Noise figure

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In telecommunication, noise figure (NF) is the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature (usually 290 K). The noise figure is thus the ratio of actual output noise to that which would remain if the device itself did not introduce noise. It is a number by which the performance of a radio receiver can be specified.

[edit] Mathematics

Noise figure is given by

N F = S N R i n - S N R o u t

where everything is in dB.

Sometimes the noise factor F is specified, which is the numerical ratio form of noise figure.

Noise Factor is a straight ratio of SNR ratios. Noise Figure is the deciBel equivalent of Noise Factor.

F = S N R i n / S N R o u t

where everything is a ratio

N F = 10 l o g (F)

$F = 10^{NF/10}, \quad NF = 10 \log(F)$

If several devices are cascaded, the total noise factor can be found with Friis' Formula:

$F = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \frac{F_4 - 1}{G_1 G_2 G_3} + \cdots + \frac{F_n - 1}{G_1 G_2 G_3 \cdots G_{n-1}},$

where $F n$ is the noise factor for the nth device and $G n$ is the gain (numerical, not in dB) of the nth device.

Devices with no gain (e.g. attenuators) have noise figure equal to their attenuation (in dB).

[edit] Details

In heterodyne systems, output noise power includes spurious contributions from image-frequency transformation, but the portion attributable to thermal noise in the input termination at standard noise temperature includes only that which appears in the output via the principal frequency transformation of the system, and excludes that which appears via the image frequency transformation.

Essentially, the noise figure is the ratio of the noise generated by the actual receiver to the noise output of an “ideal” receiver with the same overall gain and bandwidth when the receivers are connected to a room temperature load. The noise power from a simple load is equal to kTB, where k is Boltzmann's constant; T the absolute temperature of the load, for example, resistor; and B the measurement bandwidth. See also noise level, signal-to-noise ratio.

[edit] See also

This article contains material from the Federal Standard 1037C (in support of MIL-STD-188), which, as a work of the United States Government, is in the public domain.

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Categories: Federal Standard 1037C | MIL-STD-188 | Noise