REFLECTIONS FROM CIRCULAR BENDS 339 



When these values are set in (5.1-4) we finally obtain 



gt^ = .9822 + i.l858 

 ^To = .0048 - ^'.0255 



The following table lists values ofgj) obtained by the methods of this 

 section*. Here the bend is in the plane of E^ a/b = 2.25, \o/a = 1.400, 

 where Xo is the free space wavelength of the incident wave, pi is the 

 radius of curvature of the axis of the guide. The smallest possible value of 

 pi/a is 0.5. The term "approx." refers to equations (5.1-2) while ''1st 

 order", "2nd order", etc. refers to the order of the matrices used in the 

 computations. The ampHtude of the reflected wave is gTo and the ampli- 

 tude of the wave sent forward is gto when the incident wave is of unit ampli- 

 tude. 



Pi/a Approx. 1st order 2nd order 3rd order 



.6 .964 +^267 .980 +i.l97 .982 +i.l86 



.7 .974 +i.224 .994 +i.l05 .994 +i.lll 



.8 .984 +i.l78 .997 +^.082 .997 +i.082 



.9 .988 +tM53 .997 +t.074 .997 +i.073 



1.0 .991 +tM35 .998 +f066 .998 +i.066 



1.2 .994 +^.110 .998 +i.056 .998 +i.056 



1.5 .996 +t.084 .999 +iM3 .999 +t.044 



gio 



.6 -i.0280 .0020 -t.0074 .0056 -i.0280 .0048 -i.0255 



.7 -i.0068 -.0005 +i.0023 .0013 -t.0131 .0007-^.0066 



.8 +i.0062 -.0013 +i.0074 -.0003 +i.0039 -.0004 +Z.0051 



.9 +i.0128 - .0014 +t.0087 - .0009 -|-i.0123 - .0009 +i.0123 



1.0 +i.0143 -.0010+i.0075 - .0010 +f. 0148- -.0010 -f t.0147 



1.2 +t.0079 -.0002+^.0018 -.0005+^.0086 -.0005 +i.0085 



1.5 -i.0040 +.0003 -t.0034 +.0002 -i.0041 +.0002 -z.0042 



It appears that the values obtained from the first order matrices are quite 

 far from the true values. On the other hand there is considerable agreement 

 between the approximation and the second and third order values, especially 

 at the larger values of pi/a. 



5.2 Bend in Plane of Electric Vector 



The calculations for this case are quite similar to those presented in Sec- 

 tion 5.1. If we are to deal with the same waveguide it is necessary to 



* The computations were performed by Miss M. Darville. I am also indebted to her 

 for the values given in the tables in Section 5,2 and Appendix I. 



