1250 THE BELL SYSTExM TECHNICAL JOURNAL, NOVEMBER 1954 



where as = straight hne attenuation poefficient 

 ub = bend region attenuation coefficient 

 a = guide radius 

 R = bending radius 

 Xo = free space wavelength 

 The approximations used in deriving (11) and (12) are good when the 

 operating frecjuenc}^ is at least 50 per cent greater than cut off for TEoi . 

 For guides modified to have higher TMn attenuation both (11) and (12) 

 may be divided by the factor 



m 



m 



(13) 



where a^ and a° denote attenuation coefficients for the modified guide 

 and solid round guide respectively. On the assumption that the mode 

 coupling is the same in the modified guide as in the solid round guide, 

 use of (13) with (11) or (12) provides an estimate of bend losses in 

 modified circular-electric waveguides. 



For a fixed ratio of bend-region attenuation to straighthne attenua- 

 tion, the allowable bending radius varies inversely as the scjuare root of 

 the ratio of TMn heat loss to TEoi heat loss, varies inversely as Xo'^ , and 

 varies directly as the third power of guide radius. 



For fixed bending radius, the absolute bend loss varies inversely as 

 Xo^^; since the straight line TEoi loss varies directly as Xo'^, bend losses 

 tend to equalize the overall heat loss versus frequency characteristic of 

 the waveguide. 



IMPROVED FORMS OF CIRCULAR ELECTRIC WAVEGUIDE 



In the preceding discussion it has been indicated that added dissipa- 

 tion for the unused modes of propagation has the effect of decreasing 

 signal losses and of reducing the interference effects associated with 

 mode conversion. Dissipation can be introduced to the unused modes of 

 propagation through the addition of mode filters at intervals along the 

 line, but it appears very desirable to introduce the dissipation to the 

 unused modes on a continuous basis. Several ways of making the line 

 lossy to the non-circular electric modes have been found, and one is illus- 

 trated in Figure 26. The copper rings lie in planes transverse to the 

 direction of propagation and provide the conductivity required as a 

 boundary for the circular electric wave family. Successive rings are 

 insulated from each other, howe-\'er, and the guide provides very poor 

 conductivity in the longitudinal direction. All modes other than the 



