LAMINATED TRANSMISSION LINES. I 933 



T ^l-kB' - (-)Vl2]* 



^ (215) 



-iisgn k)lVWJWT^' - l^iA)?}, 

 wliere \\v liaxc (akcn (li(> s(iuar(» root of the coiiipk^x (luaiiiily by Dwight 

 58.2, aiul 



+ 1 if /v > 0, 

 sgn k = (216) 



- 1 if /v < 0. 



Similarly, from (209), 



^1^1 L 



■(1 + k) ^2 



e^+0^_,_(Lzi^^^e^_...] 



^ [h@' + ev-fc - 0V12] 



iti 1 j^^ ^^ ^2 



- iXsgn fc)[\/i(^iA)^ + 9k' - Wi/SiTf}, 



K2 ^ :;y^^ {[VHh/W+~9k' + K^i/5i)']' - Vs/i/^i 



- «"(sgn /c)[\/i(<i/5i)^ + 9k' - KV^OT). 



The effective skin depth of a stack of moderately thin layers in the 

 presence of slight dielectric mismatch is, from (215), 



_ (^i + ^2) _ Vsjti + t2)8i/h 



^ ~ Re r " [VHti/8,y + 9lc^ + Wi/h)']^ ' ^^^^^ 



An equation essentially equivalent to this was given by Clogston, in 

 somewhat different notation. It is clear from (211) or (218) that if the 

 layers are infinitesimally thin, we have 



A = 8i/d I k \\ (219) 



and the effective skin depth in the stack is proportional to the skin 



" Reference 1, equation (III-42). 



