Gain

Encyclopedia

In electronics

,

(often an amplifier

) to increase the power

or amplitude

of a signal

from the input to the output. It is usually defined as the mean ratio

of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale, in terms of the decimal logarithm

of the same ratio ("dB

gain"). A gain greater than one (zero dB), 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.

Thus, the term

, current

or the power

is increased by a factor of five, although

s, especially operational amplifiers, but a power gain for radio frequency

amplifiers, and for directional aerials will refer to a signal power change compared with a simple dipole. Furthermore, the term gain is also applied in systems such as sensor

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

of a photosensor. The "gain" of a bipolar transistor normally refers to forward current transfer ratio, either

In laser physics

, gain may refer to the increment of power along the beam propagation in a gain medium, and its dimension is

, in decibel

s (dB), is defined by the 10 log rule as follows:

where

A similar calculation can be done using a natural logarithm

instead of a decimal logarithm, and without the factor of 10, resulting in neper

s instead of decibels:

, 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

at input and output are equal.

, 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

at input and output are equal.

The "current gain" of a bipolar transistor,

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

, which has an open-loop gain (transconductance

) in Siemens

(mhos), because the gain is a ratio of the output current to the input voltage.

A. Voltage gain is simply:

The units

Using the expression for power,

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

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

,

**gain**is a measure of the ability of a circuitElectrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...

(often an amplifier

Amplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

) to increase the power

Power (physics)

In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

or amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

of a signal

Signal (electrical engineering)

In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity....

from the input to the output. It is usually defined as the mean ratio

Ratio

In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale, in terms of the decimal logarithm

Logarithm

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

of the same ratio ("dB

Decibel

The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

gain"). A gain greater than one (zero dB), 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.

Thus, the term

*gain*on its own is ambiguous. For example, "a gain of five" may imply that either the voltageVoltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

, current

Electric current

Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

or the power

Electric power

Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt.-Circuits:Electric power, like mechanical power, is represented by the letter P in electrical equations...

is increased by a factor of five, although

*most often*this will mean a voltage gain of five for audio and general purpose amplifierAmplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

s, especially operational amplifiers, but a power gain for radio frequency

Radio frequency

Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

amplifiers, and for directional aerials will refer to a signal power change compared with a simple dipole. Furthermore, the term gain is also applied in systems such as sensor

Sensor

A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument. For example, a mercury-in-glass thermometer converts the measured temperature into expansion and contraction of a liquid which can be read on a calibrated...

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

Responsivity measures the input–output gain of a detector system. For a system that responds linearly to its input, there is a unique responsivity. For nonlinear systems, the responsivity is the local slope ....

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).In laser physics

Laser Physics

Laser Physics is an international scientific journal published by Nauka/Interperiodica. It is distributed through the Springer.-Topics covered:The journal specializes in laser physics, but also publishes papers about:...

, gain may refer to the increment of power along the beam propagation in a gain medium, and its dimension is

*m*^{−1}(inverse meter) or 1/meter.### Power gain

Power gainPower 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 always clear. Three important power gains are...

, in decibel

Decibel

The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

s (dB), is defined by the 10 log rule as follows:

where

*P*_{in}and*P*_{out}are the input and output powers respectively.A similar calculation can be done using a natural logarithm

Natural logarithm

The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...

instead of a decimal logarithm, and without the factor of 10, resulting in neper

Neper

The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. It has the unit symbol Np. The unit's name is derived from the name of John Napier, the inventor of logarithms...

s instead of decibels:

### Voltage gain

When power gain is calculated using voltage instead of power, making the substitution (*P*=*V*^{2}/*R*)Joule's law

Joule's laws are a pair of laws concerning the heat produced by a current and the energy dependence of an ideal gas to that of pressure, volume, and temperature, respectively...

, 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 impedancesElectrical impedance

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

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 (*P*=*I*^{2}*R*)Joule's law

Joule's laws are a pair of laws concerning the heat produced by a current and the energy dependence of an ideal gas to that of pressure, volume, and temperature, respectively...

, 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 impedancesElectrical impedance

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

at input and output are equal.

The "current gain" of a bipolar transistor,

*h*_{FE}or*h*_{fe}, is normally given as a dimensionless number, the ratio of*I*_{c}to*I*_{b}(or slope of the*I*_{c}-versus-*I*_{b}graph, for*h*_{fe}).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

Si

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units. Such is the case with the operational transconductance amplifier

Operational transconductance amplifier

The operational transconductance amplifier is an amplifier whose differential input voltage produces an output current. Thus, it is a voltage controlled current source . There is usually an additional input for a current to control the amplifier's transconductance...

, which has an open-loop gain (transconductance

Transconductance

Transconductance, also known as mutual conductance, is a property of certain electronic components. Conductance is the reciprocal of resistance; transconductance, meanwhile, is the ratio of the current change at the output port to the voltage change at the input port. It is written as gm...

) in Siemens

Siemens

Siemens may refer toSiemens, a German family name carried by generations of telecommunications industrialists, including:* Werner von Siemens , inventor, founder of Siemens AG...

(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 gain*.## See also

- Active laser mediumActive laser mediumThe active laser medium is the source of optical gain within a laser. The gain results from the stimulated emission of electronic or molecular transitions to a lower energy state from a higher energy state...
- Antenna gainAntenna gainIn electromagnetics, an antenna's power gain or simply gain is a key performance figure which combines the antenna's directivity and electrical efficiency. As a transmitting antenna, the figure describes how well the antenna converts input power into radio waves headed in a specified direction...
- Aperture-to-medium coupling lossAperture-to-medium coupling lossIn telecommunication, aperture-to-medium coupling loss is the difference between the theoretical 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 controlAutomatic gain controlAutomatic gain control is an adaptive system found in many electronic devices. The average output signal level is fed back to adjust the gain to an appropriate level for a range of input signal levels...
- AttenuationAttenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
- Complex gainComplex gainComplex gain is a term used in electronics to describe the effect 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.-Example:...
- DC offset
- Effective radiated powerEffective radiated powerIn radio telecommunications, effective radiated power or equivalent radiated power is a standardized theoretical measurement of radio frequency energy using the SI unit watts, and is determined by subtracting system losses and adding system gains...
- Gain before feedbackGain before feedbackIn live sound mixing, gain before feedback 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...
- Insertion gainInsertion gainIn 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 that same part before insertion...
- Loop gainLoop gainLoop gain is an engineering term used to quantify the gain of a system controlled by feedback loops. As such, the concept of loop gain is useful in a variety of disciplines. Traditionally, most of those have been in the field of electronics, telecommunications, or control systems...
- Open-loop gainOpen-loop gainThe open-loop gain of an operational amplifier is the gain obtained when no feedback is used in the circuit.Open loop gain is usually exceedingly high; in fact, an ideal operational amplifier has infinite open-loop gain. Typically an op-amp may have an open-loop gain of around 10^5...
- Net gainNet gainIn telecommunications, net gain is the overall gain of a transmission circuit.Net gain is measured by applying a test signal at an appropriate power level at the input port of a circuit and measuring the power delivered at the output port...
- Power gainPower gainThe 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 always clear. Three important power gains are...
- Process gainProcess gainIn a spread spectrum system, the process gain is the ratio of the spread bandwidth to the unspread bandwidth. It is usually expressed in decibels ....
- Transmitter power outputTransmitter power outputIn radio transmission, transmitter power output is the actual amount of power of radio frequency energy that a transmitter produces at its output....