If someone were to ask me what my favourite electrical component was, which is more common than you think, I would have to say a NTC thermistor.
But what is a NTC thermistor, and how does it work? (And why is it objectively the best?)
To truly express the greatness of this pièce de résistance (get it?) of electric circuits, and to express my undying love for it, I devised a Haiku in its honour.
Ok but what is it actually?
The NTC thermistor and its little brother the PTC thermistor are a unique type of resistor that changes their resistance based on its temperature, for the NTC it’s negatively correlated and for the PTC its the other way around. However, the similarity in name is quite deceiving because, except for their temperature dependent characteristics, their mechanisms are vastly different. So today I’ll only focus on the, obviously superior, NTC.
But how does an NTC work?
NTC thermistors are actually just semiconductors, which just means that they’re halfway between a conductor and an insulator. So to see how a semiconductor works we’ll have to look at how conductivity works as a whole, in a solid at least. In a crystalline structure, the electrons of the atoms which orbit their nuclei overlap and interact with one another, which leads to a very interesting result because electrons are fermions.
In accordance with this fact, due to the Pauli exclusion principle (not to be confused with my brother Paul being excluded from this blog because of his affiliations with the PTC community), they can not be in identical quantum states. In other terms; two fermions, electrons in this case, can’t have the same characteristics such as orbit or spin.
The result of this is that all the orbits differ by a very very small amount, and so the energies of the electrons also differ minutely. This may sound weird because it is thought that an electron has set orbits with an exact energy level for each, but this is only really the case if the atom is in stasis. As a result of the sheer amount of atoms in just one gram of semiconductor, all these slightly different energy levels can be seen as a kind of continuum as I have illustrated right below me.
You can see bands forming, which is where this principle gets the name electronic band structure from, however there is also a void between these bands, which is called a band gap. The most prominent of these bands are the valence band, the large band closer to the nucleus, where the valence electrons reside and of course the conductivity band aren’t actually filled most of the time, but it is where electrons go if provided with enough energy and is necessary for how the atom actually conducts current.
The gaps show where the continuum ends; there are no possible energy levels for the electrons within that range, yet these gaps aren’t in the same locations for all materials or elements, in accordance of course with the orbits having different energies for different elements. These are the result of our boy Planck’s idea of quantised energy, the idea that at the smallest scale things don’t go continuously but in steps.
For regular old conductors the gap between these previously named bands is so tiny that they are negligible, so they can conduct without energy being put into the system. But for semiconductors these band gaps look more akin to that of insulators, only smaller, which is why electrons can only be excited from the valence band to the conductivity band when they receive enough (in most cases) thermal energy. It isn’t actually only the electron in the conductivity band which allows it to conduct, but more so the joint effort of it and the void which is left behind in the valence band, which allows the electrons to have more wiggle room and so carry charge.
So this is how the fabulous NTC thermistor gains its heat dependent property, how could we express this in a more fancy and “mathsy” way?
the Cold Hart truth
Two crafty folks have constructed a mathematical expression for the resistance of our favourite part. Interestingly this didn’t happen that long ago, in terms of physics at least, in the year of 1968. They may be of some surprise due to the fact that a lot of more complex physics in the field of electricity had been done years prior, I guess it took so long for it to get the attention and love it deserves. This formula, thought up by the funnily named Steinhart and just Hart, is more of an approximation or model used to describe them than anything else, yet it is still quite accurate given enough information. I say this because the equation actually has three Steinhart-hart coefficients which vary depending on the exact makeup of the semiconductor (elements, which ones? Or is it an alloy?).
Ok ok, now i’ll actually show you what the equation looks like;
The one and not even close to the only Steinhart-Hart equation, isn’t she a beaut? I say not even close to only because it has a lot of alternatives and there are also different ways of expressing the relation between the temperature (in Kelvin) and the resistance. If you truly care about the greatest thermistor in the world I implore you to look further using the B parameter equation as a jumping off point.
That the temperature is the main factor in the change in the resistance is no big shocker (or I hope so if you have read the rest of this blog), but that it’s in Kelvin, meaning that it counts from the absolute zero of temperature is way more intriguing. So I was thinking to myself, how would you go about calculating the resistance before our good ol’ friend Lord Kelvin stepped into the picture? Looking through all the formulas it seems impossible, because you could only use relative temperature Celsius if you exclusively used the difference of temperature, which none of them do sadly. So a new challenge has come to light, how do we calculate absolute zero only with our beloved NTC thermistor?, and measuring equipment because we aren’t into just guessing.
Kelvin and his method
To figure out how our superior method should work we should first take a quick peek at how our friend Kelvin figured things out. His method was by using the ideal gas law, or at least a primitive version of it as it hasn’t yet been mathematically constructed. He noticed that as he cooled a gas down it decreased in volume, so he thought: “when would I reach the point where the gas becomes infinitely small?”. By measuring the shrinkage of the gas 0℃ (to -1℃), which just so happens to equal the very familiar number of 1/273, which meant that 273 more of those steps would make the volume zero. So this is how we got to the number -273℃, which was later slightly corrected to -273,15 because I guess poor Kelvin was playing fast and loose with how accurately he measured it, and beyond that point nothing would make sense anymore. Try imagining negative volume (once you succeed please give the contact information of your drug dealer), but I suspect you already know it to be impossible. So that absolute zero was defined as the coldest temperature, however what happens when you reach it?
If you would be so kind as to imagine the temperature not as heat per se but as the average movement of the atoms, with how fast they move correlating to a higher temperature. Absolute zero then correlates to when the atoms stop moving altogether, which also funnily enough means that nothing can happen (like time stopping) but I digress. When it’s cold, fewer electrons in the valence band have the energy to go to the conductivity band, which means they’ll conduct less, but when it approaches absolute zero, none of the electrons should be able to move, so it should conduct no temperature whatsoever. At actual zero it also causes some problems because the different orbits are a result of the slightly different energy levels of the electrons if you remember from before, but with no energy except mass that wouldn’t be possible. But then again, if they don’t have different orbits, they would violate Pauli’s exclusion principle, which is another reason why it isn’t possible to actually reach that paradoxical point. But this theoretical explanation gives me an idea as to how we could use the glorious NTC thermistor to calculate absolute zero.
Calculating absolute zero
When trying to prove something it’s very important not to accidentally assume it’s true while proving it. This is quite obvious because it is, but it happens faster than you would expect. For example if you use the Steinhart-Hart equation and use the coefficients which the supplier of the NTC thermistor lists on the product info or data sheet, you’re actually also using the fact that absolute zero is at -273,15℃ because the company likely used it to calculate those coefficients. However, when you keep this in mind that equation is a very valuable tool if used correctly. By using the fact that T is the temperature starting from absolute zero you could substitute with T(absolute) = T(celsius) + x, where x is what we want to calculate. Then you could take a large amount of data points by measuring it in real life with a precise thermostat and something to measure the resistance (or the voltage and amperage). Then put these measurements in the equation, T1 with corresponding R1, T2 with R2 etc., leaving the unknown constants blank, so A, B, C and x. If you have gathered enough data points (8 is ideal but less is possible) you can keep substituting by solving for A for example, which you wouldn’t be able to calculate as a number but as an equation. Then substitute that into the A of the equation for another data point because it has to stay constant. When this is repeated enough times you’ll only be left with one unknown and the rest are just regular old numbers, which you could calculate and then work your way backwards to calculate the others. Although, if you choose wisely which to solve for – anything but x – you’ll only be left with the one you actually want to know, the degrees Celsius of the coldest possible temperature.
And voila, that’s how easy it is! Slight disclaimer though, because a tiny measuring mistake throws the calculated x off by a mile.
Final remarks
Now our journey has sadly come to an end, but I hope the great epic of the NTC thermistor will stay in your H(e)art forever. In all seriousness this whole NTC-stick is mostly for entertainment and I do not condone the harassment of other electric parts, and definitely read up on how PTC thermistors work when given the opportunity I assure you it’s a fascinating read.
There is still much to explore regarding this topic so if you have any questions, meet me in the comments and I’ll be happy to elaborate and someday I might make a follow up on how you could conduct the experiment necessary to calculate absolute zero yourself if there is enough interest in it.
But that’s all for my first solo post, and remember: don’t listen to whatever the PTC enthusiasts try to tell you!
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