20 BELL SYSTEM TECHNICAL JOURNAL 



acteristic of this type of artificial line is that it has, for all frequencies, 

 the same iterative impedance as a uniform line with the same total 

 series and shunt impedances. This artificial line will be considered 

 in more detail in the next section of this paper. 



Lattice Artificial Lines 



Up to this point we have considered the properties of artificial line 

 networks which were supposed to be given. In practice the problem 

 is ordinarily reversed, and we ask the questions: May the locations 

 of the bands be arbitrarily assigned? May additional conditions be 

 imposed? How may the corresponding network be determined, and 

 what is its attenuation in terms of the assigned critical frequen- 

 cies? These questions might be answered by a study of Fig. 7, in 



Fig. 14 — Lattice Artificial Line 



all its generality, but it seems simpler to base the discussion upon 

 the artificial line shown in Fig. 14, which is to be a generalization 

 of Fig. 13 to the extent of making the two impedances Zi and Z2 

 any possible actual driving-point impedances. It is sometimes 

 illuminating to regard this artificial line as a nest of bridges, one 

 within another, as shown by Fig. 15. 



On interchanging terminals 3 with 4 and 7 with 8 in Fig. 14 the 

 network of lines remains unchanged; thus, Zi and 4Z2 may be inter- 

 changed in the formulas for the artificial line with no change in the 

 result, except, possibly, one corresponding to a reversal of the current 

 at alternate junction points. Another elementary feature of this arti- 

 ficial line is that it degenerates into a simple shunt or a simple series 

 circuit at the resonant or anti-resonant frequencies, respectively, of 

 either Zx or Z2, and these are the critical frequencies, terminating 

 the pass bands. At other frequencies, a positive ratio Z1/4Z2 must 

 give a stop band, since the reactances are all of one sign. If a small 

 negative value of this ratio gives free transmission, as we naturally 

 expect, there will be identical transmission, except for a reversal of 



