1266 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



I 



100 



50 



20 



10 



5- 



I- 

 z 



CE 



UJ 

 Q_ 



Z 



UJ 

 CO 



< 



LU 



cm 

 u 



z 



O 1.0 



I- 

 < 



g 0.5 



UJ 



0.2 



0.1 



10 



10^ 



10" 10** 



BEND RADIUS IN FEET 



10° 



Fig, 4 — Increase in TEoi attenuation of a dielectric-coated guide in a uniform 

 bend. 2a = 2 inches; e = 2.5; X = 5.4 mm. 



very near to an optimum design with a dielectric coat for which: 



C /tmu 



t 



(28) 



For this condition conversion losses to TMn and TE12 are equal, while 

 the conversion loss to TEu is small. 



To find values which satisfy (28) we will generally have to solve (1) 

 because the TMu phase difference required by (28) is too large to be 

 calculated with the first order approximation. At a wavelength of 

 X = 5.4 mm and a dielectric constant e = 2.5 the optimum thickness of 

 the coat according to (28) is 5 = 1.25 per cent in the 2-inch pipe. In Fig. 6 

 the mode conversion loss in a dielectric-coated guide of this design is 

 plotted versus bending radius. 



2. Random deviations from straightness 



As mentioned before, random deviations from straightness change the 

 curvature only gradually and only one normal mode propagates. Mode 

 conversion loss and spurious mode level are very low. The normal mode 

 attenuation depends on the curvature. The increase in normal mode 

 attenuation as caused by curvature is obtained by adding the attenua- 

 tion terms (20) of the various straight guide modes which are contained 



