566 BELL SYSTEM TECHNICAL JOURNAL 



manner previously described further reduces the effective range to 

 2500 cycles. Thus the additional reduction due to delay distortion is 

 small. 



Fig. 10 shows similar data for two filters having rapid rates of at- 

 tenuation increase, one having coils with a (2 of 80, the other ^ having 

 coils with a (2 of 200. For 20 filters {Q = 200) in tandem the effective 

 band due to attenuation distortion alone (delay equalized) is 2800 

 cycles. The effect of delay distortion further reduces the effective 

 range to 2650 cycles. Comparing these ranges with the corresponding 

 ranges for the filters of Fig. 9 shows that the filters of Fig. 10 use the 

 allotted band, which is the same for both figures, more efficiently from 

 an articulation standpoint, i.e., the effective band is a larger fraction 

 of the allotted band. The delay distortion, however, in the filters 

 {Q = 200) of Fig. 10 is more noticeable. This will be seen by noting 

 that the amount of delay near the cutoff for the filters of Fig. 9 is very 

 much smaller than that of Fig. 10. 



The noticeableness of the delay distortion may be decreased by 

 equalizing for the delay distortion, or by using filters with coils of 

 smaller Q. Any gain made by the former method is made at the ex- 

 pense of the minimum delay, i.e., the constant delay in the major part 

 of the transmitted range. Any gain made by the latter method is 

 made at the expense of the effective frequency range as shown by the 

 effective band for 20 filters {Q = 80) of Fig. 10. Twenty filters of the 

 type shown in Fig. 9 have about the same overall performance as 20 

 filters of the type shown in Fig. 10 having coils with a (2 of 80. 



It is evident that in the design of filters, compromises must be made 

 between the rate of attenuation increase at the edge of the transmitted 

 band, the minimum delay and the dela)^ distortion. The compromises 

 that are made in an actual system depend upon many factors and their 

 discussion is beyond the scopeof this paper. 



Although the time factor appeared to be the one of most importance 

 for the phase characteristics that have been discussed here, it should be 

 pointed out that this may not be true for all types of phase characteris- 

 tics. Much work remains to be done for other types of phase char- 

 acteristics, for example, characteristics which show irregular changes 

 with frequency rather than the smooth changes of the type discussed 

 here. It seems, however, that the main thing in securing transmission 

 free from phase distortion is to provide a phase characteristic that is 

 linear with frequency over the frequency range of interest. 



'' Q refers to the ratio of the reactance of a coil to its effective resistance. 



