CONFORM A L TRA NSFORM A TION 1 07 



where a is the wide dimension of the rectangular cross-section, the guide walls 

 normal to the f axis are at f = and f = a, and (J is a function of x and y 

 such that 



r,o = /27rx;r'(i - Xna~V4)."' 



The guide walls are assumed to be perfect conductors and hence the tan- 

 gential component of E must vanish at the walls. This requires the normal 

 derivative of Q to vanish at those walls which are perpendicular to the 

 plane of the bend : 



^ = 0. (1-5) 



dn 



When the magnetic vector lies in the plane of the bend and the incident 

 wave consists of the dominant mode, we set 



,4 = P, B = (1-6) 



where P is a function of .\ and v such that 



^ + ^{ - TloP = 0, Too = t2x/Xo (1-7) 



dx^ oy^ 



and 



P = (1-8) 



at the walls perpendicular to the plane of the bend. In this case the guide 

 walls parallel to the plane of the bend are at f = and ^ = b. 



2. Electric Vector in Plane of Bend 



Figure 1 shows a section of the bend taken parallel to the electric vector. 

 b is the narrow dimension of the guide. Let the frequency and the wide 

 dimension a of the guide (measured normal to the plane of Fig. 1) be such 

 that only the dominant mode is freely propagated. The position of any 

 point in this section is specified by the complex number 2 = .v + iy where 

 the origin and the orientation of the axes have been chosen somewhat 

 arbitrarily. 



The constant k and related propagation constants which appear in the 

 formulas dealing with Q and electric bends are given by 



k = (26/Ao) [1 - (Xo/2a)'f = -il\ob/Tr 



yl - m' - k^; m = 0, 1, 2, • • • ; To = ik (2-1) 



Xo = free space wavelength 



