Sec. 6.2] MATRIX FORMULATION OF EXCHANGEABLE POWER 47 



with 8 a "noise column vector," 



8 = 



fc] 



(6.18) 



(6.19a) 

 (6.19&) 



Now Equation 6.17 can be rewritten as two relations: 



v' = Tu 

 V = V + 8 



If we visualize v' = K. ^, as referring simultaneously to the input 



terminals of a noise-free network T and the output terminals of a pure- 

 noise network 8, the cascade division of the system is represented in 

 Fig. 6.3. The noiseless part T does not affect the noise figure of the 

 system. Thus, for noise-figure calculations, we need consider only the 

 noise network 8 driven by a source of internal impedance Z^.^'^ 



+ 

 ^1 





h' 



v/ 



T = 



A B 

 C D 



Noise network S 



Noise-free 

 network T 



"H 



.J 



Noisy amplifier T, S 



Fig. 6.3. The general-circuit-matrix representation of a linear two-terminal-pair network 



with internal sources. 



The source equation appropriate to the right-hand terminals in Fig. 6.4 

 can be obtained from Eqs. 6.19& and 6.8 with Es = 0. 



yW = -y+8 (6.20) 



Therefore, the output exchangeable power Nei, produced by the internal 

 noise only, is given by 



y'*'88^y 



N,i = 



2y^Py 



and, since Ge = 1 for this network, we have 



Nei yWy 



F«- 1 = 



kTo A/ y^Py(2^ro A/) 



(6.21) 



(6.22) 



