688 



BELL SYSTEM TECHNICAL'' JOURNAL 



resonant frequency of a branch is independent of the terminal resistance and 

 is given by the relation 



The loaded Q of the branch, to be designated ^^ , is a function not only of the 

 inductance and capacitance in the branch, but also of the resistance, R, of 

 the terminations on the filter. For the series resonant branches, it is given 

 by 



1 . /Lr coo Lr 



~2R 



Qr = 



2R T CV 

 and for the parallel resonant branches 





(2) 



(3) 



Fig. 3 — Schematic diagram of a band-pass filter. 



It may be noted that the loaded Q can be defined in terms of the insertion 

 loss iir posed by connecting the branch between a source and receiver each 

 of resistance R. Analysis of such a circuit shows that 



g--«:a-'7)' 



(4) 



where / is the frequency; 



Po is the power available from a generator which has an internal 



resistance R; 

 Pl is the power delivered through the inserted branch to a load of 

 resistance R. 

 At the cutoff frequency, fc , defined as the frequency at which the power 



Po 



, delivered to the load is half the available power, — = 2, whence 



Pl 



Qr = 



(5) 



