696 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



in such a way that formulas for the counterparts of the usual transmission 

 line properties of inductance, capacitance and resistance are obtained. 

 The approximate formulas for attenuation, phase constant and speed 

 of propagation are then derived using conventional transmission line 

 theory. 



Some computations of attenuation are presented which illustrate the 

 interesting transmission properties of Clogston cables under ideal con- 

 ditions. Exploratory work on this type of conductor is still in the early 

 research stage, with some very difficult problems imposed by the need 

 for a large number of thin layers with very close tolerances ; 



Part I — General Discussion of Clogston Cables and a 

 Comparison with Conventional Coaxial Cable 



1. SKIN effect 



An alternating current transmitted over a solid conductor has the 

 tendency to crowd toward the surface of the wire. This phenomenon is 

 known as the skin effect and the depth of penetration of the current is 

 usually referred to as the skin depth. The skin depth is defined as the 

 distance, measured from the surface toward the center of the wire, where 

 the current density is reduced to 1/e = 0.367. For a copper conductor it is 

 given by: 



2.61 



where 



8 = Skin depth in mils. 



Fmc = Frequency in megacycles. 



When the skin depth is a fraction of the wire radius, the ac resistance 

 of the wire increases about as the square root of the frequency. 



Laminated conductors disclosed by Clogston have the property that 

 the ac resistance will remain very nearly equal to the dc resistance over 

 a wide band of frequencies, if the conducting and insulating layers can 

 be made thin enough and sufficiently uniform. The dc resistance of a 

 Clogston conductor will be higher than the dc resistance of a solid con- 

 ductor of the same over-all dimension by a factor (w + t)/w, where w and 

 t are the thicknesses of the conducting and insulating layers respectively. 

 As discovered by Clogston, the depth of penetration in a laminated 

 conductor is much greater than in a conductor of solid copper if the 



