610 BELL SYSTEM TECHNICAL JOURNAL 



The weighted available signal-to-noise ratio at the generator terminals is: 



e 



PsA ^ m_ (3) 



Pna KT,B 



The network amplifies (or attenuates) the generator's signal power by 

 the factor G, the gain of the network, so that the available signal power at 

 the output terminals of the network is : 



Pso = G ^4_ (4) 



The network amplifies (or attenuates) the generator noise power by the 

 same factor G, and also delivers noise power which originates within itself, 

 Nn , so that the total available noise power at the output terminals of the 

 network is: 



P^o = GkTiB + .¥,v (5) 



The available signal-to-noise ratio at the output terminals of the network 

 is then : 



r— 



Pso^ ^ 4Ri (6) 



P^o GkT.B + Nu 



We now express the noise figure of the network, F, which by definition is 

 the ratio of equation (3) to equation (6), thus, 



^ GkT.B + Nu ,-N 



^ = GkT^B ^^^ 



We should pause at this point to consider this equation further, for it 

 leads us to a simpler definition of noise figure. 



Definition: The noise figure of a network is the ratio of the noise power 

 output of that network to the noise power output which would exist if the 

 network were noiseless. The temperature of the signal generator resistance 

 is 290 degrees Kelvin. 



The choice of generator temperature of 290 degrees is an arbitrary one, 

 which makes kTi = 4(10)--^ watts per cycle bandwidth; — lOlog^^i = 

 204 db below one watt per cycle. Putting Ti = 290 in equation (7) gives: 



Gk 290 B -{- Nf, . s 



Gk290B ^ ^ 



Rearranging (8) we have: 



iV^ = (F - l)Gk 290 B (9) 



