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Linearizing our Thermistor.

The first part of our Thermistor Circuit.

We are not to the end of talking about the thermistor yet but we can see the light at the end tunnel. Last night’s post “Principles of linearization” was a long one with lots of math… tonight’s post is relatively short and mostly pictures. I think we all can use the brain break. (That is if we have not already broke our brains.)

 

To create the circuit shown above I simply took the op-amp circuit in the previous post and multiplied all the resistor values by 10,000.  The Rvar in the previous post has been replace with our thermistor and instead of using values generated to produce an exponential plot, I used the actual values we obtained from the thermistor datasheet.

The full temperature range of the thermistor.

The numbers were crunched by calculating the total resistance of Rfp in parallel with the thermistor for each temperature in the datasheet.   This then became Rf and the standard equation for an inverting amplifier was used.  The plot does not look all that bad.  However, it is very doubtful that we will ever be interested in temperatures as low as -50 C (-58 F) nor as high as 150 C (302 F) for solar experiments.

-30 C to 110 C

I threw out the high temp values above 110 C (230 F) and the low values below -30 C (-22F) and ended up with the plot shown to the left.  Things are looking even better. I still have some bow at the ends but in general we could live with this.
Let’s go one step further.

 

-20C to 70C

In this plot I threw out all temperatures above 70 C (158 F) and all below -20 C (-4 F). The cold temp is reasonable where I live (N.E. Alabama). My guess is the hot temp is also reasonable for the maximum temperature I would allow a solar temperature collector to become.

 

Now that things look all rosy, it is time to rain the the parade again.  We do have a few problems to consider.  First, this produced a negative voltage, but our A-D converter wants a positive voltage.   That would be easy to fix by using a negative Vin.  A little bigger problem is we are no-longer using the full range of the A-D convertor, but that is not much of a problem either.   We could use a higher value for Vin if we are willing to throw away the low bit values.  An even better solution for both problems would be to follow the this circuit with a summing amplifier.   We could then add a negative offset as well as increse the gain.

Our biggest set of problems is the tolerance of the components as well as 5K resistors are not available.   The tolerance problem is no so great with the resistors.  These are easily available in +/-5% tolerance and fairly easily in +/- 1% tolerance.   The big problem will be the thermistor itself.  It has a base value tolerance of +/-10% and a gain tolerance of +/- 2%.  We are going to have to figure out a way to adjust out of these problems and calibrate our circuit.   Sorry, just about the time it looked like our brains are going to get a break, I come up with a headache.

It is a whole lot easier to deal with this on paper than it is in real life so on we go… but that is a future post.   For now, celebrate!   We have come a long way!

Gary

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