Measuring mK with small RTDs

[Kleinstein]

For measuring the self heating effect, there is no need to have a current ratio of exactly 2. It jist seems that a current ratio of 2 gives the best results. Something like 1.5 or 2.5 would probably be still acceptable. The self heating effect would still be only a small error, so no need to measure it to high precision - something like a few percent uncertainty in the self heating error should be still OK.

Quite a few datasheets for the SD ADCs show examples on interfacing an RTD or thermistor (often using 1 reference resistor). There are also examples for using a DMS bridge that could as well be used for a RTD bridge (with 4 resistors). A slight difference is in the sensor impedance and power: the DMS usually are 350 Ohms and often use more power.

The design shown below with the AD7195 looks good for very sensitive readings using AC excitation.

[tszaboo]

It will take me hours to read all papers and ideas posted here so I'll just write a small note for now -- the question "why?". I need to do an initial adjustment of many fast-response thermistors in the production of radiosondes and sensors for drone-based atmospheric research. This leads to several in-house use cases. For example, to characterize the variation in temperature across the volume of my calibration chambers and the fluctuation over short time spans (>= 10 Hz). Of course, I also need reference thermometers that can go a year between traceable calibration. I'd be happy to discuss this fascinating area more but I don't want to change the topic of this thread.

And you need to measure mK for that? Meteorological measurements work in the order of 0.1K accuracy.
Even if you would calibrate it at one point, nothing prevents your thermistor from having very different curve than the one in the datasheet.

This reminds me the time my boss told me to select a voltage reference with 0.003ppm temperature coefficient. I told him not possible. He gave me two days to research it. Told him, still not possible. "Yes its possible, 0.003ppm or 0.003 parts per mille"
Its probably the most difficult part of the job to tell bosses when their ideas or specification is just bad or dont make sense.

[JohnPi]

If you can separate the calibration (accuracy) from the resolution, then using a simple Si diode (e.g. 1N914 or 1N4148) may be a good choice.

As you showed, with acceptable self-heating currents, you get 0.03 uV/mK. A Si diode has a tempco of about -2mV/° over a wide range of bias currents. If you bias at a reasonable 1 - 10 uA, you will get a sensitivity of about -2 uV/mK on a 1 V range on the DMM. A 1 % change in current will also give a 0.3 mV (300 uV) change in V, or approximately 150 mK, so the current needs to be quite stable. 

[Anders Petersson]

There's some truth to the argument that 1 mK resolution in air isn't meaningful, as there are many complicating factors besides the ADC. For example, with a relative air movement of 2 m/s, the dynamic pressure increase created when the air is slowed by hitting the sensor causes a rise in temperature of 2 mK. At 5 m/s, it's 12 mK. (Example calculated at 0 C.) I also expect that IR radiation complicates measurements. Etc.

However, radiosondes (and many other sensors) have 10 mK resolution. The self-heating should be below this figure and preferrably below 5 mK. According to my initial post, it's not obvious how to do even this with small sensors. Also, it's my hope that it's possible to measure temperature fluctuations in a chamber of a few liters with better resolution than 10 mK, even if not down to 1 mK. So I still think the question I posed is reasonable.

Yes, solids have a more well-defined temperature where 1 mK is a more reasonable resolution. For that case, the thermal coupling will also be much better so self-heating will decrease, giving margin for a larger excitation current and longer integration time.

Thanks for all tips and papers, I will have a look. I hoped there was already a schematics out there... oh well.

[Anders Petersson]

The optimization of self-heating corrections in resistance thermometry, Pearce, 2013
https://www.researchgate.net/publication/258263469_The_optimization_of_self-heating_corrections_in_resistance_thermometry

I've read the paper now and I don't think the technique is applicable to air measurements. They assume that the excitation continues until the self-heating has stabilized. Then after measuring at the higher current, the sensor must be given time to cool off. Their examples quote measurement times of 10-20 minutes. In air, the wind draft will create a hot wire anemometer effect, where the transport of the self-heating to the environment depends on the air draft at the moment.

But it made me realize another option, if we can rely the self-heating to be linear during, say, the first 10 ms of a pulsed excitation. After an initial delay to let the filters stabilize, two consecutive AD conversions should reveal the rate of self-heating given the momentary air draft, humidity and excitation current. Working backwards, the resistance at the start of the excitation should be easy to calculate. After the measurement, the sensor should rest until the self-heating has dissipated again. See attached diagram. (But I guess the measured value will be the average during the integration period, when using an oversampling ADC.)
I will try this out sometime soon-ish.

[Kleinstein]

Measuring the self heating as a function of time makes sense. In a closed environment the self heating would not change much over time and would only add some offset to the sensor. The same effect would also apply to the sensor calibration, if done togehter with the same read out. So one may not need to actually measure the self heating part.

It would only be in moving air and maybe with variable pressure that the self heating may change. The heat capacity of the sensor would normally not change much - so just the initial linear part may not need to be measured each time, it would be more like the later part, so how fast and to what level the temperaure would settle, that can change.

[DeltaSigmaD]

The acquisition of PT1000 sensors is not too complicated. For a digital temperature controller with resolution in the mK range I developed a Delta-Sigma-AD converter for a PT1000 half bridge. A CMOS SPDT switch forms the second half of the bridge. The switch is controlled with a Delta-Sigma-PWM. This technique has the advantage that it is a ratiometric measurement: the absolute bridge supply voltage is canceled out of the measurement. Only one stable resistor is required, all other error sources have a lower order of influence. The third order DeltaSigma engine is running in a microcontroller with about 2mA consumption (can be reduced by reducing measurement rate). The sampling frequency is 20 kHz, so that 100 measurements/s are possible, while the theoretical resolution is more than 23bits. The ADC noise is about 2.5uV rms resp. about 0.8 mKpp of temperature measurement. No precise long-term stability data are available, since the obtained 10mK limit is sufficient for my application. To digitise a PT1000, you need 1 uC, 1 OP, 1 SPDT switch, 1 stable 1kOhm resistor, and a number of passive elements, that's all. The circuit including a 19bit DS-DA converter (required to close feedback loop of the temperature controller) needs about 9.5cm². The bridge linearisation can be made by software in the uC: a combined second order bridge/PTx linearisation is sufficient for <5mK deviation in a 40K temperature range. Individual PT1000 sensor calibration would be possible without hardware modification or adjustment, this was not realised until now.

[Anders Petersson]

@DeltaSigmaD, very interesting. Can you share schematics?

[DeltaSigmaD]

Unfortunately, it is a proprietary design, so it can't be disclosed here. But it might be helpful to know what is possible. It is better to spend work for a development if you can be sure that there will be success.
To the DS circuit technique: even higher accuracy is possible, the repeatability is excellent. The switch resistances and dynamic losses cause a weak non-linearity of the ADC. However, in case of a PT sensor bridge only one combined linearisation is required. In this case the uC-DS technique is attractive because it has a lower total circuit complexity (=lower cost, excluding software cost). High resolution ADC-ICs (>20bit) are the superior solution for high absolute precision and linearity.

[KT88]

As DeltSigmaD confirmed, a ratiometric set-up together with a high precision ADC is an excellent way to measure RTDs here is a comprehensive selection of circuits for RTDs: https://www.analog.com/en/design-center/reference-designs/circuits-from-the-lab/CN0383.html#rd-overview
It covers a lot of viable configurations - even multi-channel measurement with only one reference resistor.

Cheers

Andreas