THE ELF.CTRIC ir^WB-riLTRR 5 



that the percentage reduction in amplitude and the change in phase, 

 in passing from the end of one section to the corresponding point of 

 the next section, do not depend upon either the absolute amplitude 

 or phase; they depend, instead, only upon the magnitudes, angles 

 and interconnections of the impedances between the two points and 

 of the impedances beyond the second point. These impedances 

 are, since the line is assumed to be periodic and infinite, identically 

 the same for corresponding points between all sections of the line, 

 and, therefore, the relative changes in the wave will be identical at 

 corresponding points in all sections. This proves the exponential 

 falling off of the disturbance and the constancy of phase change; the 

 ordinary reciprocal property shows that the wave will fall off identic- 

 ally whichever be the direction of propagation. By the superposition 

 property it follows that the steady state on any finite portion of a 

 periodic recurrent structure must be the sum of two equally attenuated 

 disturbances, one propagated in each direction. 



The fundamental w^ave propagation theorem may be generalized 

 for any periodic recurrent structure irrespective of the number and 

 kind of connections between periodic sections, provided the dis- 

 turbance is such as to remain similar to itself at corresponding points 

 of each of these connections. 



Equivalent Generalized Artificial Line 



Since, at a given frequency, any network employed solely to con- 

 nect a pair of input terminals with a pair of output terminals may be 

 replaced by either three star-connected impedances or three delta- 

 connected impedances, the general artificial line of Fig. 1 may be 



2 4-68 



Fig. 2 — Equivalent Artificial Line Obtained by Substituting Star Impedances 



6 8 



Fig. 3 — Equivalent Artificial Line Obtained by Substituting Delta Impedances 



