1212 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



theoretical interest nevertheless. In the second case, a dielectric sector of 

 constant permittivity is attached to the inner surface of the bend nearest 

 the center of curvature; the angle of the sector is determined to satisfy 

 the decoupling condition. Such a sector may be an effective compensator 

 if the guide is small enough to propagate only 40 to 50 modes at the 

 operating frequency, as, for example, a f -inch guide at a wavelength of 

 5.4 mm. Finally, we consider a compensator made of three dielectric 

 sectors, whose angles and spacings are chosen to decouple the modes 

 (TE21 and TE31) with phase velocities closest to TEoi . The three-sector 

 compensator may be necessary if the guide is large enough to propagate 

 200 to 300 modes, say a 2-inch guide at 5.4 mm. 



In Section 2.4 we investigate the effect of increasing the attenuation 

 of the spurious modes generated by the compensated bend. The con- 

 clusion is that it is not feasible to add enough loss to the worst spurious 

 modes to reduce appreciably the power which they abstract from TEoi . 



As a sample of numerical results, it appears possible to negotiate a 

 90° bend of radius 20 inches in the |-inch guide at 5.4 mm with an inser- 

 tion loss of about 0.3 db. This assumes a single-sector polyfoam compen- 

 sator with a relative permittivity of 1 .036 and a loss tangent of 5 X 10~^ 

 (polyfoam with approximately these constants is currently available). 

 About 0.2 db of the quoted loss is due to mode conversions and 0.1 db to 

 dielectric dissipation. For a 2-inch guide with a three-sector polyfoam 

 compensator, a bending radius of about 12 feet appears feasible. The total 

 loss in a 90° bend should be about 0.35 db, with approximately 0.1 db 

 going into mode conversion and about 0.25 db into dielectric dissipation. 

 The dielectric loss is proportional, of course, to the total bend angle, and 

 for a 180° bend would be double the above figures. 



CENTER OF 

 CURVATURE 



CENTER OF 

 CURVATURE 



b+a 



Fig. 1 — Coordinates used in circular bend in circular waveguide. 



