LAMINATED TRANSMISSION LINES. II 1123 



The cross section of a coaxial Clof>stoii 2 cable is shown schematically 

 in Fig. 11. It consists of a laminated coaxial stack bounded internally 

 by a cylindrical core of radius a, which may be equal to zero so far as 

 the theoretical analysis is concerned, and externally by a cylindrical 

 sheath of radius b. We denote the radial impedance looking into the 

 core at p = a by Za(y), and the radial impedance looking into the 

 sheath at p = h by Zb(y). 



In this section we shall assume the laminae to be infinitesimally thin, 

 so that the stack may be regarded as a homogeneous, anisotropic medium, 

 completely characterized by its average electrical constants. The case 

 of finite lamina thickness will be treated in Section XI. We shall neglect 

 dielectric and magnetic dissipation throughout, except in Section XIII. 



For modes of the type which we consider, whose only field components 

 are Hj^ , Ey , E^ in the plane line or //^ , E^ , E, in the coaxial line, the 

 average electrical constants of the stack are given by equations (90) 

 of Section III, namely, 



€ = €2/(1 - d), 



n = en, + {I - e)n, , (268) 



g = 6gi ■ 



As observed in Section III, Maxwell's equations for the average fields 

 in such an artificial anisotropic medium take the form, for a plane 

 stack, 



dHJdz = iwiEy , 



dHJdij = -gE,, (269) 



dEy/dz - dEJdy = iwflH^ ; 



while for a cylindrical stack, 



dH^/dz = —iweEp , 



d(pH^)/dp = gpE. , (270) 



dE,/dp - dEp/dz = luifiH^ . 



We wish to determine the modes which can propagate in the laminated 

 medium when guided by plane or cylindrical impedance sheets. This 

 problem was solved for a homogeneous, isotropic dielectric in Section 

 II of Part I ; and the method of solution is so similar for the anisotropic 



