REDUCTION OF SKIN EFFECT LOSSES 



521 



schematically in Fig. 15. The modes we have discussed to this point have 

 all been antisymmetric in current density about the center plane. It will 

 be clear from Fig. 15 that there are in addition another set of modes sym- 

 metric in the current density. For the completely filled case these are the 

 modes w = 2, 4, 6 • • • , and for the partially filled case the modes n = 

 l',2',3', •••. 



An important point can now be made. For the completely filled case, 

 there are higher modes such as w = 3 where a net current flows on one side 

 of the center plane. The corresponding mode, however, for the partially 

 filled case with s<^h has nearly zero net current on either side of the center 

 plane. Thus, for the partially filled case with s much smaller than h there 

 are no modes except the fundamental with large fields in the interior of 

 the line. 



Fig. 16 — Junction between two plane parallel transmission lines, one of which is filled 

 with laminations. 



VII. Termination of a Laminated Line 



The discussion of modes of transmission in the last two sections enables 

 us now to consider what occurs at the junction of an unlaminated trans- 

 mission line and one partially or completely filled with laminated material. 

 We will, for simplicity, consider mainly the case of the completely filled 

 line as shown in Fig. 16. To the left oi x = there is an unlaminated line 

 such as shown in Fig. 8 filled with a dielectric of dielectric constant ei . To 

 the right of a; = there is a line of the type considered in Section V filled 

 with laminated material of average transverse dielectric constant e and 

 average longitudinal conductivity a. We shall consider separately what 

 happens to a wave incident upon the boundary from left or right. 



When expressing the fields in the unlaminated line, we shall have to in- 

 clude certain unpropagated modes which have not yet been discussed. These 

 modes must attenuate to the left, and can be written 



nwy riTxid 

 Hz = cos — i^ e 



(VlI-1) 



