Measuring temperature using a Pt100 sensor (platinum resistance thermometer)

Introduction

I used Pt100 sensor to control the temperature of the nozzle of my 3D printer.
A resistance thermometer is a temperature sensor that utilizes the characteristics of metal whose resistance value changes with temperature.
Pt100 is a platinum resistance thermometer with a resistance value of \(100 {\rm \Omega}\) at \(0^\circ {\rm C}\).
The higher the temperature, the greater the resistance.

Resistance of Pt100

The resistance \(R_t [\Omega]\) of Pt100 at temperature \(t [ ^\circ \rm C] \) is expressed in the following equation.
Where \(t \geqq 0\).
$$
R_t = R_0 (1 + A t + B t^2)
$$
$$
A = 3.9083 \times 10^{-3}
$$
$$
B = -5.775 \times 10^{-7}
$$
$$
R_0 = 100 [\Omega]
$$

If a graph is drawn, it looks like the figure below.

Measurement Circuit

In order to convert the resistance of Pt100 to a voltage and input it to the microcontroller's AD converter, I built a circuit as shown below.
Connect Pt100 to the connector J1.

First, the bridge is configured with the resistance \(R_t\) of Pt100 and \(R_1\), \(R_2\), and \(R_3\), and the voltage \(V_1\) is obtained according to the resistance \(R_t\).
The output voltage of the bridge, \(V_1 [\rm V]\), is expressed in the following equation
$$
V_1 = 3.3[{\rm V}] \times \left( \frac{R_t}{R_1 + R_t} - \frac{R_3}{R_2 + R_3} \right)
$$

\(R_4\), \(R_5\), \(C_1\), \(C_2\) and \(C_3\) constitute the low-pass filter.

Next, the AD627 instrumentation amplifier is used to amplify it by about 25 times to bring it into a range that can be easily handled by an AD converter.
The relationship between the output voltage \(V_2 [\rm V]\) of the instrumentation amplifier and temperature \(t [ ^\circ \rm C]\) is shown in the figure below.

This relationship can be used to calculate \(t\) backwards from the AD conversion result.