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Noise factor is a measure of how the the signal to noise ratio is degraded by a device:
Where Sin is the signal level at the input
Nin is the noise level at the input,
Sout is the signal level at the output
and Nout is the noise level at the output.
The noise factor of a device is specified with noise from a noise source at room temperature (Nin=KT), where K is Boltzman's constant and T is approximately room temperature in Kelvin; KT is somewhere around -174 dBm/Hz. Depending on where devices are positioned in an amplification chain, the individual noise factors will have different effects on the overall noise, according to Friis (see below). Thanks for clarifying this, Andreas!
Signal to noise ratio always worsens from input to output due to entropy or one of those other depressing laws of the universe; as the S/N ratio at output is less than S/N ratio at input, noise factor is always greater than unity.
Noise figure is the noise factor, expressed in decibels:
NF (decibels)=noise figure =10*log(F)