930 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



If the conducting layers are copper, we find that equation (200) for the 

 fractional increase in attenuation becomes, numerically, 



Aa/ao ^ 0.121(^i)Li8/L . (202) 



If for example the copper layers are 0.1 mil thick and the polyethylene 

 layers 0.05 mil thick, since we are assuming 6 ^ 2/3, then the attenuation 

 constant has increased by 10 per cent of its "flat" value at a frequency of 

 about 9.1 Mc-sec~ . 



We may also ask for the upper crossover frequency, above which the 

 Clogston cable will have a higher attenuation constant than a standard 

 air-filled coaxial of the same size. Such a crossover frequency must exist 

 because the dielectric loading of the Clogston cable (in our case eor = 

 6.78) introduces a factor -s/eor ii^to the asymptotic expression for the 

 attenuation constant at extremeh^ high frequencies when the stacks look 

 like solid metal walls; in addition there will be slight differences due to 

 the fact that the geometric proportions of the conventional and Clogston 

 cables are not exactlj^ the same. 



We assume, subject to a posteriori verification, that the upper cross- 

 over frequency lies between the critical frequencies f-i and /s , defined by 

 (178), for each stack. Then we have in effect infinitelj^ deep stacks of 

 moderately thin laminae, whose surface resistances are equal and are 

 given by (182) to be 



Ri = R.2 ^ 7rM//V3 = 5.79 X 10"'(;i)„u,s/mc ohms. (203) 



The attenuation constants of the conventional and Clogston cables are 

 obtained from (151) and (176) respectively, where for the conventional 

 coaxial we set 770 = rj^ . After a little arithmetic we find for the upper 

 crossover frequency in this particular case, 



/mc ^ 2.79/(«i)Li8 . (204) 



Thus if the copper layers are 0.1 mil thick, the upper crossover frequency 

 is about 280 Mc-sec~ , which turns out to lie well inside the interval 

 between the critical frequencies /o and /a for both stacks. 



Comparing this result with the result at the end of Section IX, we see 

 that a 0.375-inch Clogston 1 cable with 0.1 -mil copper conductors and 

 the other specifications given by (155) is nominally better than a con- 

 ventional air-filled coaxial cable of the same size in the frequency range 

 from about 1 Mc -sec" to 280 Mc -sec" . We are still neglecting the effect 

 of failure to .satisfy Clogston's condition exactly, the effect of stack non- 

 uniformity, and dielectric losses. All of these factors will be present to a 

 greater or less degree in any physical embodiment of a Clogston cable, 



