. The Bell System technical journal . lines. In this section we shall assume that the laminae are infinitesimallythin, so that the stacks may be completely characterized by their averagel)roperties e, fi, and g. The case of finite laminae will be taken up in thenext section. We shall also assume throughout that dielectric and mag-netic dissipation may be neglected except, as in Section VII, where thecontrary is explicitly stated. In general the current density and the other held (|uantities in a planestack of infinitesimally thin layers will be linear combinations of thefunctions sh Tfij and c
. The Bell System technical journal . lines. In this section we shall assume that the laminae are infinitesimallythin, so that the stacks may be completely characterized by their averagel)roperties e, fi, and g. The case of finite laminae will be taken up in thenext section. We shall also assume throughout that dielectric and mag-netic dissipation may be neglected except, as in Section VII, where thecontrary is explicitly stated. In general the current density and the other held (|uantities in a planestack of infinitesimally thin layers will be linear combinations of thefunctions sh Tfij and ch Tdj, where y is distance measured into the stack,and T( is the propagation constant per unit distance, as given by (93).The qualitative behavior of the fields in a cylindrical stack will be particular, if the stack is thick enough the current density and thefields will fall off as e^^, and we can define an efTective skin depth A by A = l/(Re r,). (100) Cloiistons fundamental observation was that in order to minimize the. Fig. 6—Coaxial Clogston 1 transmission line. 910 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 ohmic losses in a stack carrying a fixed total current the current densityshould be uniform across the stack, and that we can achieve uniform cur-rent density by adjusting the mo«o product of the main dielectric so as tomake Tf equal to zero. If in equation (93) we set 7 = To = iu-\/tioeo , (101) then Ti will be zero if M0€0 = fii = [dn, + (1 - e)M2][62/(l - d)]. (102) Equation (102) will be referred to henceforth as Clogstons conditionIf the permeabilities of the various materials are all equal, the conditionreduces to eo = 6 = 62/(1 - e) , (103) which is the form employed by Clogston in Reference 1. When Clogstons condition is satisfied, r^ = 0 and the effective skindepth of the stack is infinite ;^^ that is, the current density is uniform inany stack of finite total thickness. The quantities Tt and K vanishsimultaneously, but the limiting valu
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