32 



CANONICAL FORM OF LINEAR NOISY NETWORKS [Ch. 4 



of any number of independently noisy networks of any size, provided the 

 total number of terminal pairs is preserved. 



We shall be interested in cases in which the number of terminal pairs 

 is reduced upon interconnection. A simple example is the interconnection 



Fig. 4.3. Lossless interconnection of w-terminal-pair and «- terminal-pair networks. 



of several two-terminal-pair amplifiers, with feedback, to form a new 

 two -terminal-pair amplifier. In such a case, the effect of the reduction 

 can be understood by applying the reasoning of Sec. 3.4 to the available 

 terminals of the network in Fig. 4.3. The conclusion is immediate. 



The eigenvalues of the characteristic-noise matrix of an n-terminal-pair 

 network constructed by lossless interconnection of independently noisy com- 

 ponent networks having m terminal pairs in all, m > n, must lie within the 

 range defined by the most extreme eigenvalues of the component networks. 



