TRANSMISSION PROPERTIES OF CLOGSTON TYPE CONDUCTORS 707 



copper. The other parameters are: 



w = Thickness of copper layers in mils. 

 t = Thickness of insulating layers in mils. 

 n = Total number of layers. 

 Fmc = Frequency in megacycles. 



With curvature disregarded, equation (16) also gives the ac resistance 

 of the laminated conductor shown in Fig. 6. For only one copper layer, 

 n = 1, and t = 0, (16) reduces to: 



R^. = R..[l + ^+ ....'\, (17) 



which is exactly the expression for a copper tube at frequencies where the 

 ac resistance begins to depart from the dc resistance and 3^(D — d) = w. 

 For a single layer, the effect of curvature is very small^ and can be dis- 

 regarded. It will be assumed that (16) also holds to a fair degree of ac- 

 curacy for a laminated conductor made up of a large number of layers. 

 Since n is large, the small fraction one-fifth can be neglected. For the 

 optimum condition (minimum attenuation) Clogston^ has shown that: 



w = 2t. (18) 



The total number of layers can be obtained from the following expression : 



D-d D-d, _^ ,^^, 



n = -^, — -r = —5 for w = 2/. (19) 



With (18) and (19) substituted in (16) the ac resistance is given by: 



^^\ 



_ 82080 r w\Ti-drFl^ 



. '° S^^^L 3710 +••••!' (20) 



where the diameters and the copper layer thickness are given in mils 

 and the frequency in megacycles. The resistivity of copper is taken to 

 be 1.724 X 10"' ohms/cm'. 



2. CLOGSTON I CABLE 



2.1 Resistance 



The ac resistances of the inner and outer laminated conductors of 

 ClogstoD I cable, shown in Fig. 1, can be obtained from (20) above by 

 substituting Di and di for the inner conductor and D2 and ^2 for the 



^ Schelkunoff, S. A., The Electromagnetic Theory of Coaxial Transmission 

 Lines and Cylindrical Shields. Bell System Tech. J., 13, pp. 532-579, Oct., 1934. 

 BSTJ, October, 1934, by S. A. Schelkunoff. 

 ;■ ^ Loc. cit. 



