. The Bell System technical journal . arbitrary and have no relation to one another. Figs. 18(a) and 19(a)represent a partially filled cable with the same dimensions, namelya = , pi = , and pa = , as in Fig. 14(a), whileFigs. 18(b) and 19(b) represent a completely filled cable, as in Fig. 14(b).The following table shows, as a function of the filling ratio (si + S2)/6,the quantity (xp6)^ for p = 1, 2, 3; this quantity is just the ratioof the attenuation constant of the given mode to the attenuation con-stant of the principal mode in a completely filled Clogston 2. (Sl + S
. The Bell System technical journal . arbitrary and have no relation to one another. Figs. 18(a) and 19(a)represent a partially filled cable with the same dimensions, namelya = , pi = , and pa = , as in Fig. 14(a), whileFigs. 18(b) and 19(b) represent a completely filled cable, as in Fig. 14(b).The following table shows, as a function of the filling ratio (si + S2)/6,the quantity (xp6)^ for p = 1, 2, 3; this quantity is just the ratioof the attenuation constant of the given mode to the attenuation con-stant of the principal mode in a completely filled Clogston 2. (Sl + S2)/b (xi6)2 (x2)2 (x36)2 We note that although the proportions of the partially filled cable werefound in Section IX to be optimum, in the sense of minimizing the at-tenuation constant, for the principal mode in a cable with filling , there is no reason to believe that the same proportions will be opti-mum for the second and third modes with the same filling ratio. #. H OR E H OR E Fig. 18—Fields of second stack mode in partially and completely filled coaxialClogston lines with fio = m, eo = «. LAMINATED TRANSMISSION LINES. II 1103 XI. EFFECT OF FINITE LAMINA THICKNESS. FREQUENCY DEPENDENCE OFATTENUATION IN CLOGSTON 2 LINES Wo shall now study Clogstoii 2 lines with laminae of finite thickness,and shall investigate the important practical (|uesti(»n of how \\\o propa-gation constant varies with freciuency in such lines. Much of the analysisof the present section will deal with parallel-plane structures, but wemay be confident that the results will also gi\^e at least a good qualitativeestimate of the behavior of coaxial cables. The notation for the i)lane Clogston 2, shown in Fig. 10, is the sameas before, except that we now assume the tiiicknesses of the individualconducting and insulating layers to be t\ and f-^ respectively. For definite-ness we shall suppose that there are 2n conducting layers and 2n in-
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