# Does anyone know the bandwidth of a thermistor?

I had an experiment I was working on where I needed to know the temperature of a circuit element down to 10uS time resolution.

I had a thermistor handy, so I thought I would attach it to the element, force a constant current into it, and look at the voltage change on a scope. This would give proper temperature and time resolution, but then I happened to think, just how fast is a thermistor? Or, for the thermistor transfer function R/T what is the gain/phase vs. frequency? I did some quick googling and got nowhere. All the vendor datasheets and notes show time series data with the time axis having second gridlines. Then I was thinking of buck circuits which use an NTC in their compensation, and those are stable, so maybe it's less than 10KHz (or something), so I just switched to measuring temperature with a diode, which I know is fast but loses temperature resolution due to the log scale. But speed is more critical for this experiment, so it works.

But the question has remained in my head. How fast is a thermistor? It seems like must depend on the package. A 0201 thermistor should be faster than a 2512 due to its smaller mass, no? And a PTC is likely different than an NTC. I was thinking when this setup is all done, which is definitely some time from now, I would redo the measurement with a Vishay 0402 NTC, which I often see used in regulators, and compare to the diode. That could give a rough estimate.

A 0201 thermistor should be faster than a 2512 due to its smaller mass, no?
Kind of yes, but the actual answer will also depend on the power available on the source and its connection to the thermistor.
Should it take on a high power electric discharge and it'll be vaporized very fast...

I had an experiment I was working on where I needed to know the temperature of a circuit element down to 10uS time resolution.
Measuring temperature on this scale will be a real killing task. I think I would rather measure power on the element and I would give some educated guess based on a modell.
Maybe you can try finding something based on thermal radiation.

Ps.: try google 'high speed pyrometer' or 'fast non-contact temperature measurement'

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rbelli1
Gold Member
temperature of a circuit element down to 10uS time resolution

How big is this element? How much power and cooling are we talking about?

BoB

jim hardy
Gold Member
Dearly Missed
Ten microseconds isn't much time for heat to flow into or out of a sensor..
In my power plant the fastest temperature sensors we had were platinum RTD's with 1 second response time constant
as measured by plunging into a water bath , measuring time to reach 63% of final value.

Some bright fellows on a university research project figured out that they could equally well use self heating of the RTD to measure its time constant .
They took control of the sensing current and applied a step change to it, recording what temperature it reported.
As the element established heat conduction out to ambient they measured and plotted its temperature versus time.. Of course it heated to some few degrees above ambient.
Knowing how much power they were putting in, that let them estimate its thermal mass and its thermal resistance to ambient.

Their first experiments used a simple Wheatstone bridge to provide sensing current to the element. .
The same approach could work with a thermistor.
With low excitation voltage you balance the bridge so it gives zero output
Then suddenly increase the excitation voltage.
As the sensor self heats due to increased sensing current , the bridge becomes unbalanced and gives a voltage output.

The hard part was finding suitable resistors from which to make their bridge. They must have very near zero temperature coefficient else they too will change value when you change excitation voltage.
We loaned them some General Radio precision resistance boxes with manganin wire-wound resistors inside that were quite stable and worked well.

Their other problem was common mode voltage interference from a line operated power supply.
Its power transformer wasn't shielded so interwinding capacitance coupled objectionable 60 hz noise into the bridge and it upset their differential amplifier.
We jury rigged a supply from 6 volt lantern batteries to cure that problem.

Keep in mind that for us one second was a doggone fast sensor. They were immersed directly in the flowstream to avoid the thermal inertia of a thermowell. .
If you're really interested in microseconds of response time then you're in a different league than me.
But maybe something above will help you come up with an approach

Try starting with maybe 1 milliwatt in your sensor and double it.

Good Luck !

old jim

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rrogers, NascentOxygen, davenn and 3 others
Using any mass, as a thermistor, I do not think will get anywhere close to 10uS - heck what are you even measuring, will not heat uniformly in 10uS. But an IR sensor may be the best bet, since the radiation will be seen as soon as the surface of the item changes.

For buck regulators - as with other protection schemes there are different methods employed. Thermal - it typically an overload, or long-time protection, and not used for short-circuits. For fast protection direct current measurement, and in larger power semiconductors - denaturation protection.

Edit-> Oh - the DS for some of the TDK 0201 does include the Thermal Time constant - so Yes someone does know.

Paul Colby
Gold Member
Random suggestion of questionable utility: IR photo diode with a lens system might provide enough bandwidth.

Asymptotic, Averagesupernova and jim hardy
jim hardy
Gold Member
Dearly Missed
I had an experiment I was working on where I needed to know the temperature of a circuit element down to 10uS time resolution.
I like brainstorming..... Optical sounds promising

Expanding on my primitive power plant experience above

What is this thing you're measuring, some kind of fast melting fuse or detonator ?
Ohm's Law calculation to monitor its resistance change, (even copper is used for measuring temperature, its coefficient is close to platinum's ). :
divide voltage across it by current through it (Rogowski coil for high current pulse?)
division by analog divider
gives you ohms

Just a thought , i've not done or even researched it. And can only guess at what is your application.

I shouldn't have written any details on the experiment as it doesn't matter for my question and my employer wouldn't want me posting on it.

Thanks for the links all. They've been very helpful. The idea of making a temperature impulse by moving from one bath to another, as Amphenol did, really demonstrates how slow thermistors are. I expected a thermistor to be too slow for this experiment, and I am a bit surprised as to just how slow thermistors are, but the diode worked reasonably well, although we did not hit 10uS resolution target at no attenuation.

The experiment I did to confirm the thermal bandwidth of the system was: Couple a diode (it's DFN1006, roughly 1mm on a side, so think very tiny) to the circuit element under test and force a constant forward current through the diode. Force another very slow sine of current, with known safe pp magnitude and offset, through the element under test. I used T=300S, which I am confident is inside the channel's bandwidth. With the setup in a thermal chamber with known Ta, observe Vpp on the diode and determine Tpp from it (I curved traced this diode in the chamber at a few temperatures, so I know the diode equation parameters for this part). Call that Tpp=1. Decrease T on sine until Tpp=0.7. That T determines the 3db frequency of the system and I got frequency just under 10KHz. In the experiment, I'll still sample at 10uS as previously planned, but naturally, the signal will be significantly attenuated at that sample rate which is a good thing from a DSP point of view. We will have to make due. :)

I was also thinking some kind of IR measurement could be interesting but I'm not sure how I could make it work as everything is very small and I wouldn't want to mess with lenses.

Jim, the experiment in post #5 is very clever, and I like the approach. Thanks for sharing!

jim hardy
For buck regulators - as with other protection schemes there are different methods employed. Thermal - it typically an overload, or long-time protection, and not used for short-circuits. For fast protection direct current measurement, and in larger power semiconductors - denaturation protection.

I didn't mean for protection. I meant when doing temperature compensation for L DCR current sensing in current programmed bucks. An example would be figure 2 in this app note.

https://www.richtek.com/m/~/media/AN%20PDF/AN026_EN.pdf

sophiecentaur
Gold Member
2020 Award
IR photo diode with a lens system might provide enough bandwidth.
I like brainstorming..... Optical sounds promising
I was thinking that too but what are the temperatures involved? Anything 'warm' could be a candidate but we do't know. This is very typical of a PF thread about a practical problem - not enough detail for a satisfactory answer. Very frustrating for someone with a lot of experience of practical measurements. Signal o noise ratio is always the prime consideration and we don't know either of those quantities.

jim hardy and Asymptotic
Paul Colby
Gold Member
I thought the original question has been answered in a sense. How fast is a thermistor. Answer: for 10 microsecond time scale measurements, not fast enough.

sophiecentaur
Gold Member
2020 Award
I thought the original question has been answered in a sense. How fast is a thermistor. Answer: for 10 microsecond time scale measurements, not fast enough.
It isn't as clear cut as that - at least not if the Engineering of the experiment is being discussed. There will be an exponential (or thereabouts) rate of change of the sensor temperature as the test component changes temperature. The sensor will lag behind the test temperature (this has all been mentioned higher up the thread). What is meant here by a "10μs timescale measurement"? There is a Time Constant involved - basically a Low Pass Filter and the response of a simple LP filter is finite at all frequencies. So detecting / measuring a change will actually depend on the LP filter response at the frequency of interest and the system noise. Sensitivity and accuracy can be improved by using a differential measurement - involving an additional reference element, working at a chosen 'standard' temperature.

jim hardy and Asymptotic
Paul Colby
Gold Member
Yes. For an answer we would have to invent a problem and solve it.

sophiecentaur
Gold Member
2020 Award
Yes. For an answer we would have to invent a problem and solve it.
There was a specific problem which has not been disclosed fully enough for an answer. One thing which is never made clear in this sort of post is how much trouble the OP wants to go to or how much money is available. (We have all been there.) Perhaps there should be a coding system which starts with "as a matter of interest", goes through "is there a cheap, off the shelf answer?", "is there an expensive solution available" up to "is it fundamentally possible?". We all tend to aim for the last option and that scares newcomers.

jim hardy, Asymptotic and Paul Colby
There was a specific problem which has not been disclosed fully enough for an answer. One thing which is never made clear in this sort of post is how much trouble the OP wants to go to or how much money is available. (We have all been there.) Perhaps there should be a coding system which starts with "as a matter of interest", goes through "is there a cheap, off the shelf answer?", "is there an expensive solution available" up to "is it fundamentally possible?". We all tend to aim for the last option and that scares newcomers.

Thought I'd read something years ago in NASA Tech Briefs magazine to do with high speed temperature measurements that were conducted during the space shuttle program. Didn't find it, but hit a recent article concerning high speed IR thermography into the sub microsecond range for measuring fireballs. So it is possible, but it looks like a fair amount of effort and cash are involved.

jim hardy
Gold Member
Dearly Missed
Decrease T on sine until Tpp=0.7. That T determines the 3db frequency of the system

And if you keep on going you'll see whether it's a simple first order .

and I got frequency just under 10KHz.
Wow ! That's fast......

sophiecentaur
Gold Member
2020 Award
but hit a recent article concerning high speed IR thermography into the sub microsecond range for measuring fireballs
This uses quantum detection (a souped up digital camera) and not straight thermal (a thermistor). Depending on the actual requirement of the OP, the spectrum (i.e. temperatures) that's involved may or may not allow this approach. Looking for a tiny blip in the thermal image is along the lines of looking for a tiny dip in the light from a distant star when one of its planets passes in front of it - and we know what an effort it takes to achieve that. AS I keep pointing out, it's a matter of Signal to Noise Ratio - pure and simple.

Paul Colby
Gold Member
My problem is usually how much "signal" is really leaking in by some non-relavent instrumental means or shortcoming like stray RFI. It's not always possible to tell, well for me anyway.

Baluncore
I had an experiment I was working on where I needed to know the temperature of a circuit element down to 10uS time resolution.
The thermal mass of the element and the thermal coupling is as important as thermistor mass and time constant.

If the element temperature is changing then the thermistor element will be forever following the element temperature in an exponential pursuit. Once you know the time constant of the coupling you can compute the actual element temperature based on the thermistor resistance now and it's the rate of change.

There is a poorly conditioned numerical trick you can use to predict the final settled value of an exponentially changing value. It works both backwards and forward in time. Take three equally spaced readings, p, q and r, then predict the final value s = (p*r – q*q) / (p – 2*q + r). That can be run in real time on a continuous data stream. You must find a way to ignore the noise during division by zero.

If the element has some form of thermal coefficient, or diode substrate, you can measure that parameter to identify temperature. You have not identified the type of element you need to monitor.

sophiecentaur
Gold Member
2020 Award
My problem is usually how much "signal" is really leaking in by some non-relavent instrumental means or shortcoming like stray RFI. It's not always possible to tell, well for me anyway.
Which is why I was suggesting a reference channel, identical in as many ways as possible - just not pointing at your test component. Interfering signals could be largely subtracted out - although internal noise would not be correlated so you would need some careful filtering.

jim hardy
Given your application, I think you should start doing Multiphysics modeling on any measurement method. I like Comsol (because it's flexible and is user-friendly (so to speak); but it's expensive (as are the commercial alternatives). There is a free program I tried and it seems to work: Elmer --- https://www.csc.fi/web/elmer and is not too hard; but not as good/easy as Comsol.
To see the physical problems and techniques you might look at https://arc.aiaa.org/doi/pdf/10.2514/1.J055801 for work done with "hot-wire anemometers" which are probably faster than a thermistor.
I could envision a closed loop system that keeps the thermistor at constant resistance and reacts fast, but that would require research because moving poles out 10^6 is really hard and typically not robust. Furthermore, you probably want to measure the surface of the coating in which case you have information loss because of the thermal diffusion equation; that information loss is absolute. And the whole thing is deeply dependent upon the contact between the surface of the thermistor epoxy and the thing to be measured. I can't imagine 10usec being useful for any organic entity though, so I would presume your doing laser surgery or some such. In that case, you should be looking at the color of the area as I think that would be more indicative of tissue change/damage, and there are really fast photodiodes.
In fact, moving to fast photodiodes (repackaged) might be the reasonable way to go. Some packaging customization would probably be required. A challenging task, but similar to your diode solution just more refined.