CIRCUIT DESCRIBED IN TERMS OF NORMAL MODES 247 



The earlier derivation^ leads to an expression identical with (6.55) except 

 that ^n appears in place of ^„ . In this earlier derivation a sign was im- 

 plicitly assigned to the direction of flow of reactive power (which really 

 doesn't flow at all!) by saying that the reactive power flows in the direction 

 in wliich the amplitude decreases. If we had assumed the reactive power to 

 flow in the direction in which the amplitude increases, then, with the same 

 definition of ^n , for a passive modern would have been replaced by — '^„ 

 which is equal to S^„ (for a passive mode, ^n is imaginary). 



In deriving (6.55), no such ambiguity arose, because the power flow was 

 identified with the complex Poynting vector for the particular type of wave 

 considered. In any practical sense, ^ is merely a parameter of the circuit, 

 and it does not matter whether we call Im SE' reactive power flow to the right 

 or to the left. 



The existence of a derivation of (6.55) not limited in its application to 

 lossless transverse magnetic waves is valuable in that practical circuits often 

 have some loss and often (in the case of the heUx, for instance) propagate 

 mixed waves. 



6.4 Iterated Structures 



Many circuits, such as those discussed in Chapter IV, have structure in 

 the z direction. Expansions such as (6.55) do not strictly apply to such struc- 

 tures. We can make a plausible argument that they will be at least useful 

 if all field components except one differ markedly in propagation constant 

 from the impressed current. In this case we save the one component which 

 is nearly in synchronism with the impressed current and hope for the best. 



