COAXIAL AND BALANCED TRANSMISSION LINES 



297 



where i? is a resistance equal to K at the mean-frequency of the filter. 

 For narrow bands this gives a very large value for d, the shunt capacity. 

 A more practical arrangement is to replace the two series condensers 

 Ci and the shunt condenser C2 by a tt network consisting of two shunt 

 condensers Ca separated by a series condenser Cb- These have the 

 values 



C1C2 . ^ Ci" 



Ca 



2Ci + C2 



Cn = 



2Ci + C2 



(60) 



With this arrangement we find that for narrow bands Ca — Ci and Cb 

 is a very small capacity. This can readily be obtained physically by 

 inserting a partition with a small hole in it at the middle of the section. 

 Then Ca will be the capacity of the inside conductors to the partition, 

 and Cb will be the capacity of one inside conductor to the other looking 

 through the small hole. By adjusting the size of this hole, this 

 capacity can be made as small as desired. 



-0, 



Cl C3 



-02 



Fig. 10— A shunt terminated transformer. 



The transformer discussed above is suitable for transforming from 

 line impedances down to very low impedances, but cannot be used to 

 transform from line impedances up to very high impedances such as 

 the impedance of a vacuum tube. This generally requires a shunt 

 type of termination rather than the series type discussed above. One 

 such transformer is shown in Fig. 10. It consists of two shunt lines 

 connected together by a T or x network of capacities. The constants 

 of such a transformer are readily calculated, and for the condition of 

 maximum transformation for a given band wndth — which occurs when 

 C3 -^ 00 , and for eighth wave-length conductors on each end — these 

 have been found to be 



^^= 1 + 



C2 



/ = 



8/„ 



(61) 



