12 BELL SYSTEM TECHNICAL JOURNAL 



When the indexes are left off, W < 1 and \ A\ < 1 by definition. 



In a manner analogous to that of Section 1.1 it can be shown that the 



coupled attenuation constants are 



ai + OcAV Wia . Wia 1 T - 



"« "" . I Ti^ ~ ^ "1 T?^ + "2 f77 l-'^-' 



1 -r *' •• tot.ll l>' total 



"2 + ayW ]V\b . TF26 1 T Q 



"'' = 1 I w ^ "' w — + "' w — 



1 "T n Ik total It total 



The attenuation constants of the coupled waves are found by combining 

 the uncoupled attenuation constants in the same proportion as the energies 

 traveling in the two lines. 

 The coupled phase constants are 



ft = ^i^' 1.2-% 



From equations 1.2-5 to 1.2-8 one sees that the coupled propagation 

 constants are conveniently described in terms of the power ratio W. JT 

 itself is a known function of the complex coupling determinant k which is 

 shown on the attached Fig. 4 for the following three special cases: 



Case 1. 



The two lines have equal phase constants and diferenl attenuation con- 

 stants: /32 = /Si 0L2 ^ «i 



K is an imaginary number. 



W changes its character abruptly at the critical coupling. 



I K critical [ = 1 

 For I K I < 1 



W < 1; OCb ^ OLa \ l^b = ^a 



For I /c 1 ^ 1 



IF =1; cvb = a„ ; ^b ^ Ha 



Case 2. 



The lines have dif event phase constants and equal attenuation consia.n\.s. 



K is a real number 



IF changes asymptotically from 



PFo = to 



TFi = 0.172 and to 



IFoc = 1 



