680 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1054 



90 



\ ^^^ \ 



V ^ V 



\ N x 



\. 'n \ 



X \^ X 



X ^ X 



X N X 



X ^ x 



N !i \ 



"424 42 



|cxi IN RADIANS 



Fig. 16 — Wave amplitude and phase factors versus the integrated coupling 

 strength ex for tightly coui)led transmission lines having identical propagation 

 constants. 



Let us now assume that the phase constants of the two lines are un- 

 equal, l)ut the attenuation constants are the same. Then 



cxi — a? — a, and 



(ti - 72) = i(^i - /32), (28) 



and equations (21) and (22) reduce to 



77- _ -ta+>{c+(/3i+/32)/2)]x r' * /2Q^ 



where 



E* = cos 



^(^1 - /S.) 1 



y^ 



- 02y 



^c" 



-f 1 ex 



2c 



/^ 



^2)^ 



+ 



- sin r/(A 



1 ^ ^ 



- 02)' 



4c2 



+ 1 



ex 



4c2 



TJ _ -[a+t(c+(/9i+^2)/2)]xjp * 



(30) 

 (31) 



