FILTER-TYPE CIRCUITS 193 



ponent in the z direction). We find that for the structure under consideration 

 there is a transverse magnetic solution. We can take it either on the basis 

 of other experience or as a result of having solved the problem that the 

 correct form for the x component of magnetic field for v > is 



H. = Hoe'-'"-'^'' (4.1) 



Expressing the electric field in terms of the curl of the magnetic field, we have 



. ^ dHz dHy „ 



ay dz 



. ^ OHx dHz 



J(X)et,j = — -— 



dz ax 



(4.2) 



coe 



Hoe'-'"-''" (4.3) 



. dHy dHx , . 



ji^iE^ = ~—^ -— (4.4) 



dx dy 



E.= - j 1 Hoe'-'"-'''' (4.5) 



we 



We can in turn express H^ in terms of Ey and E. 



dEz d 

 dy dz 



j.,H, = "-^ - ^y (4.6) 



This leads to the relation 



/32 _ y = co-yue (4.7) 



Now, l/v jue is the velocity of light, and co divided by the velocity of light 

 has been called /3o , so that 



/32 - 7- = /3o- (4.8) 



Between the partitions, the field does not vary in the z direction. In any 

 space between from y = to y = —h, the appropriate form for the magnetic 

 field is 



^^^^^c^s^o(y + A) (4^^ 



cos /3o« 



From this we obtain by means of (4.4) 



E,= _igog^sin/Jo(y + /0 ^^^^^^ 



coe cos |So^ 



Application of (4.6) shows that this is correct. 



