REDUCTION OF SKIN EFFECT LOSSES 

 and for the attenuation 



^(« = -^l/"f 



513 



(IV-32) 



It is observed at once ^ that the attenuation expressed in equation (IV-21) 

 is independent of frequency, while that given in equation (IV-32) increases 



FREQUENCY 

 Fig. 9 — Comparison of conventional and laminated lines. 



as the square root of the frequency. If we take the ratio of equation (IV-32) 

 to equation (IV-21) we obtain 



attenuation of regular line 



attenuation of laminated line 



■)V 



^/^^ (IV-33) 



(IV-34) 



which is of course a thoroughly reasonable result. A sketch of the attenua- 

 tion curves for the two lines is shown in Fig. 9. 



As a final point, we observe that the attenuation given in equation 



(IV-21) is proportional to _ \/c. Therefore, for stacks in which the lamina- 



(7 



tions have the dimensions shown in Fig. 5, the attenuation is seen from 

 equations (11-19) and (11-20) to be proportional to 



(■ + w)/'+? 



W 

 This expression has a minimum for — = 2. Thus, the optimum arrange- 



I 



