908 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



where 



/.. = Ir{l\Ps), Kr. = Kr(V,p,), (99) 



and r^ and K are given, as in the plane case, by (93) and (94). 



IV. PRINCIPAL MODE IN CLOGSTON 1 LINES WITH INFINITESIMALLY THIN 

 LAMINAE 



An idealized parallel-plane Clogston 1 transmission line is shown 

 schematically in Fig. 5. It consists of a slab of dielectric of thickness b, 

 with electrical constants mo , «o , bounded above and below by laminated 

 stacks each of thickness s. Outside each stack there may be an insulating 

 or a conducting sheath, of which nothing more will be assumed at present 

 than that its normal surface impedance Zn(y) is known. The total dis- 

 tance between the sheaths will be denoted by a, where a = b -\- 2s. 



The corresponding Clogston 1 coaxial line is shown in Fig. 6. We de- 

 note the thickness of the inner and outer stacks by Si and So respectively, 

 while a is the radius of the inner core (if any), and b is the inner radius 

 of the sheath around the outer stack. The inner and outer radii of the 

 main dielectric are pi = a + Si and p2 = b — So , respectively. In practice 

 the core may be a dielectric rod and the sheath may be a conducting 

 shield, but in the present theoretical analysis we shall merely assume that 

 the radial impedances Za(y) and Zb(y) looking into the core and the 

 sheath are known. 



In Part I of this paper we shall deal with "extreme" Clogston 1 lines, 

 in which the space occupied by the stacks is small compared to the 

 space occupied by the main dielectric. We may then regard the laminated 

 boundaries as impedance sheets guiding waves whose phase velocity is 



Zn(r) 



Fig. 5 — Parallel-plane Clogston 1 transmission line. 



