A voltage divider is a simple passive linear circuit that produces an output voltage (V_out) that is a fraction of its input voltage (V_in). It is formed by two resistors connected in series across a voltage source.
How it Works
When two resistors, R1 and R2, are connected in series and a voltage V_in is applied across the combination, the voltage across R2 is lower than V_in. This is because the total voltage is divided proportionally between the two resistors based on their resistance values.
The Formula
The fundamental formula for a voltage divider is:
V_out = V_in * (R2 / (R1 + R2))
Where:
V_out is the output voltage across Resistor 2 (R2).
V_in is the input voltage applied across the series combination of R1 and R2.
R1 is the resistance of the first resistor (connected between V_in and the output node).
R2 is the resistance of the second resistor (connected between the output node and ground/common).
Key Concepts
Proportionality: The output voltage is directly proportional to the input voltage and the ratio of R2 to the total resistance (R1 + R2).
Resistance Ratio: If R2 is much larger than R1, V_out will be close to V_in. If R1 is much larger than R2, V_out will be close to 0V. If R1 = R2, V_out will be exactly half of V_in.
Load Effect: This formula assumes no significant current is drawn from the output (V_out). In practice, connecting a load resistance in parallel with R2 will reduce the effective resistance of R2, leading to a lower V_out. This is known as the "loading effect."
Applications
Voltage dividers have numerous applications in electronics:
Level Shifting: Reducing a higher voltage to a lower voltage required by a component (e.g., an Arduino analog input).
Reference Voltages: Creating stable reference voltages for comparators or analog-to-digital converters.
Sensor Interfacing: Many sensors change their resistance (e.g., thermistors, photoresistors). When used in a voltage divider, their resistance change can be converted into a voltage change that can be read by a microcontroller.
Simple Attenuators: Reducing signal amplitude.
Example Calculation
Let's say you have an input voltage of 12V (V_in = 12V), a resistor R1 of 1000 Ohms, and a resistor R2 of 2000 Ohms.