Voltage divider rule

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In electronics, the voltage divider rule, or simply the voltage divider, resistor divider or potential divider, is a design technique used to create a voltage (V_out) which is proportional to another voltage (V_in).

1 Resistor divider
2 Loaded voltage divider
3 Impedance divider
4 See also
5 External links

[edit] Resistor divider

Two resistors are connected as shown in the following diagram:

The output voltage V_out is related to V_in as follows:

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

As a simple example, if R₁ = R₂ then

$V_\mathrm{out} = \frac{1}{2} \cdot V_\mathrm{in}$

Any ratio between 0 and 1 is possible.

[edit] Loaded voltage divider

Note that the resistor divider rule (above) only works if the divider is unloaded, i.e. the load resistance is infinite and all of the current flowing through R₁ goes into R₂. If current flows into a load resistance (through V_out), that load resistance must be considered in parallel with R₂ to determine the voltage at V_out. In this case, the voltage at V_out is calculated as follows:

$V_\mathrm{out} = \frac{R_2 \| R_\mathrm{L}}{R_1+R_2 \| R_\mathrm{L}} \cdot V_\mathrm{in} = \frac{R_2}{R_1+R_2+\frac{R_1R_2}{R_\mathrm{L}}} \cdot V_\mathrm{in}$

where R_L is a load resistor in parallel with R₂.

[edit] Impedance divider

A voltage divider is usually thought of as two resistors, but capacitors, inductors, or any combined impedance can be used. For general impedances Z₁ and Z₂, the voltage becomes

$V_\mathrm{out} = \frac{Z_2}{Z_1+Z_2} \cdot V_\mathrm{in}$

For instance, a divider can be made with a resistor and capacitor:

The resistor's impedance is simply its resistance:

Z R = R

The capacitor's impedance is a large resistance at low frequencies and a low resistance at high frequencies. The exact formula is:

$Z_\mathrm{C} = {1 \over j \omega C}$

where j is the imaginary unit, and ω is frequency in radians per second. This divider will then have the voltage ratio:

${V_\mathrm{out} \over V_\mathrm{in}} = {Z_\mathrm{C} \over Z_\mathrm{C} + Z_\mathrm{R}} = {{1 \over j \omega C} \over {1 \over j \omega C} + R} = {1 \over 1 + R j \omega C}$

The ratio then depends on frequency, in this case decreasing as frequency increases. This circuit is, in fact, a basic (first-order) lowpass filter, or, in the world of audio, a treble-cut filter. The ratio contains an imaginary number, and actually contains both the amplitude and phase shift information of the filter. To extract just the amplitude ratio, calculate the magnitude of the ratio, or just use the reactance of the capacitor instead of the impedance.