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In electronics, gain is a measure of the ability of a circuit (often an amplifier) to increase the power or amplitude of a signal. It is usually defined as the mean ratio of the signal output of a system to the 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 ambiguous. For example, "a gain of five" may imply that either the voltage, current or the power is increased by a factor of five. Curiously, the term gain is also applied in systems such as sensors 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^{-1} (inverse meter) or 1/meter.

- $Gain=10\; log\; left(\{frac\{P\_\{out\}\}\{P\_\{in\}\}\}right)\; mathrm\{dB\}$

A similar calculation can be done using a natural logarithm instead of a decimal logarithm. The result is then in nepers instead of decibels.

When power gain is calculated using voltage instead of power, making the substitution (P=V ^{2}/R), the formula is:

- $Gain=10\; log\{frac\{(frac^2\}\{R\_\{out\}\})\}\{(frac^2\}\{R\_\{in\}\})\}\}\; mathrm\{dB\}$

In many cases, the input and output impedances are equal, so the above equation can be simplified to:

- $Gain=10\; log\; left(\{frac\{V\_\{out\}\}\{V\_\{in\}\}\}\; right)^2\; mathrm\{dB\}$

and then:

- $Gain=20\; log\; left(\{frac\{V\_\{out\}\}\{V\_\{in\}\}\}\; right)\; mathrm\{dB\}$

This simplified formula is used to calculate a voltage gain in decibels, and is equivalent to a power gain only if the impedances at input and output are equal.

- $Gain=10\; log\; \{\; left(frac\; \{\; \{I\_\{out\}\}^2\; R\_\{out\}\}\; \{\; \{I\_\{in\}\}^2\; R\_\{in\}\; \}\; right)\; \}\; mathrm\{dB\}$

In many cases, the input and output impedances are equal, so the above equation can be simplified to:

- $Gain=10\; log\; left(\{frac\{I\_\{out\}\}\{I\_\{in\}\}\}\; right)^2\; mathrm\{dB\}$

and then:

- $Gain=20\; log\; left(\{frac\{I\_\{out\}\}\{I\_\{in\}\}\}\; right)\; mathrm\{dB\}$

This simplified formula is used to calculate a current gain in decibels, and is equivalent to the power gain only if the impedances at input and output are equal.

A. Voltage gain is simply:

- $frac\{V\_\{out\}\}\{V\_\{in\}\}=frac\{10\}\{1\}=10\; mathrm\{V/V\}.$

- $frac\{V\_\{out\}^2/50\}\{V\_\{in\}^2/50\}=frac\{V\_\{out\}^2\}\{V\_\{in\}^2\}=frac\{10^2\}\{1^2\}=100\; mathrm\{W/W\}.$

- $G\_\{dB\}=10\; log\; G\_\{W/W\}=10\; log\; 100=10\; times\; 2=20\; mathrm\{dB\}.$

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 unity gain.

- 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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Last updated on Saturday October 11, 2008 at 13:51:34 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday October 11, 2008 at 13:51:34 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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