REDUCTION OF SKIN EFFECT LOSSES 



501 



where we has been neglected against a as before. Now, letting 77 = viajMoo- , 

 we can write within any conducting lamina 



H^ = Ae"' + Be-'" 

 E, = 1 [Ae"" - Be-"'] 



(III-3) 

 (III-4) 



K fl'o and £0 are the values of Hz and Ex at the lower surface of a particular 

 lamination, and if Hi and £1 are their values at the upper surface of the 

 lamination, one can find from equations (III-3) and (III-4) 



Hi = Hq cosh -nW -\- Eq - sinh riW 



El = Ho- sinh vW + Eo cosh rjW 



If we wish, this can be expressed as a matrix equation 



Hi 



El 



)> = < 



cosh TfW 



sinh r)W 



(111-5) 

 (III-6) 



(ni-7) 



For the dielectric laminae, equations (II-8) and (II-9) become 



d'H, 

 df 



= (k^ — (a^ floe) He 



to)€ dy 



(III-8) 



(ni-9) 



Just as for the conducting lammae, let ^1 and £1 be the values of H^ and Ex 

 at the lower surface of a dielectric lamination and let H2 and £2 be these 

 values at the top surface. Then, if ^ = \/F — (jo"^ moc , one has 



H, 



> = < 



cosh ^i 



tooe 



twe 



sinh ^t 



(III-IO) 



From equations (III-7) and (III-IO), we can find the variation of H^ and 

 Ex from the bottom surface of a conducting lamination designated as point 

 zero, to the top surface of the adjacent dielectric lamination designated as 

 point two. Thus, 



