30 



CANONICAL FORM OF LINEAR NOISY NETWORKS [Ch. 4 



The ^th eigenvalue is the negative of the exchangeable power of the ^th 

 source. Thus, we have proved the following theorem: 



The exchangeable powers of the n Thevenin sources of the canonical form 

 of any n-terminal-pair network are equal and opposite in sign to the n 

 eigenvalues of the characteristic noise matrix N of the original network. 



Ideal transformers 

 1 



Fig. 4.1. Series connection of networks (Z', E') and — Zrem- 



Since ideal transformers may be applied to each terminal pair of the 

 foregoing canonical form in a manner that reduces either all resistors or 

 all \Ek\ to unit magnitude, there are actually only n independent (real) 

 parameters contained in the canonical form. This fact proves the 

 following theorem: 



