CURVED WAVE GUIDES 29 



For small deflection angles, Mdm « 2 



Q^avernge OL\ 



-2 

 1+^ - 



-M'el'^ 



6 



If a p% increase in attenuation is the tolerance limit 



Qm ^ ,^,> A/ - . . Substituting the value of M from 6-3, 

 ^ _ 0.105 V? j/Xo 



Urn — , . 



The maximum deflection equals 



Afl — 0.5 dm. Hence, in view of 3-11 



. ^ 0.032V?X^ ,. 1.84X^ ^ /""^ ^ 



Afl ^ -„ — , — -^— radians = — ^— A / - — ^ — ^ degrees 



= J^ n ~h /72 'y 1 _ „2 ^"o 



a Vl — »'" 



1.84X^ / /> 

 a^ y 1 - 



y' 



3. Sinusoidal Bends with Predominantly Supercritical Curvature. 



Sinusoidal bends cannot be supercritically curved over their entire length 

 because at the inflection points the curvature drops to zero. For sufficiently 

 short bends, however, no great error is caused by treating the entire length 

 as supercritical. In that case, equations 7-3 and 7-4 remain valid. 6 

 takes the new value 



a Gm , 0m . 7r(5 — Sm) 



6 — — + — sm — 



Zi Zr ^^ffl 



Hence 



Mdm . t(s — Sm) 



\p = ——- sm 



2 2s„ 



. (X2 — ai f .2 



"average = CCi + / SHl 



Sm Jo 



For small deflection angles, Mdm « 2 



r2/,2 



Mdm . Tr(s — Sm)! , 



a-z — ai M dm f . 2 7r(i- — Sm) , 



ttuverage = "i + — - / Sm dS 



Sm 4 Jo 2Sm 



= ai + [ai - aO -^ - aj 1 + M'dm 



. 0.026\Wp >. 1.49X5 /~7~, 



Aj = -5 — ■ - radians = — r— A/ -^ — ^degrees 



o S/l - v^ a2 |/ 1 - ;/2 « 



The tolerance limit for sinusoidal deflections is 20% smaller than for 

 circular S bends. 



