64 NETWORK REALIZATION OF OPTIMUM PERFORMANCE [Ch. 7 

 where 



P' = 2RPR+ = RPR-^ = 



■ ■ [: -?] 



(7.19) 



Combining Eqs. 7,18 and 7.19, we obtain for the noise measure, Eq. 6.25, 



w^SV^w 1 



M. = 



w\F' - T'F'T'^)w kTo Af 



(7.20) 



with 



Lw2j ^ 2lyi-y2\ 



The noise measure expressed in terms of the voltage and current variables 

 is optimized when y is an eigenvector of the noise matrix N. Correspond- 

 ingly, the noise measure is also optimized in terms of the wave formulation 

 if w is an eigenvector of the noise matrix 



N' = (P' - T'P'T'"^)-i8'5 



/T>/rr/t\-iFFT 



(7.22) 



The requirement that Re (>'2^^V3'/^^) > imposed on the eigenvector 

 y^^^ imposes a corresponding limitation on w^^\ From Eq. 7.21, 



^2 



( Zs"" - 1 \ 

 U^* + 1/ 



(7.23) 



Thus, W2/W1 is the negative-conjugate reflection coefficient corresponding 

 to the source impedance Zs. Therefore, we must have 



^2 



< 1 



(7.24) 



From Eqs. 7.15, 7.16, 7.19, and 7.22, it is easily found that, for the net- 

 work of Fig. 7.1a, 



N' = 



5/ 



2s /S /* 



\u? - 1 



l-dTW 



\u\^di 82 



IwP - 1 



-IT^ 



2 1 J 



(7.25) 



