LAMINATED TRANSMISSION LINES. II 



1103 



XI. EFFECT OF FINITE LAMINA THICKNESS. FREQUENCY DEPENDENCE OF 

 ATTENUATION 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 analysis 

 of the present section will deal with parallel-plane structures, but we 

 may be confident that the results will also gi\^e at least a good qualitative 

 estimate of the behavior of coaxial cables. 



The notation for the i)lane Clogston 2, shown in Fig. 10, is the same 

 as before, except that we now assume the tiiicknesses of the individual 

 conducting and insulating layers to be t\ and f-^ respectively. For definite- 

 ness we shall suppose that there are 2n conducting layers and 2n in- 

 sulating layers in the whole stack, with a conducting layer next to the 

 lower sheath and an insulating layer next to the upper sheath, though 

 the precise arrangement is of no real impoi'tance if the nimiber of la.yers 

 is large. The total thickness a of the stack is 2n(ti + to), and the frac- 

 tion of conducting material will as usual be called 6. 



The boundary conditions for any mode (having Hj, , Ey , and E^ 

 field components only) require that the sum of the impedances looking 

 in opposite directions normal to any plane y — constant be zero. If 

 we match impedances at the lower sheath y = —\a and use equation 

 (65) of Section III for the impedance looking into the stack, we have 



iZ„(T)(Kxe'"'^ + K.e-'"'^) -f K^K.sh 2nV 



-f Z„(7) = 0, (437) 



Z„(7) sh2nr + hiK^e-'-"^ + K.e'"'^) 

 where F, Ki , and Ki are given by equations (61) and (63). If equation 



f )fjL P 



(a) 



(b) 



m////////////j//////m//////m^^^^^ 



H OR E 



H OR E 



Fig. Ill Fields of third stuck mode in parti;dl\ and completely filled coaxial 

 Clogston lines with mo = m, eo = «. 



