LAMINATED TILVNSMISSION LINES. II 1133 



insulation, and no inner core, we have 



h = 187.5 mils, eor = 2.26, (321) 



and the crossover frequency is about 50 kc-sec~ . 



It must be emphasized that several factors which have not yet been 

 taken into account will conspire to reduce the practical improvement in 

 transmission that can be obtained with a Clogston 2 cable. As we have 

 already seen for Clogston 1 lines in Part I, the effect of finite lamina 

 thickness in a Clogston 2 ^^^ll be to cause the attenuation constant to 

 increase with increasing frequency, and ultimately to become higher 

 than the attenuation constant of a conventional coaxial cable. Dissipa- 

 tion in the insulating layers may also contribute appreciably to the total 

 loss at the upper end of the frequency band. Perhaps most important of 

 all, the a\'erage electrical properties of the laminated mediimi must be 

 held extremely uniform across the stack, or the field pattern of the 

 principal mode Anil be distorted and its attenuation constant corre- 

 spondingly increased. In later sections we shall discuss these effects, in 

 order to estimate the stringency of the requirements on a physical 

 Clogston cable if its factor of improvement over a conventional cable is 

 to approximate closely to the theoretical limit given, for example, by 

 equation (319). 



IX. PARTIALLY FILLED CLOGSTON LINES. OPTIMUM PROPORTIONS FOR 

 PRINCIPAL MODE 



The distinction which has heretofore been made between Clogston 1 

 and Clogston 2 lines is rather artificial, inasmuch as both structures 

 are limiting cases of the general Clogston-type line in which an arbitrary 

 fraction of the total space is occupied by laminated material and the 

 rest by an isotropic main dielectric. We shall now consider the modes 

 which can propagate in a general partially filled line, restricting ourselves 

 for simplicity to stacks of infinitesimally thin layers backed by high- 

 impedance walls. Under these assumptions we first set up equations 

 which must be satisfied by the propagation constants and the fields of 

 all modes having only H^ , Ey , Ez or H^ , Ep , Ez field components in a 

 partially filled Clogston line, and then proceed to a study of the lowest 

 or principal mode. We exhibit field plots for this mode at various stages 

 of the transition between the extreme Clogston 1 and the complete 

 Clogston 2 geometry, and investigate the conditions under which the 

 attenuation constant passes through a minimum as the space occupied by 

 the stacks is increased. This leads to the determination of certain opti- 

 mum proportions for a line intended to transmit the principal mode. 



