Noise figure

The noise figure, sometimes called noise factor, is in communications technology, a key figure for the noise of a linear two-port network. A two-port network can represent, for example, an amplifier stage in this context.

The concept of noise figure is also used to describe the noise of optical amplifiers.

General

To determine the noise figure is assumed that in the drawing on the generator with the generator voltage feeds the input of the network an ideal impedance and additionally thermally rushes to the useful signal. This is represented by the hatched recorded noise voltage source which the band-limited noise voltage

Generated. describes the real part of the impedance generator.

The rushing resistor located on a noise temperature of 290 K. This temperature value corresponding approximately to room temperature, is arbitrary and means the standard noise figure.

At the input of the two-port is supplied with a signal power and a noise power, which ratio is the signal -to-noise ratio ( SNR) of the input:

At its output, the two-port then emits a signal power and noise power to the impedance. In an ideal adopted, noise-free two-port network is the SNR of the output

Equal to the SNR of the input.

In real two promoters, such as, for example, an electronic amplifier with the gain factor G, the amplifier internal to the generator uncorrelated noise sources, thereby improving the signal -to-noise ratio at the output is always less than the signal -to-noise ratio at the input:

The challenge consists of an amplifier in this context is the signal to add as little self noise, so that the useful signal S at the output despite deterioration of the signal -to-noise ratio above the noise level of the subsequent processing stages.

Definition

The noise figure F is given by the ratio:

However, if the gain G of the amplifier, the attenuation is usually considered a front, such as in a cable, then

Often, the noise figure is logarithmically in decibels (dB ) as noise:

Since the sizes generally depend on the frequency, the noise figure is chosen a sufficiently small bandwidth in the context of noise measurement for the practical determination within which all the variables on the frequency are approximately constant. So that the noise figure becomes a function of frequency, which is then referred to as spectral noise figure F (f).

Linear two-port network

Further, it is possible to describe the noise figure of the additionally generated in the linear two-port device noise power. The output side noise power consists of an inputted to increased noise power and the noise power generated in the two-port network:

Thus, the noise figure of the linear two-port network can be represented:

With the additionally introduced by the two-port noise figure:

When is the ideal, noise-free two-ports

Consequently, the noise figure for the ideal, noise-free linear two-port network is ( independent of frequency ):

Cascade

If more than two gates connected as a cascade in series - this is for example in a series of amplifiers along a long line of case - can the noise figure of a cascade Fg with n two-ports generalize to:

This extended form of the noise figure is also known as Friis formula.

Noise temperature

The noise figure of a two-port network can also be expressed with the help of the noise temperature Te:

Here, T0 is the reference temperature, which is set for the standard noise figure with 290K.

An ideal, noise-free amplifier has a noise temperature of Te = 0 K, which corresponds to a noise figure of 1. A real amplifier, for example, a noise temperature of Te = 290 K is located, has a noise figure of 2, which means that the SNR at the output of the amplifier degrades by 3 dB. In particular, for input amplifier and to achieve a high SNR, it is therefore necessary to keep the noise temperature of the amplifier as low as possible.

Non-linear two-port network

Nonlinear Two goals can the spectra of net power and noise power at Zweitoreingang change so that may arise less than 1 by filtering measures in favorable cases, noise figures. A typical example is a demodulator for frequency-modulated information signals, which produces an improved signal -to-noise ratio at the demodulator output for signal -to-noise ratios at the input is above a threshold value.

Optical amplifier

The noise figure here describes the decrease of the signal-to -noise ratio for a coherent optical signal as it passes through an optical amplifier. To the signal-to -noise ratios are considered of the electric current that would provide the quantum efficiency of 1 before or after the optical amplifier, an ideal photodetector. The factors included in the S / N ratios electrical services are therefore proportional to the square of the corresponding optical performance.

Although the input signal is assumed to be ideal, its performance due to the quantum nature of the photon is not completely constant but varies as a result of shot noise.

To the already contained in the input signal and amplified in the optical amplifier noise more noise components are added, resulting in the amplifier. In most cases, dominates the mixed product of signal and ASE. Neglecting the other noise components, we obtain the noise figure of the optical amplifier (EDFA )

With

• G gain
• H Planck's constant
• F frequency of the input optical signal in Hz

For Raman amplifier applies a different formula, as along the fiber takes place simultaneously gain and attenuation.