TRANSMISSION PROPERTIES OF CLOGSTON TYPE CONDUCTORS 711 



From (25) and (26) above it is evident, however, that the product of 

 Le^Cex remains constant, since it is independent of the diameter ratio 

 d2/Di , which in a Clogston II cable approaches unity. With (27) in- 

 serted in (24) and with L^ = and Cex = <», the impedance of a 

 Clogston II cable may be written: 



The internal inductance of a Clogston II cable is not known, but will 

 be taken equal to 0.1609 X 10"^ Henries/mi, which is the internal 

 inductance of a pair of wires at low frequency. Thus: 



17.35 , 

 Zn = —7^ ohms, (37) 



where e is the dielectric constant of the insulating layers. 



The attenuation is obtained by dividing i^aci + i^ac2 from (34) by 

 2Zii , where leakance is disregarded. 



The phase constant, in the frequency range considered, is equal to 

 the phase constant of a Clogston I cable since L^C^x is a constant value. 



4. Comparison of Results with V allies Obtained from Rigorous Formulas 



S. P. Morgan^ has developed rigorous formulas for the attenuation of 

 Clogston cables, assuming infinitesimal thickness of the layers but re- 

 taining a fixed ratio of copper to insulating layer thicknesses. A correc- 

 tion term gives the increase in attenuation with frequency for layers of 

 finite thickness. 



The attenuation of a one-half filled Clogston I cable computed by the 

 approximate formulas given in the present paper was 1.1 per cent higher 

 than the value computed using Morgan's rigorous formulas. Similar 

 computations on a completely filled Clogston II cable gave values 8.6 

 per cent higher. This decrease in accuracy with increase in fill is in line 

 with the expectation that uniform distribution of the current is more 

 closely approximated with low percentages of fill. 



5. SUMMARY OF FORMULAS 



The formulas developed in the second part of this paper and those 

 for which the derivation has been indicated are summarized below. Con- 

 ductuig layers of copper, and insulating layers with a dielectric constant 



8 Loc. cit. 



