682 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



100 

 60 



40 



20 



10 



6 



. 4 



1.0 

 0.6 

 0.4 



El* E£ 



0.001 0.004 0.01 



0.04 0.1 0.2 0.4 1.0 2 4 6 10 20 40 

 20 LOG IeI 



Fig. 18 — Wave amplitude factors at the maximum power transfer value of ex 

 versus (/3i — ^2)/c when the coupled lines have equal attenuation constants. 



are plotted in Fig. 18 as a function of the ratio (/3i — ^2)/c. It is evident 

 that this maximum energy transfer may be made very small for suitably 

 large values of (/3i — /32)/c. The behavior of £"1* and E2* as a function of 

 coupling length x is shown with greater accuracy in the wide amplitude 

 range of interest in Figures 19 and 20 respectively. 



Consider now the case in which the coupled lines have identical phase 

 constants, |Si = 182 = (3, and unequal attenuation constants so that 

 (ti "" 72) = («i " «2). Then (21) and (22) reduce to 



iii = e 



-[ai+i{c+d)]x 



1 



2 



(q!i — 0:2) 



+ 



2V(ai - «2)2 - 4c2_ 

 (ai — 0:2) 



1 , 



.2 2\/lai - a 



,[(ai-a2)/2+}.^V(«l-«2)2-4c2]j; 



,[(ai-a2)/2-M\/(«l-«2)2-4c2]x 



and 



P _ -[ai + i(.c+fi)]x 



2)2 - 4c\ 

 ic 



(35) 



(35') 



|e[(«l-«2)/2+J^\/(«l-<*2)2-4c2]x 



V(ai - a^Y - 4c2 ^ (36) 



— e[(«l-a2)/2->^V(«l-«2)2-4c2]xl 



or 



XV2 — e ii2 



(36') 



