Voltage divider rule

From Free net encyclopedia

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 Impedance divider
3 See also
4 External links

[edit]

Resistor divider

Two resistors are connected as shown in the following diagram:

Image:Resistor Divider.png

The output voltage V_out is related to V_in as follows:

<math>

V_\mathrm{out} = \frac{R_2}{R_1+R_2} \cdot V_\mathrm{in} </math>

As a simple example, if R₁ = R₂ then

<math>

V_\mathrm{out} = \frac{1}{2} \cdot V_\mathrm{in} </math>

Any ratio between 0 and 1 is possible.

Note that this rule 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 resistance must be considered in parallel with R₂ (see resistor) to determine the voltage at V_out.

[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

<math>

V_\mathrm{out} = \frac{Z_2}{Z_1+Z_2} \cdot V_\mathrm{in} </math>

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

Image:Capdivider.png

The resistor's impedance is simply its resistance:

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

<math> Z_C = {1 \over j \omega C} </math>

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

<math>{V_\mathrm{out} \over V_\mathrm{in}} = {{1 \over j \omega C} \over {1 \over j \omega C} + R} = {1 \over 1 + R j \omega C}</math>

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.

[edit]