The Bell System Technical Journal 



Vol. XXVIII Janitarv, 1949 No. 1 



Propagation of TEqi Waves in Curved Wave Guides 



By W. J. ALBERSHEIM 



TFloi waves transmitted through curve wave guides lose power by conversion 

 to other modes, especially to TMn. 



This power transfer to coupled modes is explained by the theor\- of coupled 

 transmission lines. It is shown that the power interchange between coupled lines 

 and their propagation constants can be derived from a single couiJJing dis- 

 criminant. 



Earlier calculations of TEoi conversion loss in circular wave guide bends are 

 confirmed and extended to S-shaped bends. 



Tolerance limits for random deflections from an average straight course arc 

 given. 



THE TEoi mode of propagation in circular wave guides has great 

 potential value for the transmission of wide-band signals because 

 its attenuation decreases with frequency. In order to take full advantage 

 of this property one must use sufficiently large wave guides to operate well 

 above the cutoff of the lowest transmitted frequency. The difficulty of this 

 transmission method lies in the fact that TEoi is not the dominant mode 

 and that energy may be lost by transfer to the many other modes capable 

 of transmission in the wave guide. In an ideal wave guide, which is perfectly 

 straight, perfectly circular and perfectly conducting, the propagation is 

 undisturbed; but slight imperfections and especially a slight curvature of 

 the wave guide axis may produce serious disturbances. 



The character of these disturbances has been investigated in several 

 publications by Prof. M. Jouguet^ and in unpublished work by Mr. S. O. 

 Rice of the Bell Telephone Laboratories. Both Jouguet and Rice use the 

 method of perturbations, which is a form of calculus invented by astronomers 

 to compute the deviations from the exact elliptical orbits of the planets 

 which are caused by the disturbing influences of their fellow planets. 

 Although the above-mentioned authors obtained valuable results, the 

 interpretation of their solutions is difficult due to this rather abstract 

 mathematical formulation. To most engineers the understanding of a 

 physical problem is greatly helped if it is possible to use a method of analysis 

 which is elementary in character and easily interpreted in familiar physical 

 terms. The familiar concept on which the present treatment will be based 

 is that of coupled circuits. 



' See References 2 and 3, listed on page 7. 



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