In
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, gain is a measure of the ability of a
two-port circuit (often an
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost t ...
) to increase the
power or
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
of a
signal from the input to the output port
by adding energy converted from some
power supply
A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As ...
to the signal. It is usually defined as the mean
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of the
signal amplitude or power at the output
port
A port is a maritime facility comprising one or more wharves or loading areas, where ships load and discharge cargo and passengers. Although usually situated on a sea coast or estuary, ports can also be found far inland, such as H ...
to the amplitude or power at the input port.
It is often expressed using the
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 ...
ic
decibel (dB) units ("dB gain").
A gain greater than one (greater than zero dB), that is amplification, is the defining property of an
active component or circuit, while a
passive circuit
Passivity is a property of engineering systems, most commonly encountered in analog electronics and control systems. Typically, analog designers use ''passivity'' to refer to incrementally passive components and systems, which are incapable of p ...
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 (''voltage gain''),
current (''current gain'') or electric power (''power gain'').
In the field of audio and general purpose amplifiers, especially
operational amplifiers, the term usually refers to voltage gain,
but in
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
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 ''h''
FE ("beta", the static ratio of ''I''
''c'' divided by ''I''
b at some operating point), or sometimes ''h''
fe (the small-signal current gain, the slope of the graph of ''I''
''c'' against ''I''
''b'' at a point).
The gain of an electronic device or circuit generally varies with the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of the applied signal. Unless otherwise stated, the term refers to the gain for frequencies in the
passband, the intended operating frequency range of the equipment.
The term ''gain'' has a different meaning in
antenna
Antenna ( antennas or antennae) may refer to:
Science and engineering
* Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves
* Antennae Galaxies, the name of two collid ...
design;
antenna gain is the ratio of
radiation intensity from a directional antenna to
(mean radiation intensity from a lossless antenna).
Logarithmic units and decibels
Power gain
Power gain, in
decibels (dB), is defined as follows:
:
where
is the power applied to the input,
is the power from the output.
A similar calculation can be done using a
natural logarithm instead of a decimal logarithm, resulting in
nepers instead of decibels:
:
Voltage gain
The power gain can be calculated using voltage instead of power using
Joule's first law ; the formula is:
:
In many cases, the input impedance
and output impedance
are equal, so the above equation can be simplified to:
:
:
This simplified formula, the
20 log rule, is used to calculate a voltage gain in decibels and is equivalent to a power gain if and only if the
impedances
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.
Quantitatively, the impedance of a two-terminal circuit element is the ratio of the compl ...
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:
:
:
This simplified formula is used to calculate a current gain in decibels and is equivalent to the power gain if and only if the
impedances
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.
Quantitatively, the impedance of a two-terminal circuit element is the ratio of the compl ...
at input and output are equal.
The "current gain" of a
bipolar transistor,
or
, is normally given as a dimensionless number, the ratio of
to
(or slope of the
-versus-
graph, for
).
In the cases above, gain will be a dimensionless quantity, as it is the ratio of like units (decibels are not used as units, but rather as a method of indicating a logarithmic relationship). 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
The operational transconductance amplifier (OTA) is an amplifier whose differential input voltage produces an output current. Thus, it is a voltage controlled current source (VCCS). There is usually an additional input for a current to control t ...
, which has an open-loop gain (
transconductance) in
siemens (
mho
The siemens (symbol: S) is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and ...
s), 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'' = ''V''
2/''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 (equivalent to 0 dB) where both input and output are at the same voltage level and impedance is also known as ''
unity
Unity may refer to:
Buildings
* Unity Building, Oregon, Illinois, US; a historic building
* Unity Building (Chicago), Illinois, US; a skyscraper
* Unity Buildings, Liverpool, UK; two buildings in England
* Unity Chapel, Wyoming, Wisconsin, US; a ...
gain''.
See also
*
Active laser medium
*
Antenna gain
*
Aperture-to-medium coupling loss
In telecommunication, aperture-to-medium coupling loss is the difference between the theoretical antenna gain of a very large antenna, such as the antennas in beyond-the-horizon microwave links, and the gain that can be realized in practice.
'' ...
*
Automatic gain control
*
Attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at var ...
*
Complex gain In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal. The term ''complex'' is used because mathematically this effect can be expressed as a complex number.
LTI systems
Considering the gener ...
*
DC offset
In signal processing, when describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean amplitude of the waveform. If the mean amplitude is zero, there is no DC bias. A waveform with n ...
*
Effective radiated power
*
Gain before feedback
*
Insertion gain
*
Loop gain
*
Open-loop gain
*
Net gain
*
Power gain
*
Process gain
*
Transmitter power output
References
* {{FS1037C
Antennas (radio)
Electronics concepts
Transfer functions
Electrical parameters