SIGNAL - TO - NOISE RATIO

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SIGNAL-TO-NOISE RATIO (SNR)

 
SNRrx = Prx - 10 log ( k Ta B )  { dB }
where: 

SNRrx = signal-to-noise ratio at detector ( dB )
k = Boltzman's constant = 1.380 · 10-23 ( J/K )
Ta = ambient temperature ( K )
B = receiver bandwidth at detector ( Hz )
 

NOISE FIGURE
 
Noise figure is the increase in noise power of a device from the input to the output that is greater that the signal gain. In effect, it is the amount of decrease of the signal-to-noise ratio. Like gain, noise figure can be expressed either as a ratio or in decibels.

Cascade noise figure calculation is carried out by dealing with gain and noise figure as a ratio rather than decibels, and then converting back to decibels at the end. As the following equation shows, cascaded noise figure is effected most profoundly by the noise figure of components closest to the input of the system as long as some positive gain exists in the cascade. If only loss exists in the cascade, then the cascaded noise figure equals the magnitude of the total loss. The following equation is used to calculate cascaded noise figure as a ratio based on ratio values for gain and noise figure (do not use decibel values)
  

nfcascade = , where N = number of stages

Example cascaded system
Click here to view an
example cascaded system.
Conversion to decibels:
Click here to see Agilent's online App Note 1303 on using a spectrum analyzer to measure noise figure.
 

NOISE POWER

 
Noise power is based on the thermal noise power at the input of the system, along with system gain and noise figure:

Multiply by 1000 to obtain milliwatts and then convert to dBm units or convert to dBW units and add 30 dB:


or

Now that we have the thermal noise at the input, add the system gain and the additional noise added by the system (the NF) to get the noise power at the output: