1160 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



mode is defined b.y 



1 = -coVoeo + hi, = -47rVXo + hi (426) 



to the present approximation, and the cutoff wavelength is 



2. ^ 2fe-P.) (^27) 



hm mFm{pi/p2) 



which tends to zero with the thickness po — pi of the main dielectric. 

 As in the parallel-plane case, when the mth dielectric mode is just 

 able to propagate the effective skin depth in the stacks is of the order of 

 5i , and the stack impedances are approximately 



Z, = Z, = K = Tf/g, (428) 



under the present assumption of infinitesimally thin laminae. The power 

 dissipated in the stacks and the corresponding attenuation constant 

 may be calculated b}^ a straightforward procedure if desired. 



Before leaving the subject of higher dielectric modes in a Clogston 

 cable, we should point out that although we have mentioned only the 

 transverse magnetic modes with circular symmetry, in reality there exist 

 a double infinity of both transverse magnetic and transverse electric 

 higher modes. These modes are discussed in textbooks^^ for coaxial lines 

 bounded by perfect conductors, and they "^ill propagate, ^ith minor 

 changes due to wall losses, in either ordinar}^ or Clogston-type coaxial 

 cables if the frequency is high enough. At ordinary engineering fre- 

 quencies, however, the higher modes contribute only to the local fields 

 excited at discontinuities, and are therefore not of any great practical 

 importance. 



To find the stack modes in a Clogston cable we assume, subject to a 

 posteriori verification, that in the main dielectric we shall have | kqp \ <K 1 

 for all the modes of interest. Then if we set T( = ix, equation (417) re- 

 duces, as in Section IX, to 



1 Ji{xa)No{xPi) - Ni(xa)MxPi) 



XPiJi{xa)N'i{xpi) - Ni(xa)Ji{xpi) 



(429) 



, 1 Jl(xb)No(,XP2) — Nl{xb)Jo(xP2) ^ /fO, P2 



XP-2 JiixpdN.ixh) - iV:(xP2)/i(x6) M ^ Pi ' 



which is the same as equation (364). Equation (429) has an infinite 



23 A good account is given bv N. Marcuvitz, Waveguide Handbook, M. I. T. 

 Rad. Lab. Series, 10, McGraw-Hill, New York, 1951, pp. 72-80. 



