The divider
An ADC measures voltage, not resistance, so the board puts a fixed 10 kΩ above the thermistor. SIGNAL is the voltage between them: exactly half of VCC at 25 °C, lower when it is warmer, higher when it is colder.
A voltage your board can read
An analog pin measures a voltage. It has no way to measure a resistance on its own. So the board puts a second resistor, a fixed 10 kΩ, between VCC and the thermistor, and the two share VCC between them in proportion to their resistance. The point between them is SIGNAL.
Start at 25 °C. The thermistor is 10 kΩ, the same as the fixed resistor, so each takes half: SIGNAL is 2.50 V from 5 V and 1.65 V from 3.3 V. Now warm it. The thermistor's resistance falls, its share of VCC shrinks, and SIGNAL drops. Cool it and SIGNAL climbs towards VCC.
This is the part that most often gets written backwards. The thermistor is the lower half of the divider, from SIGNAL to GND, so warmer means a lower voltage. The page this book replaces said the opposite.
The formula
The share SIGNAL gets is the thermistor's resistance over the total:
SIGNAL = VCC × R_ntc / (R_ntc + 10 kΩ)A sketch runs it backwards. Knowing SIGNAL and VCC, it solves for the thermistor:
R_ntc = 10 kΩ × SIGNAL / (VCC − SIGNAL)That is the first of the two lines every sketch in this book uses. The second, from resistance to degrees, is in counts to degrees.
The capacitor
The pale part between the thermistor and the fixed resistor is a 100 nF capacitor from SIGNAL to GND. It holds SIGNAL steady against short spikes of electrical noise picked up by the wires, and it gives the ADC a stiff source to sample from.
It does not slow the reading in any way that matters. Behind it are the two resistors in parallel, 5 kΩ at 25 °C, and 5 kΩ × 100 nF is half a millisecond. A temperature takes seconds to change.
When it does not work
Down. The thermistor is the lower half of the divider, from SIGNAL to GND. Warmer, its resistance falls, it takes a smaller share of VCC, and SIGNAL drops. Some other thermistor boards put it on top and go the other way, and their formulas are upside down for this one.
Because it matches the thermistor at 25 °C. That puts SIGNAL at half of VCC around room temperature, where the voltage changes fastest per degree, so an ordinary ADC gets the most counts per degree where most people use it.
It smooths SIGNAL. With the two 10 kΩ resistors in parallel behind it, about 5 kΩ at 25 °C, 100 nF gives a time constant of about half a millisecond: too slow to pass a spike of electrical noise, far too fast to hide a change in temperature.
No. A divider only ever gives a fraction of what it is fed. That is why VCC goes to your board's own logic supply, 3V3 on an ESP32 or Pico: SIGNAL then can never exceed what the pin is built for.
Why the exact voltage of VCC does not matter on an Uno, and does on an ESP32.
Why VCC cancels out →Edit this page — content/books/ntc-thermistor/the-divider.mdx
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