Noise figure
Encyclopedia
Noise figure is a measure of degradation of the signal-to-noise ratio
(SNR), caused by components in a radio frequency
(RF) signal chain. The noise figure is defined as 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.
s (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 matched 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 low noise amplifiers.
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
and 
are the input and output power signal-to-noise ratio
s, respectively.
The noise figure is defined as:
where
and 
are in decibel
s (dB). The noise figure is the noise factor, given in dB:
These formulae are only valid when the input termination is at standard noise temperature
, although in practice small differences in temperature do not significantly affect the values.
The noise factor of a device is related to its noise temperature
:
Attenuators
have a noise factor F equal to their attenuation ratio L when their physical temperature equals
. More generally, for an attenuator at a physical temperature 
, the noise temperature is 
, 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. In a well designed receive chain, only the noise factor of the first amplifier should be significant.
Signal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
(SNR), caused by components in a radio frequency
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
(RF) signal chain. The noise figure is defined as the ratio of the output noise power
Noise power
In telecommunication, the term noise power has the following meanings:# The measured total noise per bandwidth unit at the input or output of a device when the signal is not present.# The power generated by a random electromagnetic process....
of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature
(usually 290 KKelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
). 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
The noise figure is the difference in decibelDecibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (dB) between the noise output of the actual receiver to the noise output of an “ideal” receiver with the same overall gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...
and bandwidth when the receivers are connected to matched 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 resistorResistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
), 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 low noise amplifiers.
In heterodyne
Heterodyne
Heterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful...
systems, output noise power includes spurious contributions from image-frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the 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
System
System is a set of interacting or interdependent components forming an integrated whole....
and excludes that which appears via the image frequency transformation.
Definition
The noise factor of a system is defined as:where
and are the input and output power signal-to-noise ratioSignal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
s, respectively.
The noise figure is defined as:
where
and are in decibelDecibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
s (dB). The noise figure is the noise factor, given in dB:
These formulae are only valid when the input termination is at standard noise temperature
, although in practice small differences in temperature do not significantly affect the values.The noise factor of a device is related to its noise temperature
:Attenuators
Attenuator (electronics)
An attenuator is an electronic device that reduces the amplitude or power of a signal without appreciably distorting its waveform.An attenuator is effectively the opposite of an amplifier, though the two work by different methods...
have a noise factor F equal to their attenuation ratio L when their physical temperature equals
. More generally, for an attenuator at a physical temperature , the noise temperature is , 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 gainPower gain
The power gain of an electrical network is the ratio of an output power to an input power. Unlike other signal gains, such as voltage and current gain, "power gain" may be ambiguous as the meaning of terms "input power" and "output power" is not always clear. Three important power gains are...
(linear, not in dB) of the n-th device. In a well designed receive chain, only the noise factor of the first amplifier should be significant.
See also
- NoiseNoiseIn common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...
- Noise (electronic)
- Noise figure meterNoise figure meterA noise figure meter is an instrument for measuring the noise figure of an amplifier, mixer, or similar device. An example instrument is the 1983-era Agilent 8970A.- Measurement methods :...
- Noise level
- Thermal noise
- Signal-to-noise ratioSignal-to-noise ratioSignal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
- Y-factorY-factorThe Y-factor method is a widely used technique for measuring the gain and noise temperature of an amplifier. It is based on the Johnson-Nyquist noise of a resistor at two different, known temperatures....