252 BELL SYSTEM TECHNICAL JOURNAL 



permeability of the material of the inner conductor, and X2 and /X2 the 

 corresponding values for the outer conductor. The ratio X1/X2 will be 

 designated by n. 



The high-frequency resistance of the inner conductor may then be 

 approximately expressed by the formula :'• "^ 



R\ — y^/y^abohms per cm. (2) 



Similarly the high-frequency resistance of the outer conductor is 



approximately: 



1 If 

 -^^o = -x/v— abohms per cm. (3) 



f \ Xo 



The high-frequency inductance of the circuit is approximately ^ 



L = 2 logf y abhenries per cm. (4) 



The capacitance of the circuit is ^ 



C = abfarads per cm., (5) 



2 loge ^ 



where e is the dielectric constant of the dielectric material between 

 conductors, equal to 1/9 X 10"^" for gaseous dielectric, corresponding 

 to unity in the practical system of units. 



The high-frequency attenuation of the coaxial circuit with negligible 

 dielectric loss, obtained by combining the above formulas, is 



2 loge ^ 



The value of permeability assumed in the abov^e equation, and here- 

 after, is unity, but the methods may be used also for other values. 



If the inner diameter of outer conductor be assumed fixed, this 

 expression may be minimized with respect to the ratio r/b, which is 

 the ratio of the radii (or diameters). For convenience this ratio may 

 be designated as p. It is found that the high-frequency attenuation is 

 a minimum when the ^•alue of p is that given by 



1 P -\- ^n .^ 



log, p = . (7) 



