REDUCTION OF SKIN EFFECT LOSSES 523 



which yields 



Dn = — i-iy'-'^'A (VII-11) 



Referring to equation (V-15) we have for the power flow in the transmitted 

 wave, 



W = ^^^!^T,Dl (VII-12) 



^ = ^^ 4/4^ ~ E ^ (VII-13) 



Let us now find the ratio of the power transmitted in the fundamental 

 mode n = 1 to the total power transmitted, which is also the total incident 

 power as can be checked from equation (VII- 12). We have 



power in fundamental 8 /^ttt -, a\ 



' TT-l = -2 (VII-14) 



total power t^ 



Thus, in exciting the fundamental mode of the laminated line we have a 

 power loss which can be expressed in db as 



2 

 IT 



db loss = 10 log — 



8 (VII-15) 



= 912 

 I 



Let us next consider a wave composed of the fundamental mode of the 



laminated line incident upon the boundary from the right. For x < we 

 have in this case 



H, = Be'''' + E C. cos "^ e""^^^' (VII-16) 



m a 



E, = -B a/^ e"" - J- E C.. ('^) cos "^y e""" (VII-17) 

 where again w = 1, 2, 3, • • • and k is given by (IV-31). For x > 



H. = Me'"'' cos !^^ + E ^n cos "^ e"^''"^ (VII-18) 



£„ = j^^-Me'"- cos g + Z iV„ cos ^ .-'"'] (VII-19) 



