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# Noise Figure of Amplifiers

Posted on 2007-01-27 as part of the Photonics Spotlight (available as e-mail newsletter!)

Abstract: The article discusses what the noise figure of an amplifier really means, and uses the example of a chain of two high-gain amplifiers. It turns out that an important ingredient of the definition of the noise figure is often overlooked.

Ref.: encyclopedia articles on noise figure, amplifier noise, amplifiers

The noise figure of an amplifier (e.g. a fiber amplifier) is often said to simply be the amount by which the signal-to-noise ratio of an input signal is degraded. Then, however, it is not understandable how the noise figure of an ideal high-gain four-level amplifier can always be 3 dB. In particular, how about two such amplifiers in series? If the signal-to-noise ratio is degraded twice, the noise figure should be 6 dB. But considering the two amplifiers as a single amplifier (made as an amplifier chain), it should be 3 dB. It is not conceivable why e.g. two fiber amplifiers in series should be worse concerning amplifier noise than a single longer amplifier.

The confusion arises from the frequently encountered omission of an important condition: the noise figure is the amount by which the signal-to-noise ratio of an input signal is degraded, if the input signal is shot-noise limited. In a chain made of two high-gain amplifiers, the first device may have a shot-noise limited input. Its output will then have strongly amplified quantum noise, plus some excess noise according to the noise figure. This means that the input of the second amplifier has strong excess noise (i.e., noise at a level high above the shot noise level), so that this amplifier won't degrade the noise performance further if it also has a noise figure of e.g. 3 dB.

The exact analog of this occurs with electronic amplifiers, only that quantum noise has to be replaced with thermal noise. Obviously, the apparent mystery as described above is not one of these quantum mysteries, and is relatively simple to resolve. And the understanding of such issues is obviously quite important when considering amplifier noise, e.g. in photodetection and particularly in optical fiber communications.

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