mass than the thermometer and the thermistor. It too has to come into equilibrium.  To reduce wait time between measurements, use two thermos mugs. While one mug holds the thermistor, thermometer and the water during the measurements, prep the second mug for calibration at another temperature to give the mug time to equilibrate with the water. When the measurements with the first mug are finished, switch the thermistor and thermometer into the second mug. Use a mug with a lid to reduce heat exchange with the ambient. Randomize the order of temperature measurements ME 121: Engineering Problem Solvingpage 6

8. Calibration Equation The calibration process suggests a curve fit of the form V = f (T ): many voltage readings for each fixed temperature. We could use a polynomial for V (T ). V = c 1 T n + c 2 T n−1 + · · · + c n-1 T + c n (1) However, to control the temperature of the fish tank, we will need T = f (V ). T = a 1 V n + a 2 V n−1 + · · · + a n-1 V + a n (2) Curve fitting of the calibration data is discussed in another set of slides. ME 121: Engineering Problem Solvingpage 7