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BELL SYSTEM TECHNICAL JOURNAL 



The effect of supercritical but shallow circular and sinusoidal S bends is 

 illustrated by the following numerical examples. 



Table III 

 Increase or Attenuation in S Bends 



8. Helical Bends and Random Two-Dimensional Devlations 



A helical bend may be treated as a bend which has a constant absolute 

 magnitude, but a changing direction of curvature. As indicated in eq. 3-17, 

 the TMii wave can be polarized in all directions. At any differential 

 element of wave guide length, the TMn component polarized in the local 

 bending plane is coupled to the TEoi wave; the TMn component polarized 

 at right angles is not coupled and persists unchanged. By requiring that 

 the absolute magnitude of the TMu/TEu amplitude ratio remain constant, 

 a steady state solution can be found. 



Shallow helical bends of small curvatures may be treated as the super- 

 position of two sinusoidal bends offset by 90° in the longitudinal direction 

 and in the bending plane. The increases in attenuation due to these two 

 sinusoidal bends are computed from eq. 7-5 and added. 



It is believed that random deviations from a straight course approach 

 sinusoidal shape more closely than circular shape, hence equation 7-5 may 

 be used to establish a tolerance limit for such random deviations. For 

 quantitative results the statistical distribution of the squared deviation 

 maxima must be taken into consideration. 



9. Optimla of Wave Guide Radius, Signal Wave Length .and 



Attenuation as a Function of Angul.ar Deviation 



In a straight wave guide the attenuation decreases with wave guide radius 

 and signal frequency. However, the deterioration due to wave guide 

 curvature increases with wave guide radius and frequency. Hence, for a 

 given tolerance limit to angular deviation from the straight course there 

 exists an optimum radius for each wave length and an optimum wave length 

 for each radius. This will be shown for the case of uniform sinusoidal bends, 

 under the simplifying assumption that the cutoff radio »» « 1. 



