LAMINATED TRANSMISSION LINES. II 1155 



From (330) and (396) we have for the pth mode, 



r^ = ixv, (409) 



K, = (-1 + 0V«e/2^ Xp . (410) 



The fields maj' be obtahied by substituting T( and ko into equations 

 (333) and (334) when p is odd, or (335) and (330) when p is even. 

 For tlie modes in which we are interested, that is, for sufficiently small 

 values of p, we may replace sh kqij by k^ij and ch kqij bj^ unity when 

 \y\ ^2^. Then for the modes with odd subscripts 2p + 1 we have, 

 in the main dielectric, 



Ey ^-A/f^Hoe-"'"-'', (411) 



for —^6 ^ y ^ \h, while in the stacks, 



H, ^ Ho ^"^ X2p+xiha ^ y) g-T2p+i^ 

 "" ^ ° sin X2p+is ' 



Ey^-iA H. '^ ^^--^^^'^ ^ ^^ .-— , (412) 



K e sm X2p+iS 



E ^ ^ X2p+i ^ cos X2p+i(|a ^ y) g-72p+i^ 

 ^ "^ g sin X2p+is 



for ^& ^ I y I ^ |a, where the upper signs refer to the upper stack 

 and the lower signs to the lower stack. Of course the arbitrary amplitude 

 factor Ho need not be the same for different values of p. Similarly for 

 the modes with even subscripts 2p the fields in the main dielectric are 



H.^0, 

 F Ci-" 



gs 



for —^b ^ y ^ hh, while in the stacks, 



E, ^ i-y f^ Hoe-''-', 



gs 



