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BELL SYSTEM TECHNICAL JOURNAL 



-\-Ki in parallel, which have the impedance Z" = +2Z2i^2/(2Z2+A'2)- 

 Removing Z' together with the infinite line on the right there remains 

 on the left a closed circuit made up of the three impedances Zi, Z' 

 and Z" in series. 



After the division, the infinite line on the right will continue, with- 

 out modification, to oscillate freely, since it is an exact duplicate of 

 the original oscillating line, and so must maintain the free oscillation 

 already started. Since it oscillates freely by itself, it had originally 

 no reaction upon the simple circuit from which it was separated; 

 this simple circuit on the left must thus also continue its own free 

 oscillations without change in period or phase. 



We might continue and subdivide the entire infinite line into 

 identical simple circuits but it is sufficient to consider this one detached 

 circuit, which is shown separately in two ways by Fig. 6, since from 



V Z^ Ve""" 

 10 Um Q3 



-K, 



:2Z2 2Z2: 



+ K, 



20 



V Zj Ve"" 

 IP VWW Q3 



OAr 



Fig. 6 — Equivalent Section of Fig. 4 Terminated for Free Oscillation 



its free oscillations the mathematical formulas for the steady-state 

 propagation in the artificial line may be derived. This is deferred, 

 however, until after the physical discussion is completed, so as to 

 leave no room for doubt that the essentials of the physical theory 

 are really deduced without the aid of mathematical formulas. 



The generalized artificial line, if made up entirely of pure resist- 

 ances, will attenuate all frequencies alike, and the entire wave will 

 be in the same phase; this remains true, whatever be the impedance 

 of the individual branch of the network, provided the ratio of the 

 impedances of all branches is a constant independent of the frequency. 

 This is precisely the condition to be avoided in a wave-filter; branches 

 must not be similar but dissimilar as regards the variation of impedance 

 with frequency. This calls for inductance and capacity with neg- 

 ligible resistance, so that there is an opportunity for the positive 

 reactance of one branch to react upon the negative reactance of 

 another branch, in different proportions at diff^erent frequencies. 

 Assuming the unit network A^^ of Fig. 1 to be made up of a finite 

 number of pure reactances, the equivalent impedances Zi and Z2 of 

 Figs. 4 and 5 must also be pure reactances. Under this assumption 



