Normal Mode Bends 

 for Circular Electric Waves 



By H. G. UNGER 



(Manuscript received February 18, 1957) 



In dielectric-coated round waveguide the degeneracy or equality of phase 

 consta7its of TEoi and TMn waves is removed. In such a non-degenerate 

 waveguide, mode conversion in bends can he reduced by changing the curva- 

 ture gradually instead of abruptly. With curvature tapers, which are of the 

 order of, or longer than, the largest beat wavelength between TEoi and any of 

 the coupled waves, propagation of only one normal mode is maintained 

 throughout the bend. Linear curvature tapers can easily be made by bending 

 the pipe within the limit of elastic deformation. 



Changes in the direction of a waveguide line can thus be made by inserting 

 a dielectric-coated guide section which is elastically bent over a fixed center 

 point. A thirty degree change of direction of a 2-inch I.D. pipe with 30 ft 

 of a dielectric-coated guide yields a total bend loss at 6.4-mm wavelength 

 that is twice the TEoi loss in 30 ft of straight pipe. An optimum bend 

 geometry is found which minimizes the total bend loss. The normal mode 

 bend is a broadband device. 



I. INTRODUCTION AND SUMMARY 



A major problem in circular electric wave transmission is the question 

 of negotiating bends. In curved sections of a round waveguide the TEoi 

 mode couples to the TEn , TE12 , TE13 • • • modes and to the TMn mode. 

 The coupling to the TMu mode presents the most serious problem, since 

 the TEoi and TMn modes are degenerate in that they have equal phase 

 velocities in a perfectly conducting straight guide. TEoi power introduced 

 at the beginning of the bend will be almost completely transferred to the 

 TMn mode at odd multiples of a certain critical bending angle. This 

 power transfer can be reduced by removing the degeneracy of equal 

 phase velocity of TEoi and TMn modes. There are various methods to 

 remove the degeneracy; a simple and a very effective one is a thin dielec- 

 tric layer next to the walls of the waveguide. As a study of the dielectric- 



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