In several previous blogs, I explored the issues with making measurements using thermistors in a theoretical sense. While this is indeed a worthwhile thought-experiment, what happens when the rubber hits the road, so to speak? Is self-heating a real problem and can we measure just how much self-heating occurs, perhaps using the thermistor itself?
Table of Contents
Estimating Worst-Case Self-Heating
In previous blogs, I had indicated that self-heating is dependent on a few factors, including the medium in which the thermistor is in, the specific heat capacity of that medium, if it is flowing and at what velocity, the thermal resistance of the thermistor material itself and the specific heat capacity of the thermistor itself. However, how can we estimate the worst-case self-heating effect?
When initially reading the datasheet and drawings for the Molex thermistors, I totally missed the line listed as dissipation factor. This provides us an indicative figure of self-heating, although the actual conditions under which it is measured is not indicated. This suggests that every 1.5mW dissipated in the thermistor will result in 1°C of self-heating being developed, thus reinforcing the idea that keeping dissipated power as low as possible is favourable. It also gives us an upper bound in terms of power dissipation - if operating at 25 degrees C, the thermistor can only tolerate a 110 degree C rise, therefore the power dissipation is limited at 165mW.
I decided to switch over to focus on the 3kΩ thermistor for this blog purely to maximise the self-heating produced by a digital multimeter. This is because P = I2R, so reducing R enough to allow the DMM to kick up a range (and thus current by 10-fold) has a big impact on dissipated power. We can see just how choosing different ranges has an impact on the self-heating power developed. Unfortunately, at room temperatures, we can already see the DMM self-heating power is quite small, peaking at about 100µW. This graph should be fairly familiar from previous posts.
Knowing the dissipation factor allows the graph to be converted to one of self-heating temperature error. In the worst case, the error is about 0.72°C using the 1kΩ range of the meter which offers up 1mA of current.
At the 10kΩ range, the error is expected to peak at about 0.065°C.
This is a valuable finding as it suggests DMM self-heating is quite small if 10kΩ or greater range is used – significantly below the tolerance error for the thermistor itself and Beta model-fitting errors. If a smaller resistance range is used, the self-heating error can become larger, but still is in the magnitude of thermistor tolerance errors. As errors can be additive, reducing errors is still the best option, but taking things to the extreme level may not be necessary.
Experiment: Measuring Self-Heating by DMM
Nevertheless, I still decided it was worthwhile to try and measure self-heating by DMM by using the thermistor and DMM itself to report on its own self heating. This was accomplished using the 3kΩ thermistor and the Keithley 2110 5.5-digit DMM set to a fixed range of 10kΩ. The DMM was given four hours to warm-up, to avoid any influence of internal temperature drifts.
To ensure the thermistor could self-heat accurately would require putting it into a vacuum chamber to stop heat from being lost through convection, sealing it away from light to avoid radiation, and maintaining temperature equilibrium on its leads to avoid conduction. Obviously, this is not something I could do at home.
Instead, I proceeded with what I could do given the resources at hand. This included using a double-wall, reflective, glass vacuum carafe in which I have the thermistor suspended by its leads. The carafe is like a thermos, keeping the temperature inside relatively stable, while the mirrored reflective coating prevents external radiation from reaching into the thermistor (except via the opening at the top). The thermistor is surrounded by a plastic component sorting box to further arrest air movement, with the lead entry being padded with a putty-like substance to avoid the thermistor touching any of the walls of the plastic box. The top is covered with two pieces of Perspex with a notch cut into it to allow for the leads to pass through. Incidentally, this equipment was left over from my PhD experimentation with UV-C and other LEDs, so it was nice to see it reused.
The leads were tied to the handle of the carafe and plugged into the Keithley 2110 DMM. As the room temperature was about 16-18°C, I checked what the anticipated self-heating power would be:
Yep, 42µW. A tiny, tiny bit of power. Some microcontrollers sleep with around this much power consumption. I had little hope of detecting self-heating at all, but I thought it would be foolish to give up now that everything had been set-up.
At first, I saw an obvious and relatively rapid decline in resistance indicating heating. Eureka! But that joy quickly faded as the trend reversed and it rapidly started increasing again, indicating the thermistor was cooling again. What happened?!
As it turns out … I was off to a false-start. I had my hand on the connector of the thermistor, plugging it in (hence the connection crackle at the beginning of the trace). I didn’t factor that the heat leaving my fingers and into the thermistor leads would eventually travel down the leads and heat up the thermistor. Over time, that excess heat dissipated resulting in the trace going backwards.
To confirm this, I decided to do an exaggerated test. The room temperature was changing slowly, but I decided to grab the connection (touching the metal, forming a parallel resistance that dropped the resistance a bit). The heat from the finger caused a rapid decline in resistance again, whereby letting go resulted in it slowly returning to the overall trend of room temperature. As a result, I was to keep my hands away from the thermistor if I wanted accurate results.
To fix this, for my second attempt, I kept the connections in place but shorted the terminals at the DMM resulting in the current bypassing the thermistor (well, almost all of it). Then, when I was ready to begin, I would just yank the shorting connection which is both far away from the thermistor and had insulated plugs that the transferred heat wouldn’t be measurable.
This time, I had a much more reasonable result – as expected, the resistance fell, but only by a small amount, and plateaued over time. The temperature change was a tiny 8.86m°C!
Good experiments can be repeated, so I tried again, but this time the ambient temperature seemed to be both different and changing at the same time. The result was a very slow increase in resistance instead of it plateauing nicely. This time, the temperature delta was similar at 7.77m°C.
We can hence calculate the self-heating as 42µW/8.86m°C = 4.74mW/°C. This value is about three-times the datasheet value, but this is no surprise as it is likely that self-generated heat was being lost to the environment through conduction out of the thermistor leads and into the air. However, seeing a result that is in the same magnitude is comforting. In the end, practical applications may see heat being sunk into the wire connections and into other media rather than accumulating in the thermistor, thus self-heating seems to be a relatively minute problem in practice.
Surprise Discovery: An Accidental Radiometer!
This led me down the path of an accidental discovery. Have you ever thought of how certain lasers or light-sources have their power measured? One way is to use an integrating sphere that bounces the light around uniformly, then a detector is placed on the surface at one point which can measure the intensity of light and integrate it over the area of the sphere.
In the case of my reflective vacuum carafe, I had a not-so-perfect integrating sphere. With the clear Perspex window, I could shine light into the carafe where it would bounce around. The thermistor epoxy itself is black which is likely to absorb light quite well and convert it into heat … so I grabbed my torch and …
Behold! A makeshift radiometer/bolometer. It’s not great (look at that response time) but it definitely is not just me breathing on the apparatus - I took some care to make sure of it! With the LED torch, the thermistor heated up while the wiggles are probably due to my aiming of the torch and the non-spherical surface inside. Once the torch was turned off, the heat dissipated into the environment as expected. I then got out my red 1mW laser pointer and when pointed at the thermistor, it was able to make a smaller signal. However, turning the laser pointer off did not quite restore the original resistance (perhaps due to changes in ambient temperature which swamps the signal). Given that it could detect a 42µW self-heating over time, perhaps being able to detect a 1mW laser pointer isn’t all that exciting?
While self-heating is a problem that can be foreseen from a theoretical perspective, in applications with non-precision thermistors and regular DMMs, the actual impact seems to be relatively small compared to the effect of thermistor tolerances and Beta model fitting errors. The theoretical deviation due to self-heating can be calculated using the power dissipation figure, while practical measurement using a makeshift worst-case rig measured a value three-times as high. Instead, the impact of just a brief finger touch on the thermistor leads proved to be a much greater impact. In reality, I would expect such self-heating to be easily taken away by whatever media it is in, or by conduction through the thermistor leads themselves, provided similar levels of drive current are used (0.1mA in this case).
That being said, I did not expect that the thermistor would lend itself to so easily resolving small temperature differences in the milli-degrees Celsius range. By doing so, I had “accidentally” created a radiometer/bolometer with my shiny vacuum carafe that even a small 1mW red laser pointer was able to provoke a noticeable response.
The data is probably not all that interesting (unless perhaps you’d like to save yourself from keying in the typical resistance values for the 3kΩ thermistor), but the worksheet for this blog is also available for download - dmm-self-heating.zip
[[Characterising Thermistors Blog Index]]
- Blog #1: Characterising Thermistors - Introduction
- Blog #2: Characterising Thermistors - What's In The Box?
- Blog #3: Characterising Thermistors – A Quick Primer, Beta Value & Steinhart-Hart Coefficients
- Blog #4: Characterising Thermistors – An Inconvenient Truth, Taking Things to the Fifth Degree
- Blog #5: Characterising Thermistors – Measuring Resistance Is Not So Easy!
- Blog #6: Characterising Thermistors – Is Self-Heating a Problem or Not?
- Blog #7: Characterising Thermistors – Boiling, Freezing and Zapping the Truth Out of Them!
- Blog #8: Characterising Thermistors – Practically Running Multiple Thermistors
- Blog #9: Characterising Thermistors – Multi-T Results, Insulation R Redux, 5th Order Fits & Model Performance
- Blog #10: Characterising Thermistors – Multiple Thermistors on ESP8266
- Blog #11: Characterising Thermistors – Show Me Your Curves
- Blog #12: Characterising Thermistors – Sticking Rings on Tabs & Sinks, Absolutely Crushing It!
- Blog #13: Characterising Thermistors – Pulling Out, Overload, Response Time, Building a Flow Meter & Final Conclusion