In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude
of a signal from the input to the output by adding energy converted from some power supply
to the 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 is often expressed using the logarithmic decibel
units. A gain greater than one, 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.
The term gain alone is ambiguous, and can refer to the ratio of output to input voltage,,
current or electric power. In the field of audio and general purpose amplifiers, especially
operational amplifiers, 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 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 the responsivity of a photosensor.
The "gain" of a bipolar transistor normally refers to forward current transfer ratio,
either hFE, or sometimes hfe. The term gain has a slightly different meaning
in antenna design; antenna gain is the ratio of power received by a directional antenna
to power received by an isotropic antenna.
Logarithmic units and decibels Power gain
Power gain, in decibels, is defined by the 10 log rule as follows:
where Pin and Pout are the input and output powers respectively.
A similar calculation can be done using a natural logarithm instead of a decimal logarithm,
and without the factor of 10, resulting in nepers instead of decibels:
Voltage gain When power gain is calculated using voltage
instead of power, making the substitution, the formula is:
In many cases, the input and output impedances are equal, so the above equation can be simplified
to:
and then the 20 log rule:
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.
Current gain In the same way, when power gain is calculated
using current instead of power, making the substitution, the formula is:
In many cases, the input and output impedances are equal, so the above equation can be simplified
to:
and then:
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.
The "current gain" of a bipolar transistor, hFE or hfe, is normally given as a dimensionless
number, the ratio of Ic to Ib. In the cases above, gain will be a dimensionless
quantity, as it is the ratio of like units. 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 in Siemens, because the gain is a ratio
of the output current to the input voltage. Example
Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When
its input is 1 volt, its output is 10 volts. What is its voltage and power gain?
A. Voltage gain is simply:
The units V/V are optional, but make it clear that this figure is a voltage gain and not
a power gain. Using the expression for power, P = V2/R, the power gain is:
Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:
A gain of factor 1 where both input and output are at the same voltage level and impedance
is also known as unity gain. See also
Active laser medium Antenna gain
Aperture-to-medium coupling loss Automatic gain control
Attenuation Complex gain
DC offset Effective radiated power
Gain before feedback Insertion gain
Loop gain Open-loop gain
Net gain Power gain
Process gain Transmitter power output
This article incorporates public domain material from the General Services Administration
document "Federal Standard 1037C".