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| [[Image:Impedance Voltage divider.png|thumb|200px|Figure 1: Voltage divider]]
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| In [[electronics]] or [[Electrical engineering technology|EET]], a '''voltage divider ''' (also known as a '''potential divider''') is a [[linear circuit]] that produces an output [[voltage]] (''V''<sub>out</sub>) that is a fraction of its input voltage (''V''<sub>in</sub>). '''Voltage division''' refers to the partitioning of a voltage among the components of the divider.
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| An example of a voltage divider consists of two [[resistor]]s in [[Series and parallel circuits|series]] or a [[potentiometer]]. It is commonly used to create a reference voltage, or to get a low voltage signal proportional to the voltage to be measured, and may also be used as a signal [[attenuator (electronics)|attenuator]] at low frequencies. For direct current and relatively low frequencies, a voltage divider may be sufficiently accurate if made only of resistors; where frequency response over a wide range is required (such as in an [[oscilloscope]] probe), the voltage divider may have capacitive elements added to allow compensation for load capacitance. In electric power transmission, a capacitive voltage divider is used for measurement of high voltage.
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| == General case ==
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| A voltage divider referenced to [[ground (electricity)|ground]] is created by connecting two [[electrical impedance]]s in series, as shown in Figure 1. The input voltage is applied across the series impedances Z<sub>1</sub> and Z<sub>2</sub> and the output is the voltage across Z<sub>2</sub>.
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| Z<sub>1</sub> and Z<sub>2</sub> may be composed of any combination of elements such as [[resistor]]s, [[inductor]]s and [[capacitor]]s.
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| Applying [[Ohm's Law]], the relationship between the input voltage, V<sub>in</sub>, and the output voltage, V<sub>out</sub>, can be found:
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| :<math>
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| V_\mathrm{out} = \frac{Z_2}{Z_1+Z_2} \cdot V_\mathrm{in}
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| </math>
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| Proof:<br />
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| :<math>V_\mathrm{in} = I\cdot(Z_1+Z_2)</math>
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| :<math>V_\mathrm{out} = I\cdot Z_2</math>
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| :<math>I = \frac {V_\mathrm{in}}{Z_1+Z_2}</math>
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| :<math>V_\mathrm{out} = V_\mathrm{in} \cdot\frac {Z_2}{Z_1+Z_2}</math>
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| The [[transfer function]] (also known as the divider's '''voltage ratio''') of this circuit is simply:
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| :<math>
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| H = \frac {V_{out}}{V_{in}} = \frac{Z_2}{Z_1+Z_2}
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| </math>
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| In general this transfer function is a [[complex variable|complex]], [[rational function]] of [[frequency]].
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| ==Examples==
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| ===Resistive divider===
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| [[Image:Resistive divider.png|thumb|200px|Figure 2: Simple resistive voltage divider]]
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| A resistive divider is the case where both impedances, Z<sub>1</sub> and Z<sub>2</sub>, are purely resistive (Figure 2).
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| Substituting Z<sub>1</sub> = R<sub>1</sub> and Z<sub>2</sub> = R<sub>2</sub> into the previous expression gives:
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| :<math>
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| V_\mathrm{out} = \frac{R_2}{R_1+R_2} \cdot V_\mathrm{in}
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| </math>
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| If ''R''<sub>1</sub> = ''R''<sub>2</sub> then
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| :<math>
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| V_\mathrm{out} = \frac{1}{2} \cdot V_\mathrm{in}
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| </math>
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| If ''V''<sub>out</sub>=6V and ''V''<sub>in</sub>=9V (both commonly used voltages), then:
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| :<math>
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| \frac{V_\mathrm{out}}{V_\mathrm{in}} = \frac{R_2}{R_1+R_2} = \frac{6}{9} = \frac{2}{3}
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| </math>
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| and by solving using [[algebra]], ''R''<sub>2</sub> must be twice the value of ''R''<sub>1</sub>.
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| To solve for R1:
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| :<math>
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| R_1 = \frac{R_2 \cdot V_\mathrm{in}}{V_\mathrm{out}} - R_2 = R_2 \cdot ({\frac{V_\mathrm{in}}{V_\mathrm{out}}-1})
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| </math>
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| To solve for R2:
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| :<math>
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| R_2 = R_1 \cdot \frac{1} {({\frac{V_\mathrm{in}}{V_\mathrm{out}}-1})}
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| </math>
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| Any ratio ''V''<sub>out</sub>/''V''<sub>in</sub> greater than 1 is not possible. That is, using resistors alone it is not possible to either invert the voltage or increase ''V''<sub>out</sub> above ''V''<sub>in</sub>.
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| === Low-pass RC filter ===
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| [[File:RC Divider.svg|thumb|200px|Figure 3: Resistor/capacitor voltage divider]] | |
| Consider a divider consisting of a resistor and [[capacitor]] as shown in Figure 3.
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| Comparing with the general case, we see Z<sub>1</sub> = R and Z<sub>2</sub> is the impedance of the capacitor, given by
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| :<math> Z_2 = -jX_{\mathrm{C}} =\frac {1} {j \omega C} </math> <math> \ ,</math>
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| where X<sub>C</sub> is the [[Reactance (electronics)|reactance]] of the capacitor, C is the [[capacitance]] of the capacitor, ''j'' is the [[imaginary unit]], and ''ω'' (omega) is the [[radian frequency]] of the input voltage.
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| This divider will then have the voltage ratio:
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| :<math>
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| {V_\mathrm{out} \over V_\mathrm{in}} = {Z_\mathrm{2} \over Z_\mathrm{1} + Z_\mathrm{2}} = {{1 \over j \omega C} \over {1 \over j \omega C} + R} = {1 \over 1 + j \omega \ R C}
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| </math>.
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| The product ''τ (tau) = RC'' is called the ''[[time constant]] '' of the circuit.
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| The ratio then depends on frequency, in this case decreasing as frequency increases. This circuit is, in fact, a basic (first-order) [[lowpass filter]]. The ratio contains an imaginary number, and actually contains both the amplitude and [[Phase (waves)|phase shift]] information of the filter. To extract just the amplitude ratio, calculate the [[magnitude (mathematics)|magnitude]] of the ratio, that is:
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| :<math> \left| \frac {V_\mathrm{out}} {V_\mathrm{in}} \right| = \frac {1} {\sqrt { 1 + ( \omega R C )^2 } } \ . </math>
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| ===Inductive divider===
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| Inductive dividers split AC input according to inductance:
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| <math>V_{out} = V_{in} \cdot \frac {L_2} {L_1 + L_2}</math>
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| The above equation is for non-interacting inductors; [[mutual inductance]] (as in an [[autotransformer]]) will alter the results.
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| Inductive dividers split DC input according to the resistance of the elements as for the resistive divider above.
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| ===Capacitive divider===
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| Capacitive dividers do not pass DC input.
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| For an AC input a simple capacitive equation is:
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| <math>V_{out} = V_{in} \cdot \frac {C_1} {C_1 + C_2}</math>
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| Any leakage current in the capactive elements requires use of the generalized expression with two impedances. By selection of parallel R and C elements in the proper proportions, the same division ratio can be maintained over a useful range of frequencies. This is the principle applied in compensated [[oscilloscope]] probes to increase measurement bandwidth.
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| ==Loading effect==
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| The voltage output of a voltage divider is not fixed but varies according to the [[Electrical load|load]]. To obtain a reasonably stable output voltage the output current should be a small fraction of the input current. The drawback of this is that most of the input current is wasted as heat in the divider. An alternative is to use a [[voltage regulator]].
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| == Applications ==
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| Voltage dividers are used for adjusting the level of a signal, for bias of active devices in amplifiers, and for measurement of voltages. A [[Wheatstone bridge]] and a [[multimeter]] both include voltage dividers. A [[potentiometer]] is used as a variable voltage divider in the volume control of a radio.
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| Voltage dividers can also be used to allow a microcontroller to measure the resistance of a sensor.<ref>{{cite web|url=http://music.columbia.edu/~douglas/classes/microcontrollers/part3.html|accessdate=29 October 2013}}</ref> The sensor is hooked up in a voltage divider alongside a known resistor, and a known input voltage is given, and the output voltage is measured, and then used to determine the resistance of the sensor.
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| ==References==
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| {{reflist}}
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| == Further reading ==
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| {{refbegin}}
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| * {{cite book|last1=Horowitz|first1=Paul|authorlink1=Paul Horowitz|last2=Hill|first2=Winfield|authorlink2=Winfield Hill|title=[[The Art of Electronics]]|publisher=Cambridge University Press|year=1989}}
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| {{refend}}
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| == See also ==
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| *[[Current divider]]
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| *[[DC-to-DC converter]]
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| ==External links==
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| *[http://lab.bitluni.net/voltagedivider Voltage divider and current calculator with variable count of resistors]
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| *[http://www.sengpielaudio.com/calculator-voltagedivider.htm Voltage divider or potentiometer calculations]
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| *[http://afrotechmods.com/tutorials/2011/11/28/voltage-divider-tutorial/ Voltage divider tutorial video in HD]
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| *[http://www.magic-worlld.narod.ru Online calculator to choose the values by series E24, E96]
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| *[http://www.cl-projects.de/projects/tools/resmatch-en.phtml Online voltage divider calculator: chooses the best pair from a given series and also gives the color code]
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| *[http://www.labbookpages.co.uk/electronics/resNetworks/potentialDivider.html Java based search tool for analysing a potential divider circuit]
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| *[http://www.tedpavlic.com/teaching/osu/ece209/support/circuits_sys_review.pdf Voltage divider theory] - RC [[low-pass filter]] example and voltage divider using [[Thévenin's theorem]]
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| {{DEFAULTSORT:Voltage Divider}}
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| [[Category:Analog circuits]]
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Roberto is what's written over his birth certificate fortunately he never really appreciated that name. South Carolina is your birth place. The most beloved hobby for him and as well , his kids is so that you can fish and he's been really doing it for quite a while. Auditing is how he supports his family. Go of his website to come across out more: http://circuspartypanama.com
Here is my web-site; clash of clans gold glitch