Noise figure
Noise figure (NF) and noise factor (F) are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain.
The noise power from a simple load is equal to kTB, where k is the Boltzmann constant, T is the absolute temperature of the load (for example a resistor), and B is the measurement bandwidth.
However, in the case of satellite communications systems, where the receiver antenna is pointed out into cold space, the antenna effective temperature is often colder than 290 K.[2] 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.
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.
where SNRi and SNRo are the input and output signal-to-noise ratios respectively.
Note that this specific definition is only valid for an input signal of which the noise is Ni=kT0B.
These formulae are only valid when the input termination is at standard noise temperature T0 = 290 K, although in practice small differences in temperature do not significantly affect the values.
More generally, for an attenuator at a physical temperature T, the noise temperature is Te = (L − 1)T, giving a noise factor If several devices are cascaded, the total noise factor can be found with Friis' formula:[5] where Fn is the noise factor for the n-th device, and Gn is the power gain (linear, not in dB) of the n-th device.
The first amplifier in a chain usually has the most significant effect on the total noise figure because the noise figures of the following stages are reduced by stage gains.
From the definition of noise factor[3] and assuming a system which has a noisy single stage amplifier.
, Substituting the output SNR to the noise factor definition,[6] In cascaded systems
An input termination at the standard noise temperature is still assumed for the individual component.
The optical noise figure is discussed in multiple sources.
[7][8][9][10][11] Electric sources generate noise with a power spectral density, or energy per mode, equal to kT, where k is the Boltzmann constant and T is the absolute temperature.
Instead the energy quantization causes notable shot noise in the detector.
In an optical receiver which can output one available mode or two available quadratures this corresponds to a noise power spectral density, or energy per mode, of hf where h is the Planck constant and f is the optical frequency.
In an optical receiver with only one available quadrature the shot noise has a power spectral density, or energy per mode, of only hf/2.
Monochromatic or sufficiently attenuated light has a Poisson distribution of detected photons.
In the limit of large n the variance of photons is Gn(2nsp(G-1)+1) where nsp is the spontaneous emission factor.
Fpnf is in conceptual conflict[9][10] with the electrical noise factor, which is now called Fe: Photocurrent I is proportional to optical power P. P is proportional to squares of a field amplitude (electric or magnetic).
But for Fe in the electrical domain the power is proportional to the square of the signal amplitude.
If SNRpnf is a noise factor then its definition must be independent of measurement apparatus and frequency.
Hence it is possible to lower the frequency from optical (say 200 THz) to electrical (say 200 MHz).
But the direct detection photoreceiver needed for measurement of SNRpnf takes mainly the in-phase noise into account whereas quadrature noise can be neglected for high n. Also, the receiver outputs only one baseband signal, corresponding to quadrature.
Another optical noise figure Fase for amplified spontaneous emission has been defined.
All the above conflicts are resolved by the optical in-phase and quadrature noise factor and figure Fo,IQ.
For an optical amplifier it holds Fo,IQ = nsp(1-1/G)+1/G ≥ 1.
Quantity nsp(1-1/G) is the input-referred number of added noise photons per mode.
This article incorporates public domain material from Federal Standard 1037C.
