TRANSIENT OSCILLATIONS IN ELECTRIC WAVE-FILTERS 27 



In the foregoing argument, the theoretical limitations have been 

 carefully porn ted out and even emphasized. In practical applications, 

 however, it is believed that these limitations are of small or negligible 

 importance, and that the formula for and definition of the selective 

 figure of merit furnish all the information, as regards the behavior of 

 selective circuits to random interference, which we are in a position 

 to make use of. Thus the formula is immediately applicable to the 

 problem of determining the effect of bandwidth, number of sections, 

 dissipation, and terminal reflections on the selectivity of filters 

 with respect to random interference. It furnishes likewise, a means of 

 estimating the comparative merits of the very large number of circuits 

 which have been invented for the purpose of eliminating "static" 

 in radio communication, and leads to general deductions of practical 

 value regarding the inherent limitations imposed on the solution of 

 the "static" problem. 



The utility and significance of the foregoing formulas will now be 

 illustrated by application to some representative selective circuits. 

 It is easily shown that, to a good approximation, in the case of the low 

 pass filter (type LiC 2 ) 



S = \ 



u c (l + l/16n 2 )' 



and for the band pass filter (type LiCiL 2 C 2 ) 



s- ' 



w(l + l/lQn 2 )' 



In these formulas n denotes the number of filter sections while « c 

 is 2r times the cut-off frequency of the low pass filter and w is 2r 

 times the transmission band width of the band filter. In both cases 

 the filters are assumed to be terminated in their characteristic im- 

 pedances and to be non-dissipative. 22 These formulas show at once the 

 effect of band width and number of sections n on the behavior of wave- 

 filters to random interference, and lead to the following proposition. 



In filters designed to select a band of frequencies of width w, the ratio 

 of energy transmitted through the network by the signal and by random 

 interference is inversely proportional to the band width and increased in- 

 appreciably when the number of sections is increased beyond two. 



As regards the effect of dissipation, a second proposition is deducible. 



The effect of introducing dissipation into a network designed to select 

 a single frequency or a band of frequencies is always such as to reduce 

 the ratio of signal energy to that absorbed from random interference. 



22 These approximate formulas are in very good agreement with actual calcula- 

 tions for filters terminated in resistances. 



