CIRCULAR ELECTRIC WAVE IN SERPENTINE BENDS 1291 



E2 _ W Co aoi 



An evaluation of the TE01-TE12 coupling in the previously described 

 2-inch copper pipe for critical frequencies near X = 5.4 mm is shown in 

 Figs. 2 and 3. The mode filter loss of 1 db can be achieved for the TE12 

 wave in an 18-inch long helix waveguide. A 100-foot spacing of the 

 mode filters reduces the increase of TEoi attenuation to 9 per cent and 

 the spurious mode level to —26 db. 



APPENDIX 



The coupling coefficient for the wave coupling between the TEoi wave 

 and the TEu , TE12 , TE13 waves as well as the TMn wave have been 

 calculated by S. P. Morgan.* If c = Co/R, the factor Co is for the various 

 waves 



TMn Co = 0.18454/3a, 



0.09319(/3a)2 - 0.84204 , 



TEu Co = /^ ^ + 0.09319 V^oiajSna, 



O.loo75(l3ay - 3. 35688 , , 



TE12 Co = / ^ + 0.15575 -vBoittBioa, 



V/3oia/3i2a 



0.01376(^a)2 - 0.60216 , 



TEi3 Co = /^— + 0.01376 V^oia/3i3a, 



V/3oia/3i3a 



where a = radius of waveguide, 



/3 = free-space phase constant, 



/3„m = phase constant of TE„,„ wave. 



REFERENCES 



1. W. J. Albersheim, Propagation of TEoi Waves in Curved Wave Guides, 



^ B.S.T.J., 28, pp. 1-32, January, 1949. 



2. S. K. Miller, Coupled Wave Theorj- and Waveguide Applications, B.iS.T.J., 33, 



pp. 661-719, May, 1954. 



3. W. H. Loui.sell, Analysis of the Single Tapered Mode Coupler, B.S.T.J., 34, 



pp. 853-870, July, 1955. 



4. S. P. Morgan, Theory of Curved Circular Waveguide Containing an Inhomo- 



geneous Dielectric, pp. 1209-1251, this issue. 



