LAMINATKI) TRANSMISSION LINES. I 



907 



where s is the thickness of the stack. Tlie propagation constant T( per 

 unit distance normal to the stack and the characteristic impedance K 

 of the stack are given by 



r, = 



W / 2- I 2x 



^ (o) Me + 7 ) 



K = Tr/g = 



—^ (a;>e + 7") 



-\i 



(93) 



(9^) 



1\ and K niixy also be derived from equations (8G) and (87) by limiting 

 processes; we have 



r, = lim T/(k + ^2), 

 K = lim Ki = lim K2 



(95) 

 (96) 



It should perhaps be noted that terms of the order of coti/^i and we^/^i 

 compared to unity were omitted in the expressions (90) for e and g, 

 and in the derivations of r< and K. Since, however, under all practical 

 circumstances the omitted terms appear to be insignificant, we shall 

 not take space to write out the formally more complicated results which 

 woukl be obtained by keeping them. 



In a cylindrical stack of infinitesimal layers, the average fields satisfy 



d(pH^)/dp = gpE, , 

 ^E^/^p - dE,/dz = iwilH^ . 



(97) 



The relation between the tangential field components E, , —H^ at two 

 radii po and p„ is expressed by a matrix equation analogous to (08), 

 nameh^ 



E{p,) 



-Hipo) 



TtPniKooIln + Ki,Jm)) KT(Pn{KooI(,n — Konh 



(98) 



E(p.y 



^ (A^o/U - /Vl„/l0) TfPn(K,oIon + Kojio) /\ -^^(pj/ ' 



'2 In Reference 1, equations (11-17) through (11-26) give examples of ecjuations 

 in which these smaU terms have been retained. 



