Voltage divider

21-03-2012 12:04

A voltage divider is a special circuit that is used to output a fraction of the input voltage. For example, if you have a 5V battery and you need a 3V voltage. The voltage divider is one of the simplest and common circuits used in electronics.

Below it is possible to use this simple tool to compute the output voltage or to compute the resistance values. In order to compute one of the values, click on the its label (e.g., R₁, V_in, etc.) and insert the remaining values. Initially, the tool computes the value of the output voltage V_out.

This tool can also compute the output voltage, when this is connected to a load (i.e., the resistance R_L): when the field R_L is empty (as it is when the page is initially loaded), the voltage V_out is computed in open-circuit (i.e., as R_L would be ∞).

V_in: V

R₁: kΩ

R₂: kΩ

V_out: V

R_L: kΩ

Let's see how the voltage divider works. The input voltage is applied to the two resistances R₁ and R₂ in series, while the output voltage is the one that can be measured through the resistance R₂ alone. Ohm's Law states that the current through a conductor between two points is directly proportional to the potential difference across the two points, and thus that:

$V=R \cdot I$

Let's apply this formula to the circuit on the left, that is formed by V_in, R₁ and R₂:

$V_{in}=(R_1+R_2)\cdot I_1$

and then to the circuit on the right:

$V_{out}=R_2 \cdot I_2$

Since the currents I₁ and I₂ represent the same current (that flowing through R₂, that is the same that flows also through R₁), we have:

$V_{out}=\frac{R_1}{R_1+R_2}\cdot V_{in}$

The previous formula holds in the case of absence of the load R_L. When this is present, it is easy to follow the same computation and obtain:

$V_{out}=\frac{R_2\|R_L}{R_1 + R_2\|R_L}\cdot V_{in}$

where R₂||R_L is:

$R_2\|R_L=\frac{R_2 R_L}{R_2+R_L}$

Since the output voltage depends only on the ratio between R1 and R2, it is possible to use different values of resistance to obtain the same V_out (e.g., if R1 = R2, the value of V_out will always be one half of the input, whether R1 and R2 are 1 Ω, or they are 1 MΩ). For the great part of electronic uses, the sum of R1 and R2 should be always within 1 kΩ and 10 kΩ, as the SparkFun website advices (see the box to the right), because using lower values, the circuit would waste a lot of power (for the current flowing through R1 and R2), while using higher values, V_out could be unable to obtain enough current.

A more detailed description of the voltage divider can be found on Wikipedia. The formula can be derived as a simple application of Ohm's Law.

SparkFun has an interesting and simple tutorial on this topic.

The formula of the output voltage when there is a load R_L has been found from this webpage.

The circuit has been drawn with Webtronics, an online tool for circuit design.