NTC calibration and multiple temperature sensors

Introduction

Calibration of NTC sensors and different

NTC

Note that the temperature of the sensor rises when the current supplies through the resistor. The NTC is nonlinear; see below Calibration.

Negative Temperature Coefficient, NTCLE100E3101JB0 or similar (MF52B NTC Thermistor). The NTC is connected in series with a "shunt" resistor $R_{1}$, see Measurement of resistors: voltage divider. Usually $R_{1}=10kOhms$ is used. The total resistance of the circuit is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R = R_1 + R_{NTC}} , which gives

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} R_{NTC} &= \frac{U_\text{measured}}{U-U_\text{measured}}R_1 \\ \end{align} }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} V(R_1 + R_n) = V_in R_2 \end{align} }

Calibrating: Steinhart-Hart Equation

A nonlinear Steinhart-Hart equation is widely used

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac 1T = A + B \ln(Rt) + C (\ln (Rt))^3 }

The parameters Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C} can be obtained, if the resistance of three (3) temperatures is known.

Calibrating using known datapoints

Though the NTC sensor is nonlinear, locally it will be linear. Thus by using some known datapoints the temperature can be estimated.