920 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



attenuation constant as of an air-filled standard coaxial of the same size, 

 made of the same conducting material, is 



ac ^ 2.704 8i . . 



where /xor and eor refer to the main dielectric of the Clogston cable. 



Since the attenuation constant of a standard coaxial cable is propor- 

 tional to the sciuare root of freciuency in the range we are considering, 

 while the attenuation constant of the ideal Clogston cable is independent 

 of frequency in this range, there will be a crossover frequency above 

 which the Clogston cable has a lower attenuation constant than a con- 

 ventional coaxial cable of the same size. If we are dealing with copper 

 conductors and if frequencies are measured in Mc-sec~ and linear 

 dimensions in mils, then from equations (78) and (153) we find that the 

 crossover frequency is given approximately by 



^ 49.50 M^r) 



(Sl + S2)mils 



For example, let us take an ideal Clogston 1 cable of outer diameter 

 0.375 inches, excluding the sheath, with no magnetic loading, and assume 

 the following values: 



a = 42.8 mils 6 = 2/3 



h = 187.5 mils e^r = 2.26 (polyethylene) 



sx = 12.69 mils €o. = 3e2r = 6.78 (155) 



52 = 6.06 mils Hor — Mir = M2r = 1 



Si + So = 18.75 mils 



This cable has a lower attenuation constant than a standard air-filled 

 coaxial of the same size at frequencies above about 1 Mc-sec~ , the ap- 

 proximate formula (154) yielding 0.955 Mc-sec~^ for the crossover 

 frequency and the exact ecjuation (118), taken in conjunction with (151), 

 yielding 1.251 Mc-sec~ . 



The reader is cautioned that the comparison given by (153) between 

 Clogston and conventional cables is based upon certain highly idealized 

 assumptions. In the first place we have neglected the finite thickness of 

 the laminae, which will in fact cause the attenuation constant of a 

 physical Clogston cable to increase with increasing frequency, and 

 ultimately to cross over again and become higher than the attenuation 

 constant of a conventional air-filled coaxial. We have also neglected 

 dielectric and magnetic losses, which are likely to be directly propor- 

 tional to frequency and by no means negligible at the upper end of the 



