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In telecommunication, noise figure (NF) is a measure of degradation of the signal to noise ratio (SNR), caused by components in the RF signal chain. The noise figure 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.

General[]

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 difference in decibels (dB) between the noise output of the actual receiver to the noise output of an “ideal” receiver with the same overall gain and bandwidth when the receivers are connected to sources at the standard noise temperature (usually 290 K). The noise power from a simple load is equal to , where is Boltzmann's constant, is the absolute temperature of the load (for example a resistor), and is the measurement bandwidth.

This makes the noise figure a useful figure of merit for terrestrial systems where the antenna effective temperature is usually near the standard 290 K. In this case, one receiver with a noise figure say 2 dB better than another, will have an output signal to noise ratio that is about 2 dB better than the other. However, in the case of satellite communications systems, where the antenna is pointed out into cold space, the antenna effective temperature is often colder than 290 K. In these cases a 2 dB improvement in receiver noise figure will result in more than a 2 dB improvement in the output signal to noise ratio. For this reason, the related figure of effective noise temperature is therefore often used instead of the noise figure for characterizing satellite-communication receivers and LNA.

Definition[]

The noise figure of a system can be defined as

where and are the input and output signal-to-noise ratios, respectively. Alternatively, noise figure may be defined in terms of dB units

where and are in dB. The previous formula is only valid when the input termination is at standard noise temperature .

These definitions are equivalent, differing only in the use of dB units. The first definition is sometimes referred to as noise factor to distinguish it from the dB form.

The noise factor of a device is related to its noise temperature via

Devices with no gain (e.g., attenuators) have a noise figure equal to their attenuation L (absolute value, not in dB) when their physical temperature equals . More generally, for an attenuator at a physical temperature , the noise temperature is , thus giving a noise factor of

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

where is the noise factor for the n-th device and is the power gain (linear, not in dB) of the n-th device.

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