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An NTC (Negative Temperature Coefficient) thermistor is a resistor whose resistance falls as temperature rises. The relationship is non-linear, so two models are used: the simple Beta equation (accurate over a modest range from one reference point and a B-value) and the more precise Steinhart-Hart equation (three coefficients, accurate over a wide range).
| Model | Equation |
|---|---|
| Beta — T from R | 1/T = 1/T0 + (1/B)·ln(R/R0) |
| Beta — R from T | R = R0·eB(1/T − 1/T0) |
| Steinhart-Hart | 1/T = A + B·ln(R) + C·(ln R)³ |
All temperatures are in kelvin (K = °C + 273.15). R0 is the rated resistance at T0 = 25 °C — for example a "10k NTC" is 10 kΩ at 25 °C with a typical B of 3950 K.
An NTC thermistor's resistance falls as temperature rises, and over a modest span the relationship is well described by the beta equation:
R = R0 × eB(1/T − 1/T0)
with both temperatures in kelvin — the single most common mistake is substituting Celsius. For a typical 10 kΩ part with B = 3950:
| Temperature | Resistance |
|---|---|
| 0 °C | 33.6 kΩ |
| 25 °C | 10.0 kΩ |
| 50 °C | 3.59 kΩ |
| 85 °C | 1.09 kΩ |
The steepness is the point: resistance changes by a factor of more than thirty across that range, which gives excellent sensitivity with a simple voltage divider and no amplification. The price is strong non-linearity, so a lookup table or the beta equation in firmware is needed rather than a straight-line fit.
B itself varies slightly with temperature, which is why datasheets quote it between two specific points, such as B25/85. Over a narrow span the beta equation is accurate to a fraction of a degree; across a very wide range the Steinhart–Hart equation, with three fitted coefficients, is used instead.
Measuring resistance means passing current, and that current dissipates power in the thermistor itself, raising its temperature above the thing you are trying to measure. Datasheets give a dissipation constant in mW/°C. Keeping the measurement current low — or pulsing it only when a reading is needed — is the usual remedy, and it matters most for small parts in still air, where heat escapes slowly.
Large NTC thermistors are also used in series with mains inputs to limit inrush current into a bulk capacitor. Cold, they present several ohms; once current flows they self-heat and their resistance collapses, so steady-state loss is small. The limitation is that they need time to cool, so a rapid off-on cycle sees little protection.
A temperature-sensitive resistor whose resistance decreases as temperature increases (Negative Temperature Coefficient). It is widely used for cheap, sensitive temperature measurement.
A material constant (in kelvin) that describes how steeply the thermistor's resistance changes with temperature. Common NTCs have B around 3000–4000 K; a typical 10k NTC is 3950 K.
The reference resistance at the reference temperature, almost always 25 °C (298.15 K). A "10k NTC" has R0 = 10 kΩ at T0 = 25 °C.
With the Beta equation: 1/T = 1/T0 + (1/B)·ln(R/R0), then convert kelvin to °C by subtracting 273.15.
The Beta model is simple and fine over a limited range near the reference. Steinhart-Hart, with three coefficients, is far more accurate across a wide temperature range.
They are fitted from three known resistance-temperature points (or given in the datasheet). Once you have A, B, and C, the equation converts any resistance to temperature.
The equations are physical relationships that only work on the absolute (kelvin) scale. Always convert: K = °C + 273.15, and back with °C = K − 273.15.
The measuring current dissipates power in the thermistor and warms it slightly, biasing the reading. Use a small sense current or pulsed measurement to minimise it.
Put it in a voltage divider with a fixed resistor, read the divider voltage with the ADC, compute the thermistor resistance, then use these equations to get temperature.
NTC resistance falls with temperature (used for sensing); PTC resistance rises with temperature (used for resettable fuses and inrush/overheat protection).
Usually one equal to the thermistor's nominal value (e.g. 10 kΩ for a 10k NTC), which centres the divider's sensitivity around your temperature of interest.
With a good model and calibration, ±0.1–0.5 °C is achievable over a moderate range — excellent for the cost, though thermocouples or RTDs suit wider ranges.
R = R0 × eB(1/T − 1/T0), with temperatures in kelvin. R0 is the resistance at reference temperature T0, normally 25 °C or 298.15 K.
Because the equation involves reciprocals of absolute temperature. Substituting Celsius values produces badly wrong results, and this is the most frequent error when implementing it in firmware.
About 3.59 kΩ. The same part reads roughly 33.6 kΩ at 0 °C and 1.09 kΩ at 85 °C.
Not exactly. It varies slightly with temperature, which is why datasheets specify it between two named points such as B25/85. For wide ranges the three-coefficient Steinhart–Hart equation is more accurate.
The temperature rise caused by the measuring current dissipating power in the thermistor itself. It biases readings high and is controlled by using low measurement current or pulsing it only when a reading is taken.
Placed in series with the supply, it presents several ohms when cold, limiting the surge into the bulk capacitor. It then self-heats and its resistance falls, so running losses are small. It needs time to cool, so rapid power cycling bypasses the protection.
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