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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 (Vout) which is proportional to another voltage (Vin).
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Resistor divider
Two resistors are connected as shown in the following diagram:
The output voltage Vout is related to Vin as follows:
V_mathrm = rac cdot V_mathrm
As a simple example, if R1 = R2 then
V_mathrm = rac cdot V_mathrm
Any ratio between 0 and 1 is possible.
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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 Vout), that load resistance must be considered in parallel with R2 to determine the voltage at Vout. In this case, the voltage at Vout is calculated as follows:
V_mathrm = rac cdot V_mathrm = rac cdot V_mathrm
where RL is a load resistor in parallel with R2.
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Impedance divider
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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 = rac cdot V_mathrm
For instance, a divider can be made with a resistor and capacitor:
The resistor's impedance is simply its resistance:
Z_mathrm = 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 =
where j is the imaginary unit, and ω is frequency in radians per second. This divider will then have the voltage ratio:
= = =
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.
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See also
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