B Equation

The B equation is simpler but less precise. \[ \frac{1}{T} = \frac{1}{T_0} + \frac{1}{B} \ln \left( \frac{R}{R_0} \right) \]

Where:

T is the temperature in Kelvin.
\( T_0 \) is the reference temperature (usually 298.15K or 25°C), where the thermistor's resistance is known (typically 10kΩ).
R is the resistance at temperature T.
\( R_0 \) is the resistance at the reference temperature \( T_0 \) (often 10kΩ).
B is the B-value of the thermistor.

The B value is a constant usually provided by the manufacturers, changes based on the material of a thermistor. It describes the gradient of the resistive curve over a specific temperature range between two points(i.e \( T_0 \) vs \( R_0 \) and T vs R). You can even rewrite the above formula to get B value yourself by calibrating the resistance at two temperatures.

Example Calculation:

Given:

Reference temperature \( T_0 = 298.15K \) (i.e., 25°C + 273.15 to convert to Kelvin)
Reference resistance \( R_0 = 10k\Omega \)
B-value B = 3950 (typical for many thermistors)
Measured resistance at temperature T: 10475Ω

Step 1: Apply the B-parameter equation

Substitute the given values:

\[ \frac{1}{T} = \frac{1}{298.15} + \frac{1}{3950} \ln \left( \frac{10,475}{10,000} \right) \]

\[ \frac{1}{T} = 0.003354016 + \frac{1}{3950} \ln(1.0475) \]

\[ \frac{1}{T} = 0.003354016 + (0.000011748) \]

\[ \frac{1}{T} = 0.003365764 \]

Step 2: Calculate the temperature (T)

\[ T = \frac{1}{0.003365764} = 297.10936358 (Kelvin) \]

Convert to Celsius:

\[ T_{Celsius} = 297.10936358 - 273.15 \approx 23.95936358°C \]

Result:

The temperature corresponding to a resistance of 10475Ω is approximately 23.96°C.

Rust function

fn calculate_temperature(current_res: f64, ref_res: f64, ref_temp: f64, b_val: f64) -> f64 {
    let ln_value = (current_res/ref_res).ln();
    // let ln_value = libm::log(current_res / ref_res); // use this crate for no_std
    let inv_t = (1.0 / ref_temp) + ((1.0 / b_val) * ln_value);
    1.0 / inv_t
}

fn kelvin_to_celsius(kelvin: f64) -> f64 {
    kelvin -  273.15
}

fn celsius_to_kelvin(celsius: f64) -> f64 {
    celsius + 273.15
}

const B_VALUE: f64 = 3950.0;
const V_IN: f64 = 3.3; // Input voltage
const REF_RES: f64 = 10_000.0; // Reference resistance in ohms (10kΩ)
const REF_TEMP: f64 = 25.0;  // Reference temperature 25°C

fn main() {
    let t0 = celsius_to_kelvin(REF_TEMP);
    let r = 9546.0; // Measured resistance in ohms
    
    let temperature_kelvin = calculate_temperature(r, REF_RES, t0, B_VALUE);
    let temperature_celsius = kelvin_to_celsius(temperature_kelvin);
    println!("Temperature: {:.2} °C", temperature_celsius);
}