1124 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



medium that we shall omit details of the analysis and pass at once to 

 the results. 



In the parallel-plane line, the modes for which /7x is an even function 

 of y about the center plane y = have field components given by 



Hx = ch T(y e 

 7 



E. = 



ch Tty e 



E^ = -KshTfye"'', 



(271) 



up to an arbitrary amplitude factor, where r^ and K are defined, as 

 in Section III, by 



T/ = 



— (.w Aie + 7 ) 

 we 



K = T,/g = 



J_ /■ 2_. > 2n 



._ (w/xe + 7 j 

 [_o:eg 



(272) 



(273) 



Matching impedances at the boundaries y = ±^a leads to the condition 

 K tanh h^ia = -Zn(y). (274) 



In the odd case, the fields are given by 

 Hg, = sh Tty e~''% 



Ey = -^ sh Tty e""', (275) 



zoje 



E,= -KchTtye"", 



up to an arbitrar}^ amplitude factor, and the boundary condition be- 

 comes 



K coth iTta = -Zn(y). (276) 



General expressions for the field components in the coaxial line are 



H^ = U7i(r,p) + BKriTtpW, 



E, = — . [AhiTtp) + BKiiTtpW", 



iwe 



(277) 



E. = K[AUTtp) - BlUTtpW^ 



