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In electronics, gain is a measure of the ability of a two-port circuit (often an amplifier) lớn increase the power or amplitude of a signal from the input lớn the output port by adding energy converted from some power supply lớn the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port lớn the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units ("dB gain"). A gain greater than vãn one (greater than vãn 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 vãn one.
The term gain alone is ambiguous, and can refer lớn the ratio of output lớn 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 lớn voltage gain, but in radio frequency amplifiers it usually refers lớn 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 lớn forward current transfer ratio, either hFE ("beta", the static ratio of Ic divided by Ib at some operating point), or sometimes hfe (the small-signal current gain, the slope of the graph of Ic against Ib at a point).
The gain of an electronic device or circuit generally varies with the frequency of the applied signal. Unless otherwise stated, the term refers lớn the gain for frequencies in the passband, the intended operating frequency range of the equipment. The term gain has a different meaning in antenna design; antenna gain is the ratio of radiation intensity from a directional antenna lớn (mean radiation intensity from a lossless antenna).
Logarithmic units and decibels
Power gain, in decibels (dB), is defined as follows:
where is the power applied lớn 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:
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, sánh the above equation can be simplified to:
This simplified formula, the trăng tròn log rule, is used lớn calculate a voltage gain in decibels and is equivalent lớn a power gain if and only if the impedances at input and output are equal.
In the same way, when power gain is calculated using current instead of power, making the substitution , the formula is:
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In many cases, the input and output impedances are equal, sánh the above equation can be simplified to:
This simplified formula is used lớn calculate a current gain in decibels and is equivalent lớn the power gain if and only if the impedances at input and output are equal.
The "current gain" of a bipolar transistor, or , is normally given as a dimensionless number, the ratio of lớn (or slope of the -versus- graph, for ).
In the cases above, gain will be a dimensionless quantity, as it is the ratio of lượt thích 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 lớn 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 lớn the input voltage.
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 = V2/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 lớn 0 dB) where both input and output are at the same voltage level and impedance is also known as unity gain.
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- This article incorporates public domain name material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.