Reading the thermistor with digital pins uses far less power, and gives you the resistance of the NTC directly from the ratio of two times. Resolution is not set by the bit depth of your ADC, but by the size of the reservoir capacitor: a small ceramic 0.1µF [104] delivers about 0.01°C with jitter in the main system clock imposing a second limit on resolution near 0.01°C when using a small res-cap. However, this calibration procedure will work no matter what method you use to read your NTC thermistor.

Off-the-shelf sensors can be used as  ‘good enough’ reference thermometers provided you keep in mind that most accuracy specifications follow a U-shaped curve around some sweet spot that’s been chosen for a particular application. The Si7051 used here has been optimized for the medical market, so it has ±0.1°C accuracy from 35.8 to 41°Celsius, but that falls to ±0.13 at room temperatures and only  ±0.25 at the ice point. If you use some other sensor (like the MAX30205 or the TSYS01) make sure it’s datasheet specifies how the accuracy changes over the range of temperatures you are targeting.

Likewise, the shortened three term Steinhart–Hart equation is not considered sufficiently accurate for scientific instruments which often use a four or five term polynomial. To calculate the equation constants you need to collect three temperature & resistance data pairs which can be entered into the online calculator at SRS or processed with a spreadsheet.

While these technical sources of error limit the accuracy you can achieve with this method, issues like thermal lag in the physical system and your overall technique are equally important. In general, you want each step of this process to occur as slowly as possible. If the data from a run doesn’t look the way you were expecting – then do the procedure over again until those curves are well behaved and smooth.

Data Point #1: The freezing point of water

The most common method of obtaining a 0°C reference is to place the sensor into an insulated cup of stirred ice slurry that plateaus as the ice melts. This is fine for waterproof sensors on the end of a cable but it is not easily done with sensors mounted directly on a PCB. So we immerse the loggers in a 1200ml silicone food container filled with distilled water. This is placed inside of a well insulated lunch box and the combined assembly is left in the freezer overnight, reading every 30 seconds.

The trick is recognizing which data represents the true freezing point of water. Distilled water super-cools by several degrees, and then rises to 0°C for a brief period after ice nucleation because the phase change releases 80 calories per gram while the specific heat capacity of water is only one calorie per degree per gram. So freezing at the outer edges warms the rest of the liquid – but this process is inherently self-limiting which gives you a plateau at exactly 0°C after the rise:

Depending on the strength of your freezer, and the quality of the outer insulating container, the ice-point may only last a few minutes before temperatures start to fall again. An average of the NTC readings from that initial peak is your 0°C calibration data point.  This is usually near 33000 ohms for a 10k 3950 thermistor. Only the data immediately after super cooling ends is relevant and the insulated box can be removed from the freezer any time after that.

If the supercooling spike is not obvious in your data then change your physical configuration to slow the cooling process until it appears. You want the inner surface of your silicone container to have smooth rounded edges, as sharp corners can nucleate the ice at 0°C, preventing the supercooling. Use as much water as the container will safely hold. You do not want the water to freeze solid as this will subject the loggers to stress that could crack the housings.

Unexpected thermal excursions may happen if the freezer goes into a defrost cycle or an automatic ice-maker kicks in during the run. If you put the box in the freezer between 6-7pm, it usually reaches the supercooling point around 2am, reducing the chance that someone will open the freezer door at that plateau.

Data Point #2:  Near 40°C

We have used the boiling point of water for calibration in the past, but the centrifuge tube housings would soften considerably at those temperatures. Ideally you want to bracket your data with equally spaced calibration points and 100°C is far from the conditions we monitor. Heated water baths can be found on eBay for about $50, but my initial tests with a Fisher Scientific IsoTemp revealed thermal cycling that was far too aggressive to use for calibration – even with a circulation pump and many layers of added insulation. So we created an inexpensive DIY version made with an Arctic Zone Zipperless Coldloc hard-shell lunch box and a 4×6 inch reptile heating mat (8 watt). Unlike the ice point which must be done with distilled water, ordinary tap water can be used to collect the warm data pairs.

Data Point #3: Room Temperature

The loggers stay in the heated bath overnight, and then in the morning they are transferred to an unheated water-filled container (in this case a second Arctic Zone lunch box) where they run at ambient temperatures for another eight to twelve hours. This provides the final reference data pair:

The final step is to use those constants to calculate the temperature from the NTC data with:
Temperature °C = 1/(A+(B*LN(ohms))+(C*(LN(ohms))^3))-273.15

Also note that the hot and warm bath data points can be collected with separate runs. In fact, you could recapture any data pair and recalculate the equation constants with two older ones any time you suspect a run did not go smoothly. Add the constants to all of the data column headers, and record them in a google doc with the three reference pairs and the date of the calibration. Re-run the calibration in a year. You can then apply compensation techniques to correct for sensor drift in your dataset.

Validation

Two from this set are a bit high and could be redone, but all of the NTC temperature readings now fall within a 0.1°C band. This is a decent result from a method you can do without laboratory grade equipment, and they could be brought even closer together by normalizing the set.

Comments

Calibrating the onboard thermistor a good idea even if you plan to add a dedicated temperature sensor because you always have to do some kind of burn-in testing on a newly built logger – so you might as well do something productive with that time. I generally record as much data as possible during the calibration to fill more memory and flag potentially bad areas in the EEprom. (Note: Our code on GitHub allows only 1,2,4,8, or 16 bytes per record to align with EEprom page boundaries) . And always look at the battery record during the calibration as it’s often your first clue that a logger might not be performing as expected. It’s also worth mentioning that if you also save the RTC temperatures as you gather the NTC calibration data, this procedure gives you enough information to calibrate that register. The resolution is only 0.25°C, but it does give you a way to check if your ‘good’ temperature sensors are drifting because the DS3231 tends to be quite stable.

For any sensor calibration the reference points should span the range you hope to collect later in the field. To extend this procedure for cold climates you could replace the ice point with the freezing point of Galinstan (-20°C) although a domestic freezer will struggle to reach that. If you need a high point above 40°C, you can use a stronger heat source. Using two of those 8 watt pads in one hard sided lunch box requires some non-optimal bending at the sides, but it does boost the bath temp to 50°C. 3D printed hold-downs will start to soften at higher temps so you may need to alter the design to prevent the loggers from popping out.

If your NTC data is so noisy you can’t see where to draw an average, check the stability of your regulator because any noise on the rail will affect the Schmitt trigger thresholds used by the ICU/timer. This isn’t an issue running from a battery, but even bench supplies can give you noise related grief if you’ve ended up with some kind of ground loop. You could also try oversampling, or a leaky integrator to smooth the data – but be careful to apply those techniques to both the reference and the NTC readings in exactly the same way because they introduce significant lag. Also note that the digital pin ICU based method for reading resistors does not work well with temperature compensated system oscillators because that circuitry could kick in between the reference resistor and NTC sensor readings.

And finally, the procedure described here is not ‘normalization’, which people sometimes confuse with calibration.  In fact, it’s a good idea to huddle-test your sensors in a circulating water bath after calibration to bring a set closer together even though that may not improve accuracy. Creating post-calibration y=Mx+B correction constants is especially useful when monitoring systems that are driven by relative deltas rather than by absolute temperatures. Other types of sensors like pressure or humidity have so much variation from the factory that they almost always need to be normalized before deployment – even on ‘commercial’ loggers. Normalize your set of reference sensors to each other before you start using them to calibrate your NTC sensors.

References & Links:

SRS Thermistor Constant Calculator
Steinhart-Hart Equation Errors BAPI Application Note Nov 11, 2015
The e360: A DIY Classroom Data Logger for Science
How to make Resistive Sensor Readings with DIGITAL I/O pins
How to Normalize a Set of Sensors