1242 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Table II — Coupling Coefficients and Power Transfer to TE2i 

 AND TE31 Modes due to Single-Sector Compensator 



db, then the bending radius can be 19.5 inches. The corresponding vakie 

 of 5 is 0.036. 



If we try to use a 144° sector in a 2-inch guide at 5.4 mm, with the same 

 mode conversion criterion as before, the bending radius must be so large 

 that no currently available dielectric has a small enough value of 5 to 

 satisfy the decoupling condition. We are therefore forced to use a smaller 

 sector angle. With a sector of small angle, TE31 is the worst spurious 

 mode. It turns out that if 6 = 0.033 and if TEoi is not to lose more than 

 0.1 db by conversion into TE31 , the minimum bending radius is 1131 

 inches or 94.3 feet, and the corresponding sector angle is 4.70°. 



An approximate formula for the attenuation constant due to dielec- 

 tric losses in a single-sector compensator is given by (57), provided that 

 5 is small. The result is 



CXd 



/S'd -f 6) tan^ e' 



2h 



[01] 



360 



nepers/meter, 



(106) 



where tan <p is the loss tangent of the dielectric, and d° is the sector angle 

 in degrees. As numerical examples, we find that the dielectric loss at 5.4 

 mm in a |-inch guide compensated with a 144° sector having 8 = 0.036, 

 tan ^ = 5 X 10~\ amounts to 0.085 db in a 90° bend of radius 19.5 

 inches. In a 2-inch guide compensated with a 4.70° sector (5 = 0.033, 

 ian<p = 5 X 10"^), the dielectric loss is 0.155 db in a 90° bend of radius 

 94.3 feet. 



2.3.3 The Three-Sector Compensator 



Although the single-sector compensator should work well in a guide 

 which will propagate only 40 to 50 modes, it does not look so promising 

 for a 200- to 300-mode guide, chiefly because of the unavoidable crosstalk 

 into TE21 and/or TE31 . We are therefore led to consider the design of a 



