LAMINATED TRANSMISSION LINES. II 



1141 



tioiis may easily be obtained, if desired, from the expressions for the 

 field components. 



As a numerical example we have plotted in Fig. 13 the fields of the 

 principal mode for plane transmission lines in which the stacks fill 

 respectively one-quarter, one-half, three-quarters, and all of the total 

 available space. For simplicity we have taken /xo = ji, eo = e, and nor- 

 malized the fields so that the total one-way current is the same in all 

 four cases. The average current density is of course gEz in the stacks 

 and zero in the main dielectric. The first case approximates most nearly 

 to the extreme Clogston 1 line discussed in Part I, while the last case 

 is the complete Clogston 2, and the intermediate cases show the transi- 

 tion between these two structures. The following table gives xiS as a 

 function of the fraction s/^a of the total space filled by the stacks, and 

 also the quantity (xiO'/tt) , which is equal to the ratio of the attenuation 

 constant of the line to the attenuation constant of the complete Clog- 

 ston 2. 



The principal mode in a coaxial Clogston cable corresponds to the 

 lowest root in Ti of equation (339). For the principal mode we are 

 justified in assuming that in the main dielectric 



I /Cop 1 « 1, ' (358) 



so that the Bessel functions occurring in equation (339) may be replaced 

 by their approximate values for small argument. We thus find that, to 

 a ver}^ good approximation, equation (339) reduces to the same form as 

 equation (41) of Section II, namely 



(359) 



where the stack impedances Zi and Z2 are given by (337) and (338). 

 If as before we let 





r^ = ix, 



(360) 



then from (330) kq becomes 



2 



{ioie/g)x\ 



(361) 



