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
A two-port network (a kind of four-terminal network or quadripole) is an electrical network ( circuit) or device with two ''pairs'' of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them sat ...
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 the v ...
) to increase the
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
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 amplit ...
of a
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
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 a r ...
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
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
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 Ham ...
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 o ...
ic
decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
(dB) units ("dB gain").
A gain greater than one (greater than zero dB), that is amplification, is the defining property of an
active component
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 po ...
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, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
(''voltage gain''),
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
(''current gain'') or electric power (''power gain'').
In the field of audio and general purpose amplifiers, especially
operational amplifier
An operational amplifier (often op amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative to c ...
s, 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 upp ...
amplifiers it usually refers to power gain. Furthermore, the term gain is also applied in systems such as
sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
s 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 Responsivity measures the input–output Gain (electronics), gain of a detector system. In the specific case of a photodetector, it measures the electrical output per optical input.
A photodetector's responsivity is usually expressed in units of ...
of a
photosensor
Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation. There is a wide variety of photodetectors which may be classified by mechanism of detection, such as photoelectric or photochemical effects, or by ...
. The "gain" of a
bipolar transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar t ...
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
A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
, 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
In electromagnetics, an antenna's gain is a key performance parameter which combines the antenna's directivity and radiation efficiency. The term ''power gain'' has been deprecated by IEEE. In a transmitting antenna, the gain describes how ...
is the ratio of
radiation intensity
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visib ...
from a directional antenna to
(mean radiation intensity from a lossless antenna).
Logarithmic units and decibels
Power gain
Power gain The power gain of an electrical network is the ratio of an output power to an input power. Unlike other signal gains, such as voltage and current gain, "power gain" may be ambiguous as the meaning of terms "input power" and "output power" is not alw ...
, in
decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
s (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
The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...
instead of a decimal logarithm, resulting in
neper
The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As ...
s instead of decibels:
:
Voltage gain
The power gain can be calculated using voltage instead of power using
Joule's first law
Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor produces heat.
Joule's first law (also just Joule's law), also known in countries of former US ...
; 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
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a p ...
, 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 comp ...
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 comp ...
at input and output are equal.
The "current gain" of a
bipolar transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar t ...
,
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
ampere
The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
s. 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 Transconductance (for transfer conductance), also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciproca ...
) in
siemens
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
(
mhos), 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 h ...
gain''.
See also
*
Active laser medium
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a h ...
*
Antenna gain
In electromagnetics, an antenna's gain is a key performance parameter which combines the antenna's directivity and radiation efficiency. The term ''power gain'' has been deprecated by IEEE. In a transmitting antenna, the gain describes how ...
*
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
Automatic gain control (AGC) is a closed-loop feedback regulating circuit in an amplifier or chain of amplifiers, the purpose of which is to maintain a suitable signal amplitude at its output, despite variation of the signal amplitude at the inpu ...
*
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 variable att ...
*
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 no DC ...
*
Effective radiated power
Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power, such as that emitted by a radio transmitter. It is the total power in watts that would hav ...
*
Gain before feedback
In live sound mixing, gain before feedback (GBF) is a practical measure of how much a microphone can be amplified in a sound reinforcement system before causing audio feedback. In audiology, GBF is a measure of hearing aid performance. In both fie ...
*
Insertion gain In telecommunication, insertion gain is the gain resulting from the insertion of a device in a transmission line, expressed as the ratio of the signal power delivered to that part of the line following the device to the signal power delivered to tha ...
*
Loop gain
In electronics and control system theory, loop gain is the sum of the gain, expressed as a ratio or in decibels, around a feedback loop. Feedback loops are widely used in electronics in amplifiers and oscillators, and more generally in both elec ...
*
Open-loop gain
The open-loop gain of an electronic amplifier is the gain obtained when no overall feedback is used in the circuit.
The open-loop gain of many electronic amplifiers is exceedingly high (by design) – an ''ideal'' operational amplifier (op-amp) h ...
*
Net gain
*
Power gain The power gain of an electrical network is the ratio of an output power to an input power. Unlike other signal gains, such as voltage and current gain, "power gain" may be ambiguous as the meaning of terms "input power" and "output power" is not alw ...
*
Process gain
*
Transmitter power output In radio transmission, transmitter power output (TPO) is the actual amount of power (in watts) of radio frequency (RF) energy that a transmitter produces at its output.
This is not the amount of power that a radio station reports as its power, as i ...
References
* {{FS1037C
Antennas (radio)
Electronics concepts
Transfer functions
Electrical parameters