What an NTC thermistor is
An NTC (negative temperature coefficient) thermistor is a resistor whose resistance falls sharply as temperature rises. It is cheap, sensitive and everywhere: in battery packs, 3D printers, thermostats, car engines and kitchen appliances. A common part is the “10 kΩ NTC with B = 3950”, which reads 10 kΩ at 25 °C.
The Beta equation
Between two temperatures, an NTC follows the Beta model closely:
R(T) = R0 × exp(B × (1/T − 1/T0))
Solved for temperature:
1/T = 1/T0 + ln(R ÷ R0) ÷ B
where T and T0 are in kelvins (°C + 273.15), R0 is the nominal resistance at T0 (usually 25 °C) and B is the Beta coefficient from the datasheet, often 3435, 3950 or 4100 K.
Example
A 10 kΩ, B = 3950 thermistor that measures 5 kΩ:
- 1/T = 1/298.15 + ln(0.5) ÷ 3950 = 0.003354 − 0.000175 = 0.003179;
- T ≈ 314.6 K, or 41.5 °C (106.6 °F).
The same part reads about 33.6 kΩ at 0 °C, more than three times its 25 °C value.
Reading it with a microcontroller
The usual circuit is a voltage divider: a fixed resistor from the supply to the ADC pin, and the thermistor from the pin to ground. The pin voltage is V = Vs × R_NTC ÷ (R_NTC + R_fixed). With a 10 kΩ fixed resistor and a 3.3 V supply, 5 kΩ gives 1.1 V. Choose the fixed resistor close to the thermistor’s resistance in the middle of the range you care about, for the best resolution.
Accuracy
- The Beta model is accurate to within about ±0.5 °C over a range of 50 °C or so around T0. For wider ranges, use the Steinhart–Hart equation with three coefficients.
- Datasheets often give two B values, such as B25/50 and B25/85; use the one that matches your range.
- Thermistors have a tolerance on R0 (±1% to ±5%) and on B.
- Self-heating: the measuring current warms the part. Keep the dissipation well below the datasheet’s dissipation constant, typically a few mW/°C.
Sensitivity
The temperature coefficient is α = −B ÷ T², about −4.4% per kelvin at 25 °C for B = 3950. That is ten times more sensitive than a platinum RTD, but much less linear.