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Voltage divider

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In electronics, a voltage divider is a simple device designed to create a voltage (V_out) which is proportional to another voltage (V_in). It is commonly used to create a reference voltage, and may also be used as a signal attenuator at low frequencies. Voltage dividers are also known by the terms resistor divider and potential divider.

1 Resistive divider rule
2 Voltage divider as a voltage source
3 Use of voltage dividers
4 Impedance divider
5 See also
6 External links
7 References

Resistive divider rule

A voltage divider referenced to ground is created by connecting two resistors as shown in the following diagram: The output voltage V_out is related to V _in as follows:

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V_\mathrm{out} = \frac{R_2}{R_1+R_2} \cdot V_\mathrm{in} </math> It may be useful to note that R₁ and R₂ may each comprise many resistors in series. As a simple example, if R₁ = R₂ then

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V_\mathrm{out} = \frac{1}{2} \cdot V_\mathrm{in} </math> As a more specific and/or practical example, if V_out=6V and V_in=9V (both commonly used voltages), then:

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\frac{V_\mathrm{out}}{V_\mathrm{in}} = \frac{R_2}{R_1+R_2} = \frac{6}{9} = \frac{2}{3} </math> and by solving using algebra, R₂ must be twice the value of R₁.

To solve for R1:

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

To solve for R2:

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R_2 = \frac{R_1}{\frac{V_\mathrm{in}}{V_\mathrm{out}}-1}

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Any ratio between 0 and 1 is possible. That is, using resistors alone it is not possible to either reverse the voltage or increase V_out above V_in

Voltage divider as a voltage source

While voltage dividers may be used to produce very precise reference voltages, they make very poor voltage sources. This is because if a load is connected between the output voltage and ground the effective resistance between V_out and ground decreases. A change in the resistance of R₂ changes the load voltage, an undesirable situation for a voltage source. In terms of the above equation, 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:

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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} </math> where R_L is a load resistor in parallel with R₂. Note that for high impedance loads it is possible to use a voltage divider as a voltage source, as long as R₁ and R₂ have very small values compared to the load. This technique is rarely used, as the power disipated in such a divider would be considerable.

Use of voltage dividers

Voltage dividers are often used to produce stable reference voltages. These reference voltages may be used at a device with a high input impedance, such as an op-amp without fear of loading the divider. Alternatively, the reference voltage may be used to set the voltage being produced by a voltage source. A simple way of doing this (for low power applications) is to simply input the reference voltage into the non-inverting input of an op-amp buffer. A voltage divider is commonly used to set the DC bias of a common emitter amplifier.

Impedance divider

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

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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: The resistor's impedance is simply its resistance:

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Z_\mathrm{R} = R </math> The capacitor's impedance is a large resistance at low frequencies and a low resistance at high frequencies. The exact formula is:

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Z_\mathrm{C} = {1 \over j \omega C} </math> where C is the capacitance of the capacitor, j is the imaginary unit, and ω is the frequency of the input voltage which is measured in radians per second. (Frequency in radians/second ω is related to frequency f in Hz by ω = 2 π f ). This divider will then have the voltage ratio:

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{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 + j \omega \ C R} </math>. The product τ = CR is called the time constant of the circuit. 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.