250 



BELL SYSTEM TECHNICAL JOURNAL 



tanh - 



la 



1 - 



r- 



(2ay 



p 



(4a)2 



1 - 



P 



and 



Zi = R 



1 - 



P 



(4.75a)2 



1 - 



(3«)0\ 

 P 



P 



(6.5a)2 



(4.75a) 



P 

 (9.5a)2 



(5.5a) 



1 - 



P 



{l.Saf 



These equations determine Zx and Zy, the values of which may be 

 used in equations (27) and (28) to calculate the performance. This is 

 shown by Fig. 20, after dissipative effects have been taken into account. 



<a|3 



4 5 6 



f IN TERMS OF OC 



I'^ig. 20 — Performance of a low pass filter having linear phase through the cut-off. 



The approximation of the phase characteristic to linearity has again 

 been indicated by exhibiting departures of the slope from the average. 

 It is observed that the approximation obtained by the three-quarter 

 spacing is as close in the transition interval from 4a to 5.5a as in the 

 practical transmitting band below 4a. In practical design problems, 

 the phase shift is unlikely to be of interest beyond the first or second 

 refio^ction peak, so that the chain of impedance controlling frequencies 

 might be sooner terminated. 



