LAMINATED TRANSMISSION LINES. II 1129 



Usually we shall be able to apply these formulas down to frequencies 

 of a few kc-sec~ . 



The field components of the principal mode in a plane Clogston 2 with 

 infinitesimally thin laminae and high-impedance boundaries at ?/ = ±^a 

 are given by equations (271), on substituting for r^ from (287). We 

 have, approximately, 



Hx = Ho cos — e 



■yz 



Ev= - A/-. Ho cos ^ e-'' , (297) 



ye a 



J, TT jj . Try -y^ 



hz = — Ho sm -^ e , 



ga a 



where Ho is an arbitrary amplitude factor, and in the coefficient of the 

 expression for Ey we have replaced y by its approximate value iw\/fle. 

 The bars have been omitted from i/^ and E, since these field components 

 are continuous at the boundaries of the laminae. 



The potential difference between any two points in the same trans\^erse 

 plane is the integral of —Ey between the points. In particular, the 

 total potential difi'erence between the upper and lower sheaths is 



V= -T Ey dy = ^4/^ Hoe--". (298) 



The average value of the conduction current density J^ is 



Jz = gEz =- Ho sin ^ e"'', (299) 



a a 



and the current per unit width flowing in the positive ^-direction in the 

 upper half of the stack is 



Jo 



J, dy = Hoe"''', (300) 



so that the ratio of voltage between the sheaths to total one-way cur- 

 rent per unit width is 



The fields of the principal mode in a coaxial Clogston 2 with infinites- 

 mally thin laminae and high-impedance boundaries are given by equa- 



