Impedance Formulation 



of the Charactenstic^Noise Matrix 



We shall proceed to a close examination of the stationary-value 

 problem posed in connection with Fig. 2.4, at the end of the last section 

 and prove the assertions made about it. A matrix formulation of 

 the problem will be required, which will reduce the problem to one in 

 matrix eigenvalues. The corresponding eigenvalues are those of a new 

 matrix, the "characteristic-noise matrix." Some general features of the 

 eigenvalues will be studied, including their values for two interesting 

 special cases. The effect of lossless imbeddings upon the eigenvalues will 

 be discussed to complete the background for the noise-performance 

 investigations. 



3.1. Matrix Formulation of Stationary- Value Problem 



The network operation indicated in Fig. 2.4 is conveniently accom- 

 pUshed by first imbedding the original w-terminal-pair network Z in a 

 lossless 2w-terminal-pair network, as indicated in Fig. 2.2. Open-circuit- 

 ing all terminal pairs of the resulting w-terminal-pair network Z', except 

 the ith, we achieve the w-to-1 -terminal-pair lossless transformation 

 indicated in Fig. 2.4. The exchangeable power from the ith. terminal 

 pair of the network Z' can be written in matrix form as 



1 E/E/* 1 rE^E^t| 



19 



