REDUCTION OF SKIN EFFECT LOSSES 525 



From equations (Vn-22), (VII-23) and (VlI-25) we can find 



2 N^ cos t^^ = M f ^ _ cos ^) (VII-28) 



n la \7r Id/ 



and consequently 



N^ = m{^2-i\, (VII-29) 



and 



Nn = M-2-{- \Y''-^^'\ flr^L (VII-30) 



TT n 



The reflected power is found as before to be for the fundamental mode of 

 the laminated line 



tF. = |y/fM^(«-lJ (VII-31) 



and for the higher modes 



E»',..^/?M-z(i)". 



We can now easily check that 



(VII-32) 





+ (|-.)'-J('-^)-' 



(VII-33) 



The case of the partially filled line can be studied in a manner similar to 

 the above discussion, and will show smaller power losses for waves trans- 

 mitted through the boundary. The problem is further compUcated by the 

 presence of unpropagated modes in the partially filled fine similar to those 

 in the unlaminated fine. 



APPENDIX A 



Plane Waves 



It is interesting to inquire about the waves that exist in a laminated 

 medium of infinite extent. Let us return to equation (11-23). It is easy to 



