3.2 Theory of Operation

To measure the RTD, the Digital-to-Analog Converter (DAC) is enabled to produce an output of approximately 1.8V. The DAC on AVR EA is buffered so it can drive low-impedance loads. Since the DAC voltage is applied to a 1.8 kΩ fixed resistor in series with the RTD, the current flowing through the RTD will be under 1 mA. RTD datasheets usually provide guidance for maximum current, but generally, a current of less than 1 mA is recommended because it prevents the RTD from any significant self-heating. The ADC is used to measure the voltage across the RTD, which can be converted into the sensor resistance and thus, its temperature.

The resistance of the RTD varies in a known way as a function of temperature (T), by the following equations, where R₀ is the resistance of the RTD at a temperature of 0°C and A, B and C are constants provided by the RTD manufacturer:

For T of 0°C or higher, $R\left(T\right)=R_0(1+AT+B{T}^2)$

For T of -200°C to 0°C, $R\left(T\right)=R_0(1+AT+B{T}^2+C{T}^3(T-100\left)\right)$

If the resistance of the RTD is known, then the formulas above can be used to determine the temperature.

Here are the relevant formulas for determining the resistance of the RTD:

First, the voltage across the RTD is determined by the voltage divider equation, where R_F is the resistance of the fixed resistor and R_TD is the resistance of the RTD:

$$\begin{gathered} V_{RTD}=\left(\frac{{ \\ R}_{TD}}{R_F+R_{TD}}\right){\cdot V}_{REF} \end{gathered}$$

The ADC digital result x, when the ADC is used in differential mode, is determined by the following equation (from the device datasheet), where G_PGA is the gain of the PGA:

$x=\left(\frac{V_{RTD}\cdot G_{PGA}}{V_{REF}}\right)\cdot 2048$

The voltage divider equation from above can be substituted in for V_RTD, causing V_REF to cancel out:

$x=\left(\frac{R_{TD}}{R_F+R_{TD}}\right)\cdot G_{PGA}\cdot 2048$

This equation can be solved for R_TD, the resistance of the RTD:

$R_{TD}=\left(\frac{x\cdot R_F}{G_{PGA}\cdot 2048-x}\right)$

Note that V_REF does not appear in the equation, so errors in the reference voltage value will not affect the result. The only parameters needed to compute the RTD resistance are the resistance value of the fixed resistor, the ADC result, and the PGA gain value.