REDUCTION OF SKIN EFFECT LOSSES 507 



Finally, we desire the attenuation y^v of the laminated line at elevated 

 frequencies. Therefore we need the relation between Ex and H, at the first 

 surface of the stack which, for definiteness, we can take to be a metal lamina. 

 For a sufficiently deep stack, this ratio is the same at each successive cor- 

 responding point. Referring to equations (III-7) and (III-IO) we wish to 

 find 



i^ = § = t (III-51) 



By eliminating among these equations and using the same approximations 

 made previously, we obtain 



<jW smh riW ^ 



If use is now made of the relation jS = e""'^^+'^ ^ one finds to first order 



i? = - ^ (III-53) 



a 



Therefore, for the attenuation one has, 



1 * 



Jw = 7^7^^ Real part (a^,) 



1 



(III-54) 



2CZ^5^ 



which is equivalent to an expression used in the introduction with 1/2 CZ 

 being the value of the constant A. 



We have compared the attenuation of conventional and laminated lines 

 as a function of frequency for an insulator between inner and outer con- 

 ductors having the critical dielectric constant €i = I. It is also of interest 

 to draw the comparison as a function of dielectric constant ei at a fixed 

 frequency. The ratio of the two attenuations will be 



^ = 4- (ni-55) 



Is ^K 



This curve is drawn in Fig. 6 for Wjh = 1/3 and t/W = 1. 

 For ci = € we have, 



