Measure and Model a Thermistor

A thermistor is an inexpensive (and often, inaccurate) passive component for measuring temperature. This instructable shows how to derive model parameters for a thermistor, given a few points using only hot (boiling) and cold (ice) water.

• Thermistor - Great if we know what value it is, otherwise we can test it.
• Styrofoam Ice Chest - A small shipping container works well.
• Multimeter - Any should work, but a better quality brand gives better results.
• Soldering Iron - We need to connect some wires together.
• Hot Glue Gun - Some way to waterproof the thermistor leads is needed.
• Stove Top - We need to boil water.
• Ice - We need ice water.

Beyond that, it's just math, physics, electronics, and some modeling.

A good connection is necessary to keep the thermistor connected to the multimeter. To do so, solder two wires to the thermistor. The wire-ends should be wrapped around the multimeter leads to keep them in place. Any bare metal surfaces on the thermistor must be insulated because water is typically slightly conductive due to ions in the water. To insulate the thermistor, use blobs of hot-glue. Leave some part of the thermistor exposed.

You'll need to pour in a cup of room-temperature (not critical) water into the container. Each time a cup is added, the top level should be marked with a pencil, pen, or marker. Doing this until the container is full results in a graduated container. You can then empty the container and pour in exactly four cups by looking at the graduations (think graduated cylinder).

The Styrofoam cooler is used to keep heat transfer to and from the outside environment from having a significant impact on the water temperature inside the cooler. Do the following to collect the first measurement point at 0°C:

1. Fill the container with solid ice.
2. Add water to the container to cover the ice.
3. Place the thermistor into the container.
4. Cover the container with its lid.
5. Wait 20-30 minutes for an equilibrium temperature to be reached between water, originally at room temperature, and ice.
6. Take a measurement of the thermistor resistance at this point.

Once you're done, don't just dump the ice and water mixture out. Instead, use a strainer to remove the ice from the water. Because it's inside the cooler, it will still stay at 0°C for a long time while inside the cooler. This ice-cold water (but without ice) is needed to capture temperature points between 0°C and 100°C.

In order to model or calibrate an unknown thermistor, more points are needed. To do so, start by boiling a pot of water. Once there is a consistent rolling boil, the temperature is about 100°C. If you live at really high altitudes, adjust the boiling temperature to your specific elevation. Next do the following:

1. Measure the resistance with the thermistor in water as it is boiling. This is the 100°C point.
2. Leave only 3 cups of ice-cold (without ice-pieces) water in the cooler.
3. Place the thermistor in the cooler to measure its resistance.
4. Add 1 additional cup of the boiling water to the cooler.
5. Place the cover on the cooler.
6. Wait 10-20 minutes.
7. Take a measurement and note the ratio of hot cups vs. cold cups.
8. Repeat from (4) until cooler is full.

With these additional points, the thermistor can be modeled.

For any thermistor, the following parameters may be extracted from experimental data, or be given in a datasheet:

• Table: Some manufacturers just provide a table of resistance vs. temperature. An easy way to find the points not listed is to just assume that the distance between one point and its nearest neighbor is a line. Given two points, the slope and intercept for this small region can be found.
• Exponetial Model: Typically, the marking on a thermistor is the nominal resistance at room temperature (25°C). If the manufacturer gives a B-value, this is the B-value used in the exponential equation. Given these facts, the A-value can be calculated, along with other values of resistance. This is the most popular model for thermistors because it is easy to use.
• Steinhart-Hart Model: This is the most accurate model, but it is the most difficult to use mathematically.

The attached pictures are as follows:

• Graph: This shows the comparison of all the models. They're all pretty close to one another, except at cold temperatures.
• Bath Temperature: This is the derivation of bath temperature given mixing of hot and cold water at specific volumes.
• Exponential Model: This shows how linearization of the exponential model works.
• Steinhart-Hart Model: This shows how linearization of the Steinhart-Hart model works. I didn't derive the conversion back to resistance, this was found using Wikipedia.

Lastly, there's a spreadsheet with two tabs:

• Fitting: This tab contains actual experimental results as well as modeling data.
• Examples: This tab shows how to linearize and do a least-squares linear fitting on the linearization,

Thanks for reading!