956 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



h - ''' - ^»^' 



Ey = 0, 



H.= 



-1 dE. 



joijiQ dx 



with /3o^ = co^eoMo • If the waves are to be guided, /3^ > ^o, and, then, for 

 re < 0, we have d/dx = V/S^ - iSo^. Thus 



Hy~ _ ytoeo 

 Er ~ V^' - /3o^ ' 

 and 



^ = _ V<3^ - i8o^ 



If the admittances at the surface of the ferrite are Hy^/E/ and U^ /Ey\ 

 then Ey'^ /Ez" and U^ /Ey^ are given by the impedance transformation : 



jcoeo 





and 



^, 



^j:^f^'-tanhV^-r^W^.o 

 1 - V£EW f/ .tanh VW^^JC- X, 





^+ 



JWCO 



1 - 



— jWMo /Z"^ 



_V/3^ - /3o^ ^/_ 



•tanh V/S" - iSo" a:o 



Within the ferrite the TM-fields fall off as exp — \//3- — w^eMo^^ and the 

 TE-fields as exp — V/S^ — co^e/ieff^- We then have 



and 





ViS^ - CoVeff - /Jk/m " 



These results may now be collected and substituted in equations (IG). 

 The equation of condition so obtained is 



A + 1 



(r - /3o^) 



A + tanh V/S^ - ^x^ 



2 _ .2 



1 T> 



= jSo" cot' i/' ;— -T — / , , (17) 



^ I - B tanh ViS^ - j8o'a;o 



