LAMINATED TRANSMISSION LINES. II 1197 



air-filled line is great compared to the skin depth 8i , its atteinialioii 

 constant a, is given by equation (25), namely 



as = 1/T]vgi8ia, (571) 



where 77^ is the intrinsic impedance of free space. By o(|iiati()u (535), 

 the attenuation constant ac of the lowest mode in a plane Clogston 

 2 with infinitesimally thin layers is 



Ai 

 ac = Re ^ /^-jr . 2 . (572) 



If we assume noimiagnetic materials and put in the optimum value of 

 d, namely d = 2/3, we obtain for a uniform stack with Ai = tt^, 



12.82 \/ev /,-»«\ 



«co = V^ , (573) 



VvQia- 



where €2r is the relative dielectric constant of the insulating layers. 



The attenuation constant of the conventional line is proportional to 

 the square root of frequency, whereas the attenuation constant of the 

 uniform Clogston 2 is independent of frequency up to some frequency 

 at which the effect of finite lamina thickness begins to be appreciable. 

 If we confine ourselves to the low'-frequency, flat attenuation region, 

 and denote the ratio of attenuation constants by r, then from (571) 

 and (573), 



r = ttco/as = 12.82 V€^ 5i/a, (574) 



and the crossover frequency above which the uniform Clogston line is 

 better than the conventional line occurs when 



a/81 = 12.82V^ . (575) 



In the following numerical example we shall assume polyethylene in- 

 sulating layers, wdth 



so that (574) becomes 



€2r = 2.26, (576) 



r = 19.275i/fl. (577) 



If the stack in a Clogston line is not uniform, then regardless of the 

 thinness of the layers the attenuation constant will no longer be inde- 

 pendent of frequency, but will increase with frequency at a rate depend- 

 ing on the nature and the magnitude of the nonuniformity. Since from 

 equation (572) the attenuation constant is proportional to Re Ai , 



