LAMINATED TRANSMISSION LINES. I 981 



and will i('(lu('(\ or in cxtrcMiu^ cast's wow eliminate, tli(> freiiueney ranji;e 

 over which the C'lo^ston cable exhibits lowei' loss than a conx-ent ional 

 coaxial cable. 



VI. EFFECT OF DIELECTRIC MISMATCH 



We may think of Clogston's relation (102) as a condition imposed on 

 the phase N-elocity in a laminatctl transmission line to maximize the 

 depth of eddy current i)enetration into the stacks. If this condition is 

 not exactly satisfied, that is, if the mo^o protluct of the main dielectric is 

 not eciual to the fie product of the stacks, then the effective skin depth 

 of the stacks is finite at finite fre(|uencies and decreases with increasing 

 freciuency e\'en in the ideal case of infinitesimally thin layers, while if 

 the layers are of finite thickness the effective skin depth is even less than 

 it would be with a perfectly matched main dielectric. The losses in the 

 stacks at moderate frequencies where Clogston's penetration effect is of 

 importance are correspondingly increased by the presence of dielectric 

 mismatch. 



For a quantitative discussion we define the amount of dielectric 

 mismatch A(;Uo€o) by 



A(/i(ieo) = MoCu — Me, (205) 



and also the dielectric mismatch parameter /,■ by 



k = ^(^"^"^ = (1 - S) A(/ioeo) .,-,Q^.x 



In terms of k, the general expressions for T, Ki , and Ko in a plane stack 

 of finite layers take a relatively simple foi'm. We have 



= iM'iC- — Miifnl 



(207) 



= -/coMid + l:)ti = -(1 + Idvi'Tifi 



^^ —{i -\- k)r]iyKiti , 



after a little rearrangement, where the only approximation that has 

 been made so far is to set rjiy ^ r?, and ki '^ ai . Substituting (207) into 

 (86) and (87) gives 



ch r = ch t) - 1(1 + /Ot) sh t), (208) 



and 



