LAMINATED TRANSMISSION LINES. I 



935 



+ [Kl + /^O'e' - (1 + />■)« coth B + 1]^ coth nV], 



which simpHfios, foi- iiifiiiitcsimally thin hiyors, to 



Z„(7n) = K cotli V,s. (228) 



It" th(> stuck is ninny (effective skin (lei)ths thick, we luix'C 



Z„(7.i) = A'l , (229) 



while if tlic in(h\i(hial hiycrs arc inhnite.simally thin, 



Zo(7o) = K , (230) 



where A'l and K are given by (209) and (211), respectively. 



When Zn(7o) is known, the attenuation and phase constants of the 

 j)arallel-phine Clogston 1 are given as usual by 



a = Ke Zii(7o)/77o^, 

 = coVMoeo + Im Z„(7i,)/r7,|6. 

 For the coaxial cable we use 



2^i(7o)/pi + Z2(7o)/p2 



= Re 



(8 = coVmoco + Im 



27^0 log (p2/pi) ' 



2r/o log (p2/pi) 



(231) 

 (232) 



(233) 

 (234) 



but the impedances of the cylindrical stacks are easy to compute only if 

 we can employ the parallel-plane approximation for each stack. To take 



Ao 



Fig. 8 — Relative skin (lf'|)th \^\i, in a stack of finite layers versus dielectric 

 mismateti jiarameter A-, measured in units of {[\lh\Y. 



