Electronics

Thermistors

NTC and PTC thermistors — how they work, Steinhart-Hart, and beta equation for temperature from resistance.

Types

NTC (Negative Temp Coefficient)Resistance decreases with temperature. Used as temperature sensor, inrush limiter.
PTC (Positive Temp Coefficient)Resistance increases with temperature. Used as self-resetting fuse, heater.

Beta equation (approximate)

R(T)= R₀ · exp(β · (1/T − 1/T₀))
1/T= 1/T₀ + (1/β) · ln(R/R₀)
β typical3 000 – 4 500 K for common NTCs
T₀298.15 K (25 °C reference)

Steinhart-Hart (more accurate)

1/T= A + B·ln(R) + C·(ln(R))³
A, B, CCoefficients from calibration at 3+ temperatures

Common NTC values

R @ 25 °CUse
1 kΩLow-value thermal cutoffs
10 kΩMost common — 3D printers, HVAC, batteries
47 kΩLow-power sensing
100 kΩVery low-current sensing

Circuit notes

  • Use a voltage divider with a stable reference resistor and measure with an ADC.
  • Self-heating: I²·R warms the thermistor — minimize current (< 1 mW).
  • Non-linearity: pre-compute or use a lookup table for accurate temperature.
  • For wide range, use log-amp or choose β close to your operating range.
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