386 BELL SYSTEM TECHNICAL JOURNAL 



usual ladder type low-pass filter. Over the lower frequencies of the 

 transmitting band the phase shift-frequency characteristic is prac- 

 tically linear with frequency, but at the higher frequencies the slope 

 of this curve increases gradually with frequency and becomes very 

 large near the upper edge of the band. Phase shift varying in this 

 manner introduces much more delay distortion than can be tolerated, 

 and therefore has to be corrected. It is one of the functions of the 

 delay and loss equalizing section, which is of the lattice type, to correct 

 for this distortion. The phase shift of this lattice section is such that 

 when it is added to that of the rest of the filter the total phase shift is 

 very nearly proportional to frequency over the whole program band, 

 and delay distortion thus is almost entirely eliminated. 



The property of the lattice section by which its phase shift can be 

 made to vary with frequency in the desired manner is expressed in the 

 following characteristic equation, which holds only in the transmitting 

 band and when the section is terminated in its image impedances:^ 





Kf 1 



In this equation, B is the phase shift in radians;/ is the frequency in 

 cycles per second ; /i, /2, /s, and fc are frequencies at which the phase 

 shift of the section is successive multiples of tt radians or 180 deg., 

 fc being also the cut-off frequency of the filter; and i^ is a constant 

 controllable by assigning the proper values to the coils and condensers 

 of the section. By assigning to/i, /2, and/3 the values of frequency at 

 which it is desired that the phase shift of the section shall be tt. It, 

 and Stt radians, respectively, and by giving K the proper value, the 

 phase shift-frequency curve is made to approximate the ideal one 

 which completely would correct the delay distortion of the filter. 

 Figure 3 illustrates the building up of the phase shift characteristic. 

 The delay corresponding to the rate of change of the phase shift with 

 frequency is plotted in Fig. 4. The average delay introduced by the 

 filter is about 0.00035 sec. It may be noted that for frequencies 

 below 7,500 cycles per second, the variation from this average does 

 not exceed 0.000025 sec. Thus the delay due to 50 filters in a long 

 program circuit does not deviate from the average in this frequency 

 range by more than 0.00125 sec. Distortion of this amount ordinarily 

 would not be detected by the average listener. Above 7,500 cycles 



5 U. S. Patent No. 1,828,454 to H. W. Bode. 



