BELL SYSTEM TECHNICAL JOURNAL 



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Fig. 4 — Equivalent Ladder Artificial Line 



replaced by the equivalent artificial line of either Fig. 2 or Fig. 3. 

 By combining the series impedances in Fig. 2 and the parallel im- 

 pedances in Fig. 3, the equivalent line in Fig. 4 is obtainable. The 

 two ways of arriving at Fig. 4 give different values for the series and 

 shunt impedances Zi, Z2, and different terminations for the line, but 

 the propagation of the wave is the same in both cases, since the assumed 

 substitutions are rigorously exact. While Fig. 4 may be considered 

 as the generalized artificial line equivalent to Fig. 1, this requires 

 including in Zi and Z2 impedances which cannot always be physically 

 realized by means of two entirely independent networks, one of 

 which gives Zi and the other Z2. This restriction is of no importance 

 when we are discussing the behavior of the generalized artificial line 

 at a single frequency; accordingly, the ladder artificial line is suitable 

 for this part of the discussion. When we come to the more specific 

 correlation of the behavior of the generalized artificial line at different 

 frequencies, it will be found more convenient to replace the ladder 

 artificial line by the lattice artificial line, which avoids the necessity 

 of considering any impedances which are not individually physically 

 realizable. 



The equivalence between Figs. 1 and 4 is implicitly based upon 

 the assumption that it is immaterial, for artificial line iises, what 

 absolute potentials the terminals 1, 2; 3, 4; 5, 6; etc. have — this leaves 

 us at liberty to connect 2, 4, 6, etc., together, so long as we main- 

 tain unchanged the differences in potential between 1 and 2, 3 and 4, 

 etc. Instead of connecting 2 and 4 we might equally well connect 

 2 and 3, and then Zi would connect 1 and 4 as in Fig. 5; with these 



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Fig. 5 — Equivalent Artificial Line with Crossed Impedances 



