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| {{Other uses|Gain (disambiguation)}}
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| {{Antennas|Characteristics}}
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| 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]] from the input to the output, by adding energy to the signal converted from some [[power supply]]. 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 is often expressed using the [[logarithm]]ic [[decibel]] (dB) units ("dB gain"). A gain greater than one (zero dB), that is, amplification, is the defining property of an [[active component]] or circuit, while a [[passive circuit]] will have a gain of less than one.
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| The term ''gain'' on its own is ambiguous, and can refer to the ratio of output to input [[voltage]], (''voltage gain''), [[Electric current|current]] (''current gain'') or [[electric power]] (''power gain''). In the field of audio and general purpose [[amplifier]]s, especially [[operational amplifier]]s, the term usually refers to voltage gain, but in [[radio frequency]] amplifiers it usually refers to power gain. 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 the [[responsivity]] of a photosensor. The "gain" of a [[bipolar transistor]] normally refers to forward current transfer ratio, either ''h''<sub>FE</sub> ("Beta", the static ratio of ''I''<sub>''c''</sub> divided by ''I''<sub>b</sub> at some operating point), or sometimes ''h''<sub>fe</sub> (the small-signal current gain, the slope of the graph of ''I''<sub>''c''</sub> against ''I''<sub>''b''</sub> at a point).
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| The term ''gain'' has a slightly different meaning in [[antenna (radio)|antenna]] design; [[antenna gain]] is the ratio of power received by a directional antenna to power received by an [[isotropic antenna]].
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| ==Logarithmic units and decibels==
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| ===Power gain===
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| [[Power gain]], in [[decibel]]s (dB), is defined by the [[10 log rule]] as follows:
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| :<math>\text{Gain}=10 \log \left( {\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\ \mathrm{dB}</math>
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| where ''P''<sub>in</sub> and ''P''<sub>out</sub> are the input and output powers respectively.
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| A similar calculation can be done using a [[natural logarithm]] instead of a decimal logarithm, and without the factor of 10, resulting in [[neper]]s instead of decibels:
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| :<math>\text{Gain} = \ln\left( {\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\, \mathrm{Np}</math> | |
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| ===Voltage gain===
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| When power gain is calculated using voltage instead of power, making the substitution [[Joule's first law|(''P''=''V'' <sup>2</sup>/''R'')]], the formula is:
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| :<math>\text{Gain}=10 \log{\frac{(\frac{{V_\mathrm{out}}^2}{R_\mathrm{out}})}{(\frac{{V_\mathrm{in}}^2}{R_\mathrm{in}})}}\ \mathrm{dB}</math>
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| In many cases, the input and output impedances are equal, so the above equation can be simplified to:
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| :<math>\text{Gain}=10 \log \left( {\frac{V_\mathrm{out}}{V_\mathrm{in}}} \right)^2\ \mathrm{dB}</math>
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| and then the [[20 log rule]]:
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| :<math>\text{Gain}=20 \log \left( {\frac{V_\mathrm{out}}{V_\mathrm{in}}} \right)\ \mathrm{dB}</math>
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| This simplified formula is used to calculate a '''voltage gain''' in decibels, and is equivalent to a power gain only if the [[Electrical impedance|impedances]] at input and output are equal.
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| ===Current gain===
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| In the same way, when power gain is calculated using current instead of power, making the substitution [[Joule's first law|(''P'' = ''I'' <sup>2</sup>''R'')]], the formula is:
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| :<math>\text{Gain}=10 \log { \left( \frac { {I_\mathrm{out}}^2 R_\mathrm{out}} { {I_\mathrm{in}}^2 R_\mathrm{in} } \right) } \ \mathrm{dB}</math>
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| In many cases, the input and output impedances are equal, so the above equation can be simplified to:
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| :<math>\text{Gain}=10 \log \left( {\frac{I_\mathrm{out}}{I_\mathrm{in}}} \right)^2\ \mathrm{dB}</math> | |
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| and then:
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| :<math>\text{Gain}=20 \log \left( {\frac{I_\mathrm{out}}{I_\mathrm{in}}} \right)\ \mathrm{dB}</math> | |
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| This simplified formula is used to calculate a '''current gain''' in decibels, and is equivalent to the power gain only if the [[Electrical impedance|impedances]] at input and output are equal.
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| The "current gain" of a [[bipolar transistor]], ''h''<sub>FE</sub> or ''h''<sub>fe</sub>, is normally given as a dimensionless number, the ratio of ''I''<sub>''c''</sub> to ''I''<sub>b</sub> (or slope of the ''I''<sub>''c''</sub>-versus-''I''<sub>''b''</sub> graph, for ''h''<sub>fe</sub>).
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| In the cases above, gain will be a dimensionless quantity, as it is the ratio of like units (Decibels are not used as units, but rather as a method of indicating a logarithmic relationship). In the bipolar transistor example it is the ratio of the output current to the input current, both measured in Amperes. In the case of other devices, the gain will have a value in [[SI]] units. Such is the case with the [[operational transconductance amplifier]], which has an open-loop gain ([[transconductance]]) in [[Siemens]] ([[mho]]s), because the gain is a ratio of the output current to the input voltage.
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| ===Example===
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| Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input (<math>V_\mathrm{in}</math>) is 1 volt, its output (<math>V_\mathrm{out}</math>) is 10 volts. What is its voltage and power gain?
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| A. Voltage gain is simply:
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| :<math>\frac{V_\mathrm{out}}{V_\mathrm{in}}=\frac{10}{1}=10\ \mathrm{V/V}.</math>
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| The units ''V''/''V'' are optional, but make it clear that this figure is a voltage gain and not a power gain.
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| Using the expression for power, ''P'' = ''V''<sup>2</sup>/''R'', the power gain is:
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| :<math>\frac{V_\mathrm{out}^2/50}{V_\mathrm{in}^2/50} = \frac{V_\mathrm{out}^2}{V_\mathrm{in}^2}=\frac{10^2}{1^2}=100\ \mathrm{W/W}.</math> | |
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| Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:
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| :<math>G_{dB}=10 \log G_{W/W}=10 \log 100=10 \times 2=20\ \mathrm{dB}.</math>
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| 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''.
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| ==See also==
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| * [[Active laser medium]]
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| * [[Antenna gain]]
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| * [[Aperture-to-medium coupling loss]]
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| * [[Automatic gain control]]
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| * [[Attenuation]]
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| * [[Complex gain]]
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| * [[DC offset]]
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| * [[Effective radiated power]]
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| * [[Gain before feedback]]
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| * [[Insertion gain]]
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| * [[Loop gain]]
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| * [[Open-loop gain]]
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| * [[Net gain]]
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| * [[Power gain]]
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| * [[Process gain]]
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| * [[Transmitter power output]]
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| {{FS1037C}}
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| [[Category:Antennas (radio)]]
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| [[Category:Electronics terminology]]
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