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Cascaded Noise Figure & Noise Temperature

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.

Example cascaded system - RF Cafe
Click here to view
an example of a
cascaded system.
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).

Here is a  great article on Noise Figure Uncertainty in the October 1999 "Microwave & RF" magazine.

Note that when calculating cascaded noise figure, quantities must be expressed as ratios, NOT as decibels. By convention, lower case variables represent ratios, while upper case variables represent decibels (dB).

                     Conversions:   nf = 10NF/10     NF (dB) = 10 * log10 (nf)
In Compact Form:

nfN = Cascaded noise figure equation formula - RF Cafe, where N = number of stages
Cascaded Noise Figure In Expanded Form:

Cascaded noise figure equation - RF Cafe

Click here to see Agilent's App Note 1303 on using a spectrum analyzer
to measure noise figure.
Conversion Between Noise Figure and Noise Temperature

Noise Temperature (K) = 290 *Noise figure to noise temperature conversion equation formula - RF Cafe

Noise Figure (dB) = 10 * log10 Noise temperature to noise figure conversion equation - RF Cafe
These equations assume a room temperature reference (290 K).
If applicable, use whatever your reference temperature is in place of the 290.
Cascaded Noise Temperature Calculation

Cascaded noise temperature equation - RF Cafe

 
The following table lists a few conversions. See the Noise Power Calculator online calculator for calculating other values.

NF(dB) TN (°K)   NF(dB) TN (°K)
0.1 7 2.1 180
0.2 14 2.2 191
0.3 21 2.3 202
0.4 28 2.4 214
0.5 35 2.5 226
0.6 43 2.6 238
0.7 51 2.7 250
0.8 59 2.8 263
0.9 67 2.9 275
1.0 75 3.0 289
1.1 84 3.1 302
1.2 92 3.2 316
1.3 101 3.3 330
1.4 110 3.4 344
1.5 120 3.5 359
1.6 129 3.6 374
1.7 139 3.7 390
1.8 149 3.8 406
1.9 159 3.9 422
2.0 170 4.0 438
Noise figure equation - RF Cafe


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