1264 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



for the bend solution of the dielectric-coated guide. In this fii'st order 

 approximation the TEoi wave of the dielectric-coated guide couples to 

 the TMii and TEi„ waves of the dielectric-coated guide and the coupling 

 coefficients are the same as in the bend-solution of the plain waveguide ■} 



TE 



01 



TM 



11 



TE 



01 



TE 



TE, 



01 



11 



c — 



TEi2 



c = 



0.18454 ^ , 



"0.093 19(/3a)2 - 0.84204 



\/|8oiajSiia 



"0.15575(^a)2 - 3.35688 



TE 



01 



TE 



13 



V'i8oia/3i2a 



"0.01376(i3a)2 - 0.60216 



\/l3oia^i3a 



+ 0.09319 V/3oia/3„a 



+ 0.15575 Vl3oiai3na 



+ 0.01376 V^oia^isrt 



I 

 R' 



1 

 R' 



1 

 R' 



(26) 



j8 = free-space phase constant. 



With the coupling coefficients (26) and the propagation constants as 

 given by (10) and (14) the coupled line equations can be used to com- 

 pute the TEoi transmission through curved sections. Since the absolute 

 value of C/A7 is usually small compared to unity, the mode conversion 

 loss is given by (19), the increase in TEoi attenuation by (20), and the 

 spurious mode level by (21). 



The curves in Figs. 3, 4 and 5 have been calculated for the 2-inch 

 pipe at a wavelength of 5.4 mm. They take into account the effects of 

 the three most seriously coupled modes, TMn , TEn , and TE12 . 



In very gentle bends of a guide with a very thin coat, coupling effects 

 to the TEim modes are small and only TMn coupling influences the TEoi 

 transmission. The increase in TEoi attenuation in such bends is obtained 

 by substituting the expression (10) for the TMn phase difference in (20). 



Aa, 0.034 



11 



aoi 



Vdl 



(« 



1)252/22- 



(27) 



Note that (27) requires | C/A7 | « 1 and consequently {l/b){a/R) « 1. 

 In Fig. 4, as well as in (27), losses in the dielectric coat have been neg- 

 lected. Ecjuations (10) show that the dielectric losses are small com- 

 pared to the wall current losses for a low loss dielectric coat. 



