Voltage measurement

For the algorithm of the MPPT controller, the input voltage and the output voltage at the solar module optimiser are required. These voltages are to be measured with a ADC, which is available as a peripheral as part of the microcontroller. The measurable voltage range of these ADC is $0 V < V_{a d c} < 3.3 V$ and is thus significantly smaller than the voltages of $0 V < V_{i n / o u t} < 50 V$ applied to the solar module optimiser. In order to be able to measure the larger voltages with the ADC, a voltage divider is dimensioned as shown in figure, which only passes on a fraction of the high voltage but with the correct ratio to the ADC. The voltage divider ratio between $R_{1}$ and $R_{2}$ determines this ratio so that the input voltage of $V_{i n} = 50 V$ corresponds to a measured voltage at the ADC of $V_{a d c} = 2.9 V$ . Some free space is built in here to have protection against overvoltages.

Voltage divider

The resistance values for $R_{1}$ and $R_{2}$ are calculated as follows:

A very high input impedance $Z > 100 k Ω$ of the ADC is assumed according to the data sheet, so the voltage divider is calculated as unloaded.
The output voltage can thus be used directly according to:
$\begin{matrix} (1) & U_{o u t} = U_{i n} \frac{R_{2}}{R_{1} + R_{2}} \end{matrix}$
To prevent the current across the resistors from becoming too large and generating unnecessary losses, $R_{2} = 2.2 k Ω$ is chosen.
For $R_{1}$ $(1)$ is transformed to:
$\begin{matrix} (2) & R_{1} = R_{2} \frac{V_{i n} - V_{o u t}}{V_{o u t}} = 2.2 k Ω \cdot \frac{50 V - 2.9 V}{2.9 V} = 35.7 k Ω \end{matrix}$
Resistors are selected from the E24 resistor series with $R_{1} = 36 k Ω$ and $R_{2} = 2.2 k Ω$ .