1244 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Table III — Coupling Coefficient and Power Transfer 

 TO TE12 Mode due to Three-Sector Compensator 



and TE12 have the same angular dependence, the coupling to TE12 is 

 independent of the number and arrangement of sectors used in the com- 

 pensator so, long as the decoupling condition for T]\In is satisfied. Nu- 

 merical values are given in Table III. 



The formula analogous to (106) for the attenuation constant due to 

 dielectric loss in a three-sector compensator is 



OCd = 



^'(1 + 6) tan^ {di° + 202°) 



2h 



[01] 



360' 



nepers/meter. 



(110) 



As a numerical example, let us design a three-sector compensator for 

 a |-inch guide at 5.4 mm. Under the requirement that the TEoi loss due 

 to conversion into TE12 must not be greater than 0.1 db, the minimum 

 bending radius is 7.39 inches. If the angles are * 



di = 60°, 



62 = 30°, 



'/' = 75°, 



the value of 5 should be 0.143, which is not difficult to obtain with foam 

 dielectrics. Assuming a loss tangent of 2 X 10" we find that dielectric 

 losses in a 90° bend are about 0.12 db. 



As a second example, for a 2-inch guide at 5.4 mm with the same mode 

 conversion criterion, one needs a bending radius of 143.1 inches or 11.92 

 feet. With 5 = 0.033, the compensator angles are 



01 = 27.6°, 



do = 16.4°, 



iA = 72.5°; 



* It is not practicable to use larger angles, because if di > 60° portions of the 

 outer sectors counteract the effect of the rest of the compensator on TMu , and 

 dielectric losses make the design inefficient. 



