LAMINATED TRANSMISSION LINES. II 1135 



then 



Ko = (/coe'g)r', Kn = Vi^'e/g T/ , (330) 



and the equations tor th(^ ovon and odd modes beeome, respectively, 



hmhWi^gr^bUmhl\s = - '-^i/'y' = -^aM, (331) 



^ V 9 Mo K 9* 



il 1 / • - - T^ 7 4. 1 T1 ^" Aw€ M A 



cotli ^v^w«/^ r<6 tanh l\.s = a/ — = —~a/- 



^yg Mo K 



'^ . (332) 



g 



For reference we shall now write down the field components of llif 

 various modes. The fields in the main dielectric are given by e(iuations 

 (8) and (12) of Section II, while the fields in the stacks may be ol)tained 

 without difficulty if we recall that the tangential field components must 

 be continuous at the inner boundary of each stack and that the tan- 

 gential magnetic field must vanish at the high-impedance surface which 

 forms the outer boundary of the stack. 



Taking the even modes first, we have for the fields in the main di- 

 electric, 



Hx = Ho ch ^•()?/ e"^^ 



E„ = -Ho^ ch K„y c~^^ (333) 



icoeo 



Ez = — II -. — sh KoU 0"^% 



for — 16 ^ ?/ ^ \h, where //o is an arbitrary amplitude factor, 7 and 

 Ko are given in terms of V( by (327) and (330), and V( satisfies (331). 

 The fields in the stacks are 



i/x = //c%i?^sh^,(|aT2/)c-^^ 

 sh V(S 



E, = -Ih — . ^^4?^ sh Tciha T y) e~'\ (334) 



E, = ±Ho ^ %|?^ ch r,(ia T y) e-'% 



g sh r^s 



for ^h ^ \ y \ ^ |a, Avhere in case of ambiguous signs the upper sign 

 is to be associated with the upper stack (y > 0) and the lower sign with 

 the lower stack {y < 0). The continuity of E^ at ?/ = ±^6 is a conse- 

 quence of equation (324) or (331). 



