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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



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c 

 Fig. 31 — Driven and undriven line wave amplitudes versus (ai — a.2)lc for 



ex = 7r/2V2 and (/3i - ;32)/c = .2. 



2. At cx = 7r/2, the phase difference is therefore x radians and the at- 

 tenuation difference x nepers. The result is appreciable attenuation for 

 El*** and only a moderate ratio of £'i***/£'2***. 



Fig. 31 shows the way dissipation differences counteract the coupling 

 forces when there is a phase constant difference (/8i — ^^/c = 2. This 

 may be compared with Fig. 21 which represents the case of (/3i — ^i) — 0. 

 Very little change in E^*** occurs until {a\ — cf^/c exceeds (/3i — ^2)lc\ 

 this is again a general result. 



Finally, we may inquire as to how much power is dissipated in the 

 system when attenuation constant differences are utilized to mitigate 

 the effects of coupling. A measure of the power preserved is 



£i^ 



+ 1 E-{ 



and this ciuantity is plotted in Fig. 32 for cases previously discussed in 

 connection with Figs. 21 and 31. Either in the absence or presence of a 

 phase constant difference, the attenuation constant difference shows a 

 maximum effect in reducing the available power at {a\ — 0:2) /c = 2. 

 This is probably a general result brought on by the factor 



V(7i - 72)- - 4c2 

 found in the exponent of terms describing E\ and Ei . 



