Sec. 4.2] INTERCONNECTION OF LINEAR NOISY NETWORKS 



31 



A linear noisy n-terminal-pair network possesses not more than n in- 

 variants with respect to lossless transformations, and these are all real 

 numbers. 



Fig. 4.2. The canonical network. 



4.2. Interconnection of Linear Noisy Networks 



The canonical form is helpful in simplifying the discussion of the inter- 

 connection of noisy networks. Consider an ;^-terminal-pair noisy network 

 and an independently noisy w-terminal-pair network. Let them be 

 connected through a 2(w + w) -terminal-pair lossless network, resulting 

 in an {m -\- w) -terminal-pair network, as shown in Fig. 4.3. We shall now 

 determine the eigenvalues of the characteristic-noise matrix ^m+n 

 of the resulting (m -f- w) -terminal-pair network. 



To do so, we first reduce each of the component networks to canonical 

 form of the type shown in Fig. 4.2. This procedure places in evidence, 

 but does not alter, the eigenvalues of their respective characteristic-noise 

 matrices. Taken together, the two canonical forms represent the canoni- 

 cal form of the {m -f w) -terminal-pair network of Fig. 4.3. Accordingly, 

 the m-\-n eigenvalues of that network are merely the eigenvalues of the 

 component networks. The proof obviously covers the interconnection 



