# Gain

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## Electronics

In electronics, gain is usually taken to meaning the ratio of the signal output of a system to the signal input of the system. A gain of 10 would imply that a property of the signal (usually voltage or power) had increased by a factor of 10.

In electronics, it is common to use a logarithmic unit to measure gain. Originally, the bel was used. Gain = log (P2/P1) bels. This unit turned out to be a bit 'chunky', so the decibel (one tenth of a bel) became popular in its place. As there are 10 decibels in a bel, gain = 10 * log (P2/P1) dB. Note: base 10 logarithms are used (a similar unit involving natural logarithms is the neper).

When voltages are used instead of powers, the formula changes to 20 * log (V2/V1) dB. Strictly speaking, this 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.

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 (P = V2/R). Voltage gain = 10x. Power gain = 100x. Gain (dB) = 20 dB; it is inappropriate to state whether this is voltage gain or power gain. You can see that 10 log (P2/P1) = 20 log (V2/V1).

[ EDIT -- The previous paragraph doesn't make sense. In any context where it isn't clear whether it is voltage or power gain that is being referred to, the statement "Gain = 20 dB" is ambiguous. It could mean either "V2/V1 = 10 , P2/P1 = 100" or "V2/V1 = 100 , P2/P1 = 10000". If what was meant was "unless stated otherwise, it's assumed that gain refers to power rather than voltage", then that's what should have been said. ]

In antenna design, gain is the logarithm of the ratio of the antenna's radiation pattern to that of some ideal antenna, typically the theoretical isotropic antenna.

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

## Finance

In finance, gain is profit or increase in value of an investment such as stock and bond. Gain is calculated by fair market value or proceed from sale of the investment minus the sum of purchase price and all costs associated with it. If the investment is not converted into cash or another asset the gain is called unrealized gain.

Books: Powers, Richard, "Gain". Farrar, Straus and Giroux, 1998.

## Literature

Gain is a novel by American author Richard Powers.

## Psychology

In psychology, primary gain and secondary gain are commonly seen in somatoform disorders.

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