40 



Case 

 1 



2 

 3 



OTHER REPRESENTATIONS 



Table 5.1. Classification of Networks and Eigenvalues 

 IN T-MATRix Representation 



[Ch.5 



[i;-t]q.-[i!-tJ 

 positive definite 

 negative definite 



indefinite 



Network 

 Class 

 passive 



active (negative 

 resistance) 



active 



pT 

 <0 



>0 



^0 



Eigenvalues 

 (X.) of Nr 

 alK 



all> 



jsome > 

 Isome < 



Figure 3.1 gives directly the allowed range of pr and the eigenvalues 

 of Nr, if the notation of Table 3.1 is replaced on the figure by that 

 of Table 5.1. 



In the specific case of the mixed voltage-current representation of 

 Eqs. 5.3 to 5.5, Nr and pr can be simplified if we introduce the detailed 

 expressions for the power matrix Qy. This matrix is found most directly 

 from the explicit expression for the power P flowing into the network in 



terms of the excitation-response vector 



Comparing the resulting 



expression with Eq. 5.15 allows identification of Qr by inspection. The 

 power matrix Qr is square and of 4wth order 



Qt = 



1 



P 









 -P 



where the P's are matrices of order 2m of the form 



P = 



(5.26a) 



(5.266) 



