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Optimal NTC Bias Resistor Calculator

Find the ideal series resistor for your NTC thermistor for optimal temperature reading.

Parameters

1. NTC Thermistor Properties
Nominal resistance at 25°C. Found in datasheet (e.g., 10000 for 10k NTC).
Ohms (Ω)
Material constant of the NTC, in Kelvin (K). Found in datasheet (e.g., 3950).
K
2. Operating Temperature Range
°C
°C
3. Circuit & Optimization
Volts
"NTC (to GND)": Vsupply → RS → NTC → GND. Vout across NTC. Voltage increases with temperature decrease.
"Series Resistor RS": Vsupply → NTC → RS → GND. Vout across RS. Voltage increases with temperature increase.
"Max Voltage Swing": Uses geometric mean of RNTC at Tmin & Tmax. Maximizes ΔVout.
"Best Linearity": Sets RS = RNTC at mid-range temperature. Improves linearity around the center.

Theory & Explanation

Choosing the correct series resistor (RS, often called a bias resistor) for an NTC thermistor is crucial for maximizing the sensitivity of temperature measurements, especially when using an Analog-to-Digital Converter (ADC).

NTC Resistance vs. Temperature

The resistance of an NTC (Negative Temperature Coefficient) thermistor decreases as its temperature increases. This relationship is typically described by the Steinhart-Hart equation, or a simplified version using the Beta (β) coefficient:

R(T) = R25 * exp(β * (1/TK - 1/T25K))

Where: R(T) is resistance at T (Kelvin), R25 is resistance at 25°C (298.15 K), β is the Beta coefficient (Kelvin), TK is temperature in Kelvin (T°C + 273.15).

Voltage Divider Circuit

The thermistor is usually in a voltage divider. If Vout is measured across the NTC (NTC to GND):

Vout = Vsupply * (RNTC / (RS + RNTC))

If Vout is measured across RS (NTC to Vsupply):

Vout = Vsupply * (RS / (RS + RNTC))

Optimal Series Resistor (RS) Strategy

This calculator offers two strategies for selecting RS:

  1. Maximize Voltage Swing (Geometric Mean):

    To maximize the change in output voltage (ΔVout) across the temperature range [Tmin, Tmax], RS is chosen as the geometric mean of the NTC's resistances at these extremes:

    RS_opt_swing = sqrt(RNTC@Tmin * RNTC@Tmax)

    This is mathematically derived to give the largest voltage difference for the ADC. However, the sensitivity (dV/dT) will not be constant across the range.

  2. Best Linearity at Mid-Temperature:

    To achieve a more linear voltage response with respect to temperature around the center of your operating range, RS is chosen to be equal to the NTC's resistance at the mid-point temperature (Tmid = (Tmin + Tmax) / 2):

    RS_opt_linear = RNTC@Tmid

    This can simplify temperature conversion but might result in a slightly smaller overall ΔVout compared to the geometric mean method.

This calculator first determines the "optimal" RS based on your chosen strategy, then suggests the nearest standard E12 resistor value. You can click on the standard value to see how it impacts the output voltages.

Considerations

  • Standard Values: The calculated optimal RS is unlikely to be a standard resistor value. Using the nearest standard value will slightly alter the output characteristics.
  • ADC Resolution & Reference: The final temperature resolution depends on your ADC's bit depth and reference voltage (Vref). A larger useful ΔVout (that fits within Vref) allows more ADC steps to represent your temperature range.
  • Self-heating & Power Consumption: Current through the NTC causes self-heating. Higher resistance values for RS and RNTC reduce current and self-heating, and lower power consumption.
  • Component Tolerances: The actual RS and NTC parameters (R25, β) have tolerances, which will affect the accuracy of the real-world circuit.