A voltage divider is a linear circuit with two resistors, where the input voltage divides into two partial voltages. Voltage dividers are often used to set operating points in amplifier circuits. Here you’ll find all the formulas as well as an online calculator for easy calculations.
Calculating Voltage Dividers
In practice, we need to distinguish between an unloaded voltage divider and a loaded voltage divider. The unloaded voltage divider is essentially a series connection of two resistors.
The loaded voltage divider, on the other hand, is a combination of series and parallel connections, as in addition to the voltage divider resistors $R_{1}$ and $R_{2}$, the load $R_{L}$ is connected in parallel to $R_{2}$.
Since $R_{L}$ is often high-ohmic (for example, in an amplifier circuit) or behaves dynamically, voltage dividers are usually calculated for the unloaded condition and adjusted later as needed.
Voltage Divider Formula
For a simple, unloaded voltage divider with two resistors $R_{1}$ and $R_{2}$, you can calculate the partial voltages $U_{1}$ and $U_{2}$ using the following formulas:
$$ U_1 = U_{total} \cdot \frac{R_1}{R_1 + R_2} $$
$$ U_2 = U_{total} \cdot \frac{R_2}{R_1 + R_2} $$
In the unloaded case, the same current flows through both resistors. Therefore, we don’t need to use Ohm’s law because the voltage divides proportionally based on the resistance values.
A higher partial voltage will drop across a high-ohmic resistor, while a correspondingly smaller partial voltage will drop across a low-ohmic resistor.
Calculating Unloaded Voltage Dividers
With the following online calculator, you can calculate the output voltage at resistance 2 after entering the input voltage and the two resistance values.
Sizing the Voltage Divider
The output voltage of the voltage divider is determined by the ratio of the two resistors. But how large should the resistors be chosen?
If the resistors are too small, a significant power loss occurs in the voltage divider. If the resistors are too large, the output voltage becomes highly dependent on the connected load, and the circuit becomes unstable.
In practice, it has proven effective for the current through the load $R_{L}$ to be 5 to 10 times smaller than the current through the voltage divider. So, the ideal resistor values depend on the specific load controlled by the voltage divider.
In general, a voltage divider should only be used for high-ohmic loads. In that case, the resistors $R_{1}$ and $R_{2}$ can be in the kilohm range, resulting in low power loss for the voltage divider.
Voltage Divider Applications
A voltage divider should not be confused with a normal voltage source for large loads or consumers. Primarily, it is used to adjust high-ohmic inputs to the desired operating point.
Therefore, a voltage divider is frequently employed in transistor amplifier circuits to control the base or gate voltage of a transistor.
Voltage dividers are also used for precise voltage measurement, such as in analog-to-digital converters (ADCs). Here, the partial voltage can serve as an input signal for the ADC to convert voltages into digital values.
A potentiometer is an example of an adjustable voltage divider, where the resistance and thus the partial voltage can be varied.
