940 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



It should be remembered that mismatch of the mo^o product of the main 

 dielectric will usually be accompanied by a change in the dielectric 

 impedance \/)Lto/co • Thus under certain conditions the lower crossover 

 frequency may even be reduced by choosing eo slightly below the Clog- 

 ston value, inasmuch as the increase in dielectric impedance may more 

 than compensate for the increase in stack resistance at low frequencies; 

 but it appears that this will be paid for in a steeper slope of the attenu- 

 ation versus frequency curve and a consequent greater reduction of the 

 upper crossover frequency. 



It would be very useful to make a numerical study of the effects of 

 dielectric mismatch in Clogston cables having a variety of different pro- 

 portions; but in the present paper space limitations restrict us to a few 

 observations concerning orders of magnitude. For the cable which we 

 considered at the end of the preceding section, it turns out than an 

 increase or decrease of 1 per cent in the value of eo makes a change of 

 at most a very few per cent in either crossover frequency ; with a matched 

 dielectric, we recall, these crossover frequencies were about 1 Mc-sec~ 

 and about 280 Mc • sec" respectively. However if we had designed a 

 laminated cable with thicker stacks or thinner laminae or both, so as to 

 increase the theoretical factor of improvement over a conventional cable 

 in the working frequency range, we should have found that the tolerable 

 deviation of co from Clogston's value, instead of being of the order of 

 1 per cent, was more nearly of the order of 0.1 per cent or even smaller; 

 and the greater the improvement striven for, the more stringent the re- 

 quirement of accurate dielectric match. 



VII. DIELECTRIC AND MAGNETIC LOSSES IN CLOGSTON 1 LINES 



Dielectric and magnetic dissipation in the main dielectric and in the 

 stacks can be taken into account by introducing complex dielectric con- 

 stants and permeabilities for the lossy materials. Thus we may write 



(248) 



w^here in the most general case the loss tangents may all be different, 

 though it will be assumed that they are all small compared to unity, so 

 that the problem may be treated by first-order perturbation methods. 



