510 



BELL SYSTEM TECHNICAL JOURNAL 



is the use of a few filter sections of a type different from the usual 

 types above having phase characteristics with a negative second 

 derivative rather than positive so that the combination will postpone 

 the occurrence of phase distortion until very near the theoretical cut- 

 off and the other is the addition of all pass network sections which 

 accomplish the same general result. 



O 



0.2 



0.4 



0.6 0.8 

 FREQUE 



1.0 



1.2 



1.4 



ncy(^) 



50 

 45 

 40 

 35 -° 

 30? 



25 



Z 



o 



I- 

 < 



20 i 



I- 

 15 5 



10 



5 







1.6 



Fig. 19 — Insertion delay and attenuation characteristics for filter B of Fig. 17. 



One other point should be noted here. The shape of the insertion 

 phase curve as shown at the cut-off frequency owes its departure from 

 the image transfer phase shift without dissipation shown by the dotted 

 line more because of the reflection than dissipation. The value of the 

 Q so long as it is within the usual range makes little difference. 



Figs. 20, 21 and 22 correspond to those of 17, 18 and 19 but are for 

 high pass filters. High pass filters introduce no initial delay to signals 

 as a whole. The distortion of the signal is dependent upon sharpness 

 of cut-off, Q etc. just as for low pass filters. 



Band pass filters give an initial delay defined by the shape of the 

 phase curve. Other factors remaining the same this delay as well as 

 the amount of phase distortion is inversely proportional to /o — /i 

 the band width in cycles and is independent of the position of the band 

 on the frequency scale. The effect of reflection, dissipation, sharpness 

 of cut-off, etc., are about the same at the lower cut-off as for a high pass 

 filter and at the upper cut-off as for a low pass. As already noted one 

 distinguishing feature of the phase characteristic of a band pass filter 



