REDUCTION OF SKIN EFFECT LOSSES 503 



one has 



= H^- "-«"<"'+'»■'» (III.24) 



where (the subscript w indicates a thickness W for the conducting laminae) 



{W + t) 

 From equations (III-12) and (III-15) one has 



(III-25) 



(r^„) 



1 /y A ("^-26^ 



= cosh T^PT cosh ^^ + \(~l ^-?--] sinh ryir sinh ^^ 



As a practical matter, only rarely will k^ be greater than ten times coVoc 

 and € greater than 10 eo. Hence, ^ will be no larger than 10 \/coVo€o • Fur- 

 thermore, we will see that / should not be very different in magnitude from 



/~T" 



Wj which must be smaller than A/ . Thus, we can be sure that ^t is 



y cojuoo- 



smaller than 100 a/ 2 — , a quantity which is, as before, much smaller than 

 unity. Under these conditions, equation (III-26) becomes approximately 



(lR±I^) = coshvW + l^(^l + -^^)sinhr,W (III-27) 



\ 2 / 2 \ (T ^ tO)€ t]/ 



= cosh vW + -2 (^^ [ V + (^ ~ 7")] '^^ ''""^ "^^ 



(III-28) 



where we have again let P = wVoci as in equation (11-24). 

 Let us set 



= ^[-^ + (^ + w)(^-t)] ("^-^°) 



Then, again neglecting — , we have for ««, 



(T 



<^v, = .ttA— cosh"' [cosh vW + PivW) sinh rjW] (III-31) 

 W -f- t 



