DIELECTRIC-COATED WAVEGUIDE 1263 



and Co is the factor in the bend couphng coefficient c = Ca/R determined 

 by waveguide dimensions, frequency and the particular mode. R is the 

 bend radius. 



Equations (23) and (24) hold only as long as 



4Aa, « I Aa 1 (25) 



is satisfied. The rate of conversion loss has to be small compared to the 

 difference between the rates of decay for the unwanted mode and TEoi 

 amplitudes. If (25) is not satisfied a cyclical power transfer between 

 TEoi and the particular coupled mode occurs, and the TEoi transmission 

 is seriously distorted. 



Another case of changing curvature of the waveguide is random de- 

 viation from straightness, which must be tolerated in any practical line. 

 Such deviations from straightness change the curvature only very gradu- 

 ally, and since there is no coupled wave in the dielectric coated guide, 

 which has the same phase constant as the TEoi wave, the curvature may 

 be assumed to vary only slowly compared to the difference in phase 

 constants. Under this condition the normal mode of the straight wave- 

 guide, which here is the TEoi mode, will be transformed along the 

 gradually changing curvature into the normal mode of the curved wave- 

 guide, which is a certain combination of TEqi and the coupled modes. 

 This normal mode will always be maintained and no spurious modes 

 will be excited. 



The change in transmission loss is therefore given alone by the differ- 

 ence between the attenuation constants of the TEoi wave and the nor- 

 mal mode of the curved waveguide. The propagation constants of the 

 normal modes of the coupled fines are Fi and r2 as given by (16). Only 

 the mode with Ti will be excited here and consequently the attenuation 

 difference is given by (20). 



IV. CIRCULAR ELECTRIC WAVE TRANSMISSION THROUGH CURVED SECTIONS 

 OF THE DIELECTRIC-COATED GUIDE 



In curved sections of the plain waveguide the wave solution has been 

 described in terms of the normal modes of the straight waveguide. In this 

 presentation it has been found that the TEoi wave couples to the TMn 

 and TEi„ waves in gentle bends. Likewise, the wave solution in curved 

 sections of the dielectric-coated guide can be described in terms of the 

 normal waves of the straight dielectric-coated guide. In a wa^'eguide with 

 a thin dielectric coat the normal waves may be considered as perturbed 

 normal modes of the plain waveguide. Consequently the bend solution 

 of the plain waveguide may be taken as the first order approximation 



