340 BELL SYSTEM TECHNICAL JOURNAL 



interchange the dimensions a and b so that now h/a = 2.25 and, for the 

 same frequency, Xo/^ = 1 .400. 



For a 90° bend the approximation (4.4-4) for the reflection coefficient 

 d^i for gentle bends, i.e. for ^ = a/p\ small, becomes 



d'^^ = tf[-.0417 sin (2.23/^) + .0209 cos (2.23/^)] 



where the negUgible exponential terms have been neglected just as in the 

 analogue (5.1-2) for gFo . 



The following table, which is similar to the table at the end of Section 

 5.1, gives the results of computations for bends in the plane of the electric 

 vector. 



The agreement between the approximation for ^lo and its second order 

 matrix value is fairly good from pi/a = .7 onward. 



APPENDIX I 



Calculation of Ppm etc. for Circular Bend 



It is convenient to write Ppm and Qpm as given by (1.2-10) and (1.2-15) 

 in the form 



Ppm = 5to + Rptrn p, m = 1, 2, 3, • • • 



(Al-1) 



Qkm = dZ+Tpm , />,W = 0,1,2, • •• 



where 8Z is unity ii p — m and is zero otherwise and 



