MA XI MA LL Y-FLA T FILTERS IN WA VEGUIDE 695 



capacitance and a resistance equal to Zq ,* as in Fig. 6. The terminating 

 admittance is given by the relation (See Eq. 7 and 9) 



Yl= Fo(l+i212). (22) 



The input admittance at the end of the length of line, (, (nominally a quar- 

 ter wavelength long) is given by the relation 



where 



— = (1 + j2n) cos g + ; sin ^ 

 Fo cos 6 ^- j{\ -{- j2n) sin 6 



^ = length of line 

 X = wavelength 



(23) 



a = Q 



(H) 



letting 



^ = ^ (1 + 5) = ^ + ^^ (24) 



cos^=-sin^^^ -^^ (25) 



sin ^ = cos '^ = 1 (26) 



where 6 is a number small compared with 1. Then the admittance becomes 



This is the normalized input admittance of a circuit as shown in Fig. 8, 

 where each end of an ideally inverting hne is shunted by a tuned circuit 



whose normalized admittance is 7 — . 



9 / 

 From Eq. 24, setting -— = ;:, it follows that 



Ao 2 



'-(i-o-a-!)"- 



(28) 



* More generally, the terminating admittance can assume any value without affecting 

 the result. 



