1182 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



is less, but in all practical cases it appears that the average properties 

 of the stack must be held constant against slow variations to a fraction 

 of a per cent. The requirement of extraordinarily high precision is in 

 addition to the requirement that the individual layers must be extremely 

 thin if a Clogston cable is to improve on a conventional coaxial cable at 

 all in the megacycle frequency range. 



For purposes of analysis, we consider a parallel-plane Clogston 2 

 transmission line bounded by infinite-impedance sheaths at y = ± |a, 

 as shown schematically in Fig. 10. The individual layers are supposed to 

 be infinitesimally thin, so that near any given point the average elec- 

 trical constants of the stack are 



6 = 62/(1 - d), 



M = ^Mi + (1 - e)^l2 , (518) 



g = 0gi ■ 



The quantities e, jl, and g may vary, continuously or mth a finite num- 

 ber of finite discontinuities, as functions of the transverse cooi'dinate 

 y, owing to variations in any or all of mi , S^i , M2 , e2 , and 6; but they 

 are not supposed to vary with x or z. 



We shall be concerned with modes in which the fields are independent 

 of X, and in which the only field components are Hx , Ey , and Ez . 

 Then Maxwell's equations are given by (269) of Section VIII, and 

 reduce, if we write the field components in the form H^{y)e"'% Ey(y)e~'^\ 

 and Ez(y)e~^', to 



—jHx = iwiEy , 



dHx/dy = -gE,, (519) 



—yEy — dEz/dy = iujlHx . 



If we eliminate Ey and Ez from these equations we obtain 



j2i 



(Tlh _ldgdlh _ .^_. ^ _^ 7 

 dy^ g dy dy 



WjJit 



H, = 0, (520) 



where Hx and Ez must be continuous at any points of discontinuity of 

 e, p., or g. The tangential magnetic field must vanish on the infinite- 

 impedance surfaces at ?/ = ±^a; hence we have the boundary con- 

 ditions 



Hx{-ha) = Hxiia) = 0. (521) 



These boundary conditions, taken in conjunction with the differential 



