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BELL SYSTEM TECHNICAL JOURNAL 



For illusirau\e purposes, Fig. 22 gives graphs of A and B through- 

 out the first transniitling band (0<r<l) and part of the succeeding 

 attenualing hand, for a non-dissipative loaded line, with X = and 

 with X = ().12. Of course, A is zero in the range ()<;-< 1. 



Returning now to the general case (X^O), we see that the trans- 

 mitting bands (A =0) are characterized by the inequality sinh- r<0. 



Fig, 22 — Propagation Conslaiil I' =.1 +jS in the First Transmitting Band (0<r<l) 



and in I'art of the Succeeding Attenuating Band, of a Xon-Dissipativc Loaded 



Line with X=0 and with X=0.12 



and the attenuating bands (.1^',)) by tiic ineiiuality sinh'- r>0; antl 

 hence the transition points between the two kinds of bands are char- 

 acterized by the equation sinh- r = (). 



We seek the transition values of /), thai is, the \alues of D where 

 sinh^r=0; and we seek the transniittini; and the altcmiating ranges 

 of D, that is, the ranges of D u hert' ^\\\\\- V <() and sinh- T >0, re- 

 spectively. 



The transition \alucs of D arc perhaps most readiK fouiul from 

 the equation for sinh- V when written in the form (2-A). They are 

 the zeros of the first three factors in the right-hand member of that 

 equation. The zeros of the factor sin- 2D are at D = mir/2, with 

 w=0, 1, 2, ;j, . . . ; thus the\' subdixide the £>-scale into segments of 

 width 7r/2 each, as represented by Fig. 6; and they have the values 

 represented by (18). The zeros of the factors D tan D — \ and D cot 

 D-l-X are situated in the odd and even numbered segments, respec- 

 tively, because, X is positive; there is one and only one zero in each 



