In 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 (see Note 5) at the input port of a circuit and measuring the power delivered at the output port. The net gain in dB is calculated by taking 10 times the common logarithm of the ratio of the output power to the input power.

The net gain expressed in dB may be positive or negative. If the net gain expressed in dB is negative, it is also called the "net loss". If the net gain is expressed as a ratio, and the ratio is less than unity, a net loss is indicated.

The test signal must be chosen so that its power level is within the usual operating range of the circuit being tested.

References[link]

•  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).

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In electronics, gain is a measure of the ability of a circuit (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 gain on its own is ambiguous. For example, "a gain of five" may imply that either the voltage, current or the power is increased by a factor of five, although most often this will mean a voltage gain of five for audio and general purpose amplifiers, 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 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).

In laser physics, 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.

Logarithmic units and decibels[link]

Power gain[link]

Power gain, in decibels (dB), is defined by the 10 log rule as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=10 \log \left( {\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\ \mathrm{dB}

where P_in and P_out 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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain} = \ln\left( {\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)\, \mathrm{Np}

Voltage gain[link]

When power gain is calculated using voltage instead of power, making the substitution (P=V ²/R), the formula is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=10 \log{\frac{(\frac{{V_\mathrm{out}}^2}{R_\mathrm{out}})}{(\frac{{V_\mathrm{in}}^2}{R_\mathrm{in}})}}\ \mathrm{dB}

In many cases, the input and output impedances are equal, so the above equation can be simplified to:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=10 \log \left( {\frac{V_\mathrm{out}}{V_\mathrm{in}}} \right)^2\ \mathrm{dB}

and then the 20 log rule:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=20 \log \left( {\frac{V_\mathrm{out}}{V_\mathrm{in}}} \right)\ \mathrm{dB}

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[link]

In the same way, when power gain is calculated using current instead of power, making the substitution (P = I ²R), the formula is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=10 \log { \left( \frac { {I_\mathrm{out}}^2 R_\mathrm{out}} { {I_\mathrm{in}}^2 R_\mathrm{in} } \right) } \ \mathrm{dB}

In many cases, the input and output impedances are equal, so the above equation can be simplified to:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=10 \log \left( {\frac{I_\mathrm{out}}{I_\mathrm{in}}} \right)^2\ \mathrm{dB}

and then:

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{Gain}=20 \log \left( {\frac{I_\mathrm{out}}{I_\mathrm{in}}} \right)\ \mathrm{dB}

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, 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 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.

Example[link]

Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input (Failed to parse (Missing texvc executable; please see math/README to configure.): V_\mathrm{in} ) is 1 volt, its output (Failed to parse (Missing texvc executable; please see math/README to configure.): V_\mathrm{out} ) is 10 volts. What is its voltage and power gain?

A. Voltage gain is simply:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_\mathrm{out}}{V_\mathrm{in}}=\frac{10}{1}=10\ \mathrm{V/V}.

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V_\mathrm{out}^2/50}{V_\mathrm{in}^2/50} = \frac{V_\mathrm{out}^2}{V_\mathrm{in}^2}=\frac{10^2}{1^2}=100\ \mathrm{W/W}.

Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:

Failed to parse (Missing texvc executable; please see math/README to configure.): G_{dB}=10 \log G_{W/W}=10 \log 100=10 \times 2=20\ \mathrm{dB}.

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[link]

• 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".