LAMINATED TRANSMISSION LINES. II 



1157 



and tlie (2p + l)st stack modes will be nearly the same for sufficiently 

 large values of p (how large depends on the ratio of stack thickness to 

 main dielectric thickness). Except for differences in sign, the fields in 

 the stacks will also be the same up to second order differences which 

 our approximations do not show. The physical interpretation is that 

 for a thick enough main dielectric and/or sufficiently large values of p, 

 the fields are confined almost entirely to the two stacks, being rela- 

 tively small in the main dielectric, while the stacks act like a pair of 

 almost independent Clogston 2 lines each of thickness s and carrying a 

 particular Clogston 2 higher mode. 



Figs. 16 and 17 show field plots for the second and third stack 

 modes (i.e., the first and second higher modes) in the same four plane 

 Clogston lines that were used to exhibit the behavior of the principal 

 mode in Fig. 13. Xote however that these plots are not normalized 

 and that the horizontal scales on the figures are not all the same. The 

 following table gives X2S and xss as functions of the fraction s/^a of 

 the total space filled by the stacks, and also the quantities (x^a/Tr) 

 and (x3<j/t)", which are just the ratios of the attenuation constants of 



H --1-E 



Fig. 16 — Fields of second stack mode in partially and completely filled plane 

 Clogston lines with mo = m, «o = «• 



