LAMINATED TRANSMISSION LINES. I 



897 



(53) 



in a layer of homogeneous, isotropic material whose electrical constants 

 are e, (x, g (or a, j]), and which is bounded by planes pei'pendicular to 

 the y-axis. Hencefortli we shall always assume that the 2-dependence of 

 every field coni])on(Mit is given by the factor c~^\ where the complex 

 quantity 7, whose value may or may not be known a piiori, is the propa- 

 gation constant of \\\v wa\'e in tlu^ ^-direction. Tiicn tlic first of Maxwell's 

 equations (2) yiekls 



F^y = -[7/({/ + icoe)]//., (52) 



and on eliminating E,, from the other Maxw(»ll equations, we get 



dH./dy = -(g + iu>€)E,, 



dE./dy = -[K'/'{g -Vio:e)]H,, 



where k is dehned by equation (G). 



Xow if we formallj^ identify Hx with "current" and E^. with 

 "voltage", equations (53) are just the equations of a uniform one-dimen- 

 sional transmission line extending in the ?/-direction, with series im- 

 pedance K /{g -\- icof) per unit length and shunt admittance {g + z'we) 

 per unit length; in other words a transmission line w^hose propagation 

 constant is k and whose characteristic impedance is -qy , where 



K = a{l - y/(T-y, vv = K/'ig + iue) = 77(1 - '//</)\ (54) 



Hence we can apply the whole theory of one-dimensional transmission 

 lines with the assurance that in so doing we shall not violate the field 

 equations. For example, if £"(0), ^(0) and E{t), H(t) represent the 

 tangential field components Ez , Hx at two planes separated by a dis- 





- /»n-i 



Fig. 4 — Portion of laminated coaxial stack. 



