466 BELL SYSTEM TECHNICAL JOURNAL 



F"or positive values of Li the equation for Ls shows that (7>l/2, 

 correspontiing to ± ; and then the equation for d shows that a<?, 

 corresponding to ±. Hence 0<o-<l/2 for 7^=+.V, and 1 '2<ff<l 



for r=-y. 



The Susceptance-Compensator in /-Vg. 17 

 For aiu' \akies of G' and Li' the susceptancc S' of iliis network is 



OiCi' 



S' = 



l-J'Li'Ci' 



By equation (5) the characteristic susceptancc Q' of the loaded line 

 within its transmitting band is 



A(l-2ff')a)M 

 ^ l-4<r'(l-(7')a>Vu)/' 



Thus S' and Q' arc of the same functional form in to; and the condi- 

 tions for S' to he idcntiralK' equal to ±Q' are that 



C6'=±/!(l-2(7')/W, 



L5'=±4<r'(l-<r')/(l-2a')/;uo 



the upper and the lower sign of ± corresponding to the use of the 

 compensator as a susceptance-simulator and a susceptance-neutralizer 

 respectively. These values of Ch and Ls' are equivalent to those ap- 

 pearing in Fig. 17, because h = \'ClL' and toc = 2/ VLT. 



The equations for G' and La' show that 0<ff'<l/2 for S'=+Q', 

 and that 1 2<a'<\ for S' = - Q' . 



APPENDIX 1) 

 Gener.m, F(iRMiri,.\s FOR Tiiii Cii.\r.\cti;ristic Impedances .\nd 



THE PR0PAG.\TI0N' CONSTANT OF LOADED LiNES 



l-'or reference purposes this Appcixlix .i;i\es the general formulas 

 for the mid-section (ff = 0.5) and mid-load {a =0.^) characteristic 

 imi)edances iC 5 and K' ,i and the propagation constant Y of a jwriotlically 

 loaded line (of the series type). 



The symbols have the following meanings: d denotes the im- 

 pedance of each load, g and 7 pertain to the line before loading; 

 g denotes the characteristic impedance, and y denotes the propagation 

 constant of a segment whose length is eciual to the distance between 

 adjacent loads after the line is loaded. 



