CURVED WAVE GUIDES 



11 



and 



£10 and £20 are independent integration constants. For finite but loose 

 coupling and small attenuation constants one finds in analogy to 1.1-14 

 and 1.1-15 



r„ = ^t^^ + ^^^' ViVk^ = r, + 0.5 r.(i - Vi^~T^) 



n = 



where 



2 



ri + r2 



2 

 Ti - r 



' Vi + /c2 = r2 -f 0.5 ri(i - Vi + K-) 



K = - — - Vr, T2 

 1 1 — i 2 



1.2-3 



is the coupling discriminant. Just as in Section 1.1 the couphng coefficient 

 k is defined by the equation 



, -P12 -P21 



* " Vp.p, = Vp.p. '-^-^ 



Pi is the energy per unit length stored in line 1 ; P2 , the energy per unit 

 length stored in line 2, and Pn = P21 , the energy per unit length inter- 

 changed between the lines. The waves can travel in the coupled lines with 

 either or both of two transmission constants. Two of the amplitude 

 vectors in equations 1.2-1 and 1.2-2, for instance Eia and £26, are free to 

 satisfy boundary conditions; the other two are determined by the equation 



ELKi r„ - Ti Tb- T2 ElbK2 



E,\aK2 



Ta — V2 Fj, — Fi 



ElKx 



V K, E,bVK, ^" Ab 



1.2-5 



■£20 



-Ela f -fVo -Cob Y ^l -^b 



A is the normalized amplitude and phase ratio for two lines transformed to 

 equal wave impedances. 



E^aKi 

 EiaKi 



= Wa = 



Wb 



Wa = 



VT+T^ - 1 



= w 



Vl + k' + 1 



is the ratio of energy flow in the two lines. At the propagation constant Ta, 

 Aa = Vl + K-' - k"' = A 1.2-6 



