
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 signaltonoise ratio. Like gain, noise figure can be
expressed either as a ratio or in decibels.
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 = 10^{NF/10}
↔ NF (dB) = 10 * log_{10} (nf) 
In Compact Form:
nf_{N}_{ = }
,
where N = number of stages 
Cascaded Noise Figure In Expanded Form:

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 (dB) = 10 * log10
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

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


Check this out 
someone referenced this page on
Wikipedia!



