CURVED WAVE GUIDES 13 



Case 3. 



The phase and allciiiuilioii constants dijler by equal amounts. As shown 

 below, in section 4, this case apphes to the coupHng between the TEoi and 

 TMii modes in curved circular wave guides with finite conductivity. 



^'- is an imaginary number. 



\V clianges asymptotically from 



IFo = to 

 Wi = 0.217 and 

 W^ = 1 

 For K » 1 all three cases approach the limit 



,5. - ^'-^ ^' (l+l) 1.2-10 



(■^0 

 (■*?) 



2. Deriv.ation of Field Equations 



Consider a straight circular cylinder with an inside radius such as shown 

 on Fig. 1 A. Let the radial coordinate equal r, the azimuthal coordinate 

 equal (p and the longitudinal coordinate equal 2. Let the dielectric losses 

 inside the cylinder be negligible. 



The field equations inside the cylinder are* 



rd(p dz 



dEr BEz . 



----- = -iwnrH^ 

 dz dr 



d(rE^) dEr ■ „ 

 — = —joifxr Hi 



and 



dr dip 



dH^ 



dz =^'''^' 

 dih . J, 



dHr . p 



dip 



'> See Ref. 4, pg. 94 of the book. 



