Circuit theory of linear noisy networks by Hermann A Haus, Richard B Adler

By Hermann A Haus, Richard B Adler

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1 0. 3) where Second, expressing Z ' in terms of Z by means of Eq. 5) The conditions of Eq. 7 ) in which matrix T (not �) is to be varied through all possible values consistent with the lossless requirements upon the transformation network. Sec. 2J EIGEN VALUE FO RM ULA TION 21 The significant point now is that T is actually any square matrix of order n because Zba in Eq. 4 is entirely unrestricted ! 8) in which the elements take on all possible complex values as the lossless transformation network ZT in Fig.

3. The noiseless part T does not affect the noise figure of the system. ,� 1 o---+ <>--_ + V1 i : 'V + l 1' V1' T == [� �l I 12 __o --!. t-----I _� I + i V2 � t---�\I------o I I ' I ' ' f Noise n etwork 0 I I I N olse- ree I I n etwork T L ___ ____ _ _ _ _ _ _ _ _________ _ _ _ _ _ _ _ _ _ � Noisy a m plifier T, 6 Fig. 3. The general-circuit-matrix representation of a linear two-term i nal-pair network wi th internal sources. The source equation appropriate to the right-hand terminals in Fig. 4 can be obtained from Eqs .

1 1 _ ...!.. G. 25) According to Eq. 9, the column vector y is determined, within a constant multiplier, by the source impedance Z s at which the noise measure M. of Eq. 25 is achieved. In the discussion of the noise performance of amplifiers, it turns out to be important to bear in mind the algebraic sign that AI. assumes under various physical conditions. These are summarized in Table 6. 1 . Table 6. 1 . ALGEBRAIC SIGNS O F EXCHANGEABLE GAIN AND D ERIVED Rs >0 >0 >0 <0 <0 <0 Ro >0 >0 <0 >0 <0 <0 G.

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