Gain

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In electronics, gain is usually taken as the mean ratio of the signal output of a system to the signal input of the system. A gain of five would imply that either the voltage or power is increased by a factor of five.

Logarithmic units and decibels

In electronics, it is common to use logarithmic units to measure gain. Originally, the bel was used:

<math>Gain=log_{10}(\frac{P_2}{P_1}) (bels)</math>

where P1 and P2 are the input and output powers respectively.

Using the bel unit, however, results in small numbers, so the decibel (one tenth of a bel) became popular in its place. As there are ten decibels (dB) in a bel:

<math>Gain=10 \times log ({\frac{P_2}{P_1}})dB</math>

(A similar unit using natural logarithms is called the neper.)

When gain is calculated using voltage instead of power, making the substitution (P=V²/R), the formula is:

<math>Gain=10{\times}log{\frac{(\frac{{V_2}^2}{R})}{(\frac{{V_1}^2}{R})}}dB</math>

<math>Gain=10{\times}log{(\frac{V_2}{V_1}})^2 dB</math>

<math>Gain=20{\times}log ({\frac{V_2}{V_1}})dB</math>

This formula only holds true if the load impedances are identical. In many modern electronic devices, output impedances are low enough and input impedances high enough that load can be ignored without significantly affecting the calculation.

Example

If an amplifier produces an output of 1 volt into a 1 ohm load, then it is providing 1 watt of output power. If the amplifier is then altered to produce an output of 10 volts into the same load, it is now providing 100 watts of output power <math>(P= {{V^2}\over R}) \!\ </math>. Therefore:

voltage gain = 10 times (10 dB)

power gain = 100 times (20 dB)

A gain of factor 1 or (equivalent to 0 dB) where both input and output are at the same voltage level is also known as unity gain.

See also

• Transmitter power output
• Absolute gain
• Loop gain
• Insertion gain
• Directive gain
• Net gain
• Process gain
• Signal processing gain
• Noise gain
• Automatic gain control
• Loss, Aperture-to-medium coupling loss, Effective radiated power

de:Verstärkung (Physik)

es:Ganancia (electrónica) fr:Gain it:Guadagno ja:利得 pl:Współczynnik wzmocnienia pt:Ganho su:Gain zh:增益

Wikipedia information about Gain This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Gain". It may not have been reviewed by professional editors (see full disclaimer). Help contribute to Americola and edit this article.