Gain

For other uses, see Gain (disambiguation).

In electronics, gain is a measure of the ability of a circuit (often an amplifier) to increase the power or amplitude of a 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 may also be defined as the decimal logarithm of the same ratio.

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. 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 a photosensor.

In laser physics, gain may refer to the increment of power along the beam propagation, and its dimension is m^-1 (inverse meter) or 1/meter.

Contents 1 Logarithmic units and decibels 1.1 Power gain 1.2 Voltage gain 1.3 Current gain 1.4 Example 2 See also

Logarithmic units and decibels

Power gain

Power gain, in decibels (dB), is defined as follows:

$Gain=10\; \backslash log\; \backslash left(\; \{\backslash frac\{P\_\{out\}\}\{P\_\{in\}\}\}\backslash right)\backslash \; \backslash mathrm\{dB\}$

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. The result is then in nepers instead of decibels.

Voltage gain

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

$Gain=10\; \backslash log\{\backslash frac\{(\backslash frac\{\{V\_\{out\}\}^2\}\{R\_\{out\}\})\}\{(\backslash frac\{\{V\_\{in\}\}^2\}\{R\_\{in\}\})\}\}\backslash \; \backslash mathrm\{dB\}$

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

$Gain=10\; \backslash log\; \backslash left(\; \{\backslash frac\{V\_\{out\}\}\{V\_\{in\}\}\}\; \backslash right)^2\backslash \; \backslash mathrm\{dB\}$

and then:

$Gain=20\; \backslash log\; \backslash left(\; \{\backslash frac\{V\_\{out\}\}\{V\_\{in\}\}\}\; \backslash right)\backslash \; \backslash mathrm\{dB\}$

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

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

$Gain=10\; \backslash log\; \{\; \backslash left(\; \backslash frac\; \{\; \{I\_\{out\}\}^2\; R\_\{out\}\}\; \{\; \{I\_\{in\}\}^2\; R\_\{in\}\; \}\; \backslash right)\; \}\; \backslash \; \backslash mathrm\{dB\}$

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

$Gain=10\; \backslash log\; \backslash left(\; \{\backslash frac\{I\_\{out\}\}\{I\_\{in\}\}\}\; \backslash right)^2\backslash \; \backslash mathrm\{dB\}$

and then:

$Gain=20\; \backslash log\; \backslash left(\; \{\backslash frac\{I\_\{out\}\}\{I\_\{in\}\}\}\; \backslash right)\backslash \; \backslash mathrm\{dB\}$

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.

Example

Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input ($V\_\{in\}$) is 1 volt, its output ($V\_\{out\}$) is 10 volts. What are its voltage gain and power gain?

A. Voltage gain is simply:

$\backslash frac\{V\_\{out\}\}\{V\_\{in\}\}=\backslash frac\{10\}\{1\}=10\backslash \; \backslash mathrm\{V/V\}$

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:

$\backslash frac\{V\_\{out\}^2/50\}\{V\_\{in\}^2/50\}=\backslash frac\{V\_\{out\}^2\}\{V\_\{in\}^2\}=\backslash frac\{10^2\}\{1^2\}=100\backslash \; \backslash mathrm\{W/W\}$

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

$G\_\{dB\}=10\; \backslash log\; G\_\{W/W\}=10\; \backslash log\; 100=10\; \backslash times\; 2=20\backslash \; \backslash mathrm\{dB\}$

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

• Transmitter power output
• Absolute gain (physics)
• Loop gain
• Insertion gain
• Power gain
• Directive gain
• Net gain
• Process gain
• Signal processing gain
• Automatic gain control
• Attenuation (loss), Aperture-to-medium coupling loss, Effective radiated power

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.

This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia