LAMINATKD TK.WSMISSIOX LINES. I 1)19 



while it we lixul the iiiaiii dielectric so that ^x^, = 3/i2 iind we can take 

 fo = €2 , we have 



(cq/mo) ^ V3 (e2//X2) Qf^QN 



6gi '2gi ' 



which is just one-third of the value with no magnetic loading. 



As Clogston has pointed out, if the limitation is on the total thickness 

 of conducting material in the stacks rather than on the stack thicknesses 

 themselves, we shall find it advantageous to use a small value of 6 (a 

 high "dilution" of conducting material) so as to make the average 

 dielectric constant 62/(1 — 6) of the stacks, which has to be matched by 

 the main dielectric, as small as possible. We shall see later that the effect 

 of hnite lamina thickness is in fact to limit the total thickness of conduct- 

 hig material which it is useful to employ in a single stack at high frequen- 

 cies, so that for physical stacks of non-magnetic layers at high frequencies 

 the optimum \'alue of d is less than 2/3. Quantitative results w^hich take 

 into account the finite thickness of the layers will be obtained in 

 Section XI. 



To illustrate the use of some of the equations derived above by means 

 of a numerical example, w'e shall compare the attenuation constant of a 

 conventional coaxial cable with that of a Clogston 1 cable of the same 

 size. If a and b denote the radii of the inner and outer conductors of a 

 conventional coaxial cable, and we take b/a = 3.5911 to minimize the 

 attenuation constant, then we have from equation (48) of Section II, 

 on setting pi = a and p2 = 6, 



^-^1^^, (151) 



TjogiSib 



where 170 is the intrinsic impedance of the main dielectric, which may be 

 air. For a Clogston 1 coaxial cable with infinitesimally thin laminae, no 

 magnetic material in the stacks (mi = M2 = Mt), and the optimum propor- 

 tions given by (139) and (147), w^e have 



- 4.857 (J.2) 



7?0^l(Sl + S2)b' 



where b is the outside radius of the outer stack and rjo is the intrinsic 

 impedance of the main dielectric, which cannot be air in a Clogston cable. 

 The ratio of the attenuation constant «<; of this Clogston cable to the 



