Gain

For other uses, see (disambiguation)}}}.

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. It has wide application in amplifiers.

Logarithmic units and decibels

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

Gain = log₁₀(P₂/P₁) bel

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

This unit is generally too large, so the decibel (one tenth of a bel) became popular in its place. As there are ten decibels (dB) in a bel:

Gain = 10 * log₁₀(P₂/P₁) dB

(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:

Gain = 10 * log ((V₂²/R) /(V₁²/R) ) dB

Gain = 10 * log ((V₂/V₁)² ) dB

Gain = 20 * log (V₂/V₁) dB

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 (P=V²/R). Therefore:

voltage gain = 10 times
power gain = 100 times

— which by definition is said to be a gain of 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.

Gain

Logarithmic units and decibels

Example

See also