18 



IMPEDANCE REPRESENTATION 



[Ch. 2 



The exchangeable power determined in this way will, in general, be 

 different for different choices of the lossless network because the con- 

 tributions of the n terminal pairs of the original network are in each case 

 combined with different relative magnitudes and phases to make up the 

 output at terminals n -\- \. Therefore, we might expect the available 

 power of the original w-terminal-pair network to be the extremum value 

 of Pe,n+\ obtainable by considering every possible variation of the lossless 



/ 



Variable lossless 



network 



(possibly 



non reciprocal) 



7 



1 '^i 





En 



Fig. 2.4. Imbedding into an (n + l)-terminal-pair lossless network. 



transformation network. As we shall see shortly, this result proves to be 

 correct only in one simple case, namely, that in which the original n- 

 terminal-pair network contains only coherent signal generators. In such 

 a case Pe,n+i has only one stationary value as the lossless network is 

 varied, and this value is precisely the exchangeable power discussed 

 previously {Pg in Eq. 2.15). 



In the general situation of an arbitrary noisy network, we shall find that 

 Pe,n+\ has n stationary values as the lossless transformation network is 

 varied in all possible ways. None of these individually is the exchange- 

 able power for the original network. The sum of them, however, does 

 prove to be the exchangeable power. The major burden of the discussion 

 immediately to follow will be to interpret the stationary values of Pe,n+i 

 in terms of some physical properties of the original network. In later 

 chapters, the relationship of these results with the noise performance 

 will emerge. 



