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Principles of Linearizing the Thermistor.

Thermistor Resistance vs. Deg F.

Tonight we are going to take our first steps toward making that scary looking exponential curve of the thermistor resistance into something we can use. The plot show in the first picture is the one we created in “Our First Look at Thermistor details” and was created by simply plotting the resistance values in the data sheet after converting from degrees C to degrees F.

My Normalized Resistance Curve.

To make things a little easier to talk about in the rest of this discussion I created an exponential curve with the center value of one Ohm. This is to keep the math simple and to avoid having to worry about K Ohms, scientific numbers, and decimal points. Things will get more complicated soon enough. The voltage source will be one volt, again for the same reasons. The x-axis on this plot means nothing except the order of the way I calculated the resistance. It will be consistent thoughout this post.

Although this is frightening to look at, lets go back and think of the fundamentals.  Normally when we measure something we are measuring the voltage across some device.  The only way the voltage across this variable resistor could follow the same curve as the resistance is if we kept the current into the resistor constant.  Although it is possible to buy or build constant current sources, normally we use constant voltage sources.  Lets also think about what we desire. Ideally, we would like a constant voltage change for each of these resistor steps. However, since we will be putting this into an Analog to Digital Converter, we can use the power of the computer to help us straighten this curve if we can get a curve that does the following things:

  • Pretty much consume the full range of the A/D converter (Probably 0 to 5 V).
  • Always step up or step down with a change in resistance but not sometimes one way and other times the other way.
  • A good size change even at the “flat spots” of the curve so we can detect a change.

Simple Series Circuit.

Our first attempt to do this is to use a simple series circuit.  In this circuit, I set the resistance of the series resistor at the mid point of our resistance curve.  If you think about what is happening here, we are basically measuring the current though the circuit (V=I x R and R = 1) and both the current and voltage across the variable resistor are changing at the same time.

The voltage measure with the previous circuit.

This  actually gives us a curve that comes close to meeting our desired results.  Changing the source voltage would increase the changes to the range we desire, but the curve is still kind of flat on each end.  In the middle portion of the curve the plot is very linear.



A series-parallel circuit to linearize the resistance.

The next circuit we will try is a series parallel resistance circuit.  The resistor in parallel with our variable resistor is again chose to be at 1 Ohm, the mid-point value.  The series resistor was chosen to be at 0.5 which is the same as the parallel resistance of Rvar and the 1 Ohm at the mid point.   If we think about the probable results once the resistance of the variable resistor gets above 1 Ohm the effect of changing the resistance of Rvar has less effect on the total circuit.

Voltage measure in he Series-Parallel Circuit.

The picture to the right shows the voltage values produced by this circuit and the series circuit is shown for comparison.  A better comparison would be if this circuit is amplified and a offset was added to it.  The change of voltage is better for the smaller values of resistance, but the changes “flatten out” as the resistance of Rvar becomes greater.


Op-amp circuit for our linearization attempt.

The final way we will attempt to develop a more linear curve is to use the variable resistor to change the gain in an opamp circuit.   The circuit is circuit is a modification to our inverting amplifier.  We apply a fixed voltage in to the circuit through a resistor (Rg) and the feedback varies because of Rvar.   Since the gain of an inverting amplifier is -Rf/Rg, this circuit would be very bad if we simply used the variable resistance of Rvar as the feedback.   A better answer is to use another resistor in parallel with it.  Again the parallel resistor was chosen at the mid point value.  Rg was chosen as 0.5 Ohms to give a gain of 1 at the mid point value of Rvar.

The output of the op-amp linearization circit.

The opamp circit produces the values shown in the curve to the right.   I am not sure this is an improvement over the curve shape of the series resistor, but it does have some advantages in that it will be easier to deal with the variability of the the thermistor.  Obviously since we ended up with a negative output voltage we will have to deal with that issue also.


These three circuits and the values chosen for the resistors were chosen to make calculations simple.  I used a computer program to generate the numbers, but that was mostly done to produce nice graphs.  It could just as easily been done using a spreadsheet and with not much effort a calculator and done by hand.  Obviously, the values would not work with an actual opamp because the resistance is too low, but it is easy enough to muliply and or divide by 10000 to scale the 1 Ohm resistor mid point to our thermistor 10,000 ohm 25 deg C value.  The op-amp would be perfectly happy there.  If future posts we will have to deal with the conversion from deg C and/or deg F to resistance to get at the final calibration of this device.

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