Gain
41968
219704208
2008-06-16T14:22:14Z
Robert K S
168790
{{otheruses|Gain (disambiguation)}}
In [[electronics]], '''gain''' is a measure of the ability of a [[electrical network|circuit]] (often an [[amplifier]]) to increase the [[Power (physics)|power]] or [[amplitude]] of a [[Signal (electrical engineering)|signal]]. It is usually defined as the mean [[ratio]] of the [[Signalling (telecommunication)|signal output]] of a system to the [[Signalling (telecommunication)|signal input]] of the same system. It may also be defined as the decimal [[logarithm]] of the same ratio.
Thus, the term ''gain'' on its own is [[ambiguity|ambiguous]]. For example, "a gain of five" may imply that either the [[voltage]], [[current]] or the [[Electric power|power]] is increased by a factor of five. Furthermore, the term gain is also applied in systems such as [[sensor]]s where the input and output have different units; in such cases the gain units must be specified, as in "5 microvolts per photon" for a photosensor.
In [[laser physics]], gain may refer to the increment of power along the beam propagation in a [[gain medium]], and its dimension is m<sup>-1</sup> (inverse meter) or 1/meter.
== Logarithmic units and decibels ==
===Power gain===
[[Power gain]], in [[decibel]]s (dB), is defined as follows:
:<math>Gain=10 \log \left( {\frac{P_{out}}{P_{in}}}\right)\ \mathrm{dB}</math>
where P<sub>in</sub> and P<sub>out</sub> are the input and output powers respectively.
A similar calculation can be done using a [[natural logarithm]] instead of a decimal logarithm. The result is then in [[neper]]s instead of decibels.
===Voltage gain===
When power gain is calculated using voltage instead of power, making the substitution [[Joule's law|(''P''=''V'' <sup>2</sup>/''R'')]], the formula is:
:<math>Gain=10 \log{\frac{(\frac{{V_{out}}^2}{R_{out}})}{(\frac{{V_{in}}^2}{R_{in}})}}\ \mathrm{dB}</math>
In many cases, the input and output impedances are equal, so the above equation can be simplified to:
:<math>Gain=10 \log \left( {\frac{V_{out}}{V_{in}}} \right)^2\ \mathrm{dB}</math>
and then:
:<math>Gain=20 \log \left( {\frac{V_{out}}{V_{in}}} \right)\ \mathrm{dB}</math>
This simplified formula is used to calculate a '''voltage gain''' in decibels, and is equivalent to a power gain only if the [[Electrical impedance|impedance]]s at input and output are equal.
===Current gain===
In the same way, when power gain is calculated using current instead of power, making the substitution [[Joule's law|(''P''=''I'' <sup>2</sup>''R'')]], the formula is:
:<math>Gain=10 \log { \left( \frac { {I_{out}}^2 R_{out}} { {I_{in}}^2 R_{in} } \right) } \ \mathrm{dB}</math>
In many cases, the input and output impedances are equal, so the above equation can be simplified to:
:<math>Gain=10 \log \left( {\frac{I_{out}}{I_{in}}} \right)^2\ \mathrm{dB}</math>
and then:
:<math>Gain=20 \log \left( {\frac{I_{out}}{I_{in}}} \right)\ \mathrm{dB}</math>
This simplified formula is used to calculate a '''current gain''' in decibels, and is equivalent to the power gain only if the [[Electrical impedance|impedance]]s at input and output are equal.
=== Example ===
Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input (<math>V_{in}</math>) is 1 volt, its output (<math>V_{out}</math>) is 10 volts. What are its voltage gain and power gain?
A. Voltage gain is simply:
:<math>\frac{V_{out}}{V_{in}}=\frac{10}{1}=10\ \mathrm{V/V}.</math>
The units V/V are optional, but make it clear that this figure is a voltage gain and not a power gain.
Using the expression for power, ''P'' = ''V''<sup>2</sup>/''R'', the power gain is:
:<math>\frac{V_{out}^2/50}{V_{in}^2/50}=\frac{V_{out}^2}{V_{in}^2}=\frac{10^2}{1^2}=100\ \mathrm{W/W}.</math>
Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:
:<math>G_{dB}=10 \log G_{W/W}=10 \log 100=10 \times 2=20\ \mathrm{dB}.</math>
A gain of factor 1 (equivalent to 0 dB) where both input and output are at the same voltage level and impedance is also known as ''[[1 (number)|unity]] gain''.
==See also==
*[[Transmitter power output]]
*[[Absolute gain (physics)]]
*[[Loop gain]]
*[[Insertion gain]]
*[[Power gain]]
*[[Directive gain]]
*[[Net gain]]
*[[Process gain]]
*[[Signal processing gain]]
*[[Automatic gain control]]
*[[Attenuation]] (loss), [[Aperture-to-medium coupling loss]], [[Effective radiated power]]
*[[gain medium]]
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[[Category:Antennas]]
[[Category:Electronics terms]]
[[ar:أرباح]]
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[[de:Verstärkung (Physik)]]
[[es:Ganancia (electrónica)]]
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[[it:Guadagno (elettronica)]]
[[ja:利得 (電気工学)]]
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