Sec. 5.3] POWER EXPRESSION AND ITS TRANSFORMATION 

 obtaining 



37 



where 



and 



[1 ; -T] 



u 



= 8 



[i! -t] = m[i: -z]r 



8 = ME 



(5.6) 



(5.13) 



(5.14) 



Equations 5.12 to 5.14 summarize the transformation from one matrix 

 representation to another. 



5.3. Power Expression and Its Transformation 



In any matrix representation, the power P flowing into the network is 



V 



a real quadratic form of the excitation-response vector - - . We have 



_u_ 



V ' V 



P = --- Qr -- (5.15) 



_u J _u_ 



where Qt is a Hermitian matrix of order twice that of either u or v. In 

 the particular case of the impedance-matrix representation, 



P = \ [V+I + I+V] 



(5.16) 



Comparing Eqs. 5.16 and 5.15, we find that the Q matrix for the imped- 

 ance representation is 



1 



Qz = 



1 







(5.17) 



A transformation from one representation into another transforms the 

 Q matrix. Let us study how Q changes when we transform from the 

 impedance representation into the general representation of Eq. 5.6. 



