388 BELL SYSTEM TECHNICAL JOURNAL 



Loss Equalization 



Another function of the lattice section is to make the loss of the 

 filter constant in the program frequency band. In a dissipationless 

 filter terminated in its image impedances (which is substantially the 

 condition under which this filter is operated) the loss in the trans- 

 mitting band is zero. The effect of dissipation is to introduce a loss 

 which is given approximately in this band by the equation: 



where Ad is the loss due to dissipation, B is the phase shift of the non- 

 dissipative filter, and Q is the average dissipation factor of the coils 

 (dissipation in the condensers being negligible, ordinarily). The 

 factor Q is equal to the average of the ratios o^Le/Re, and o}/2Q in 

 equation (2) therefore may be written Re/2Le, where Re and Le are 

 the effective resistance and effective inductance, respectively, of the 

 coils. 



In the coils of the program filter, Q is about proportional to fre- 

 quency over the lower portion of the program band, but above this 

 range the factor co/lQ increases with frequency. For the filter exclu- 

 sive of the lattice section, the factor dB/dco is also greatest at the higher 

 frequencies, as may be seen from the lower curve in Fig. 3; hence this 

 part of the filter introduces much more amplitude distortion than is 

 permissible. For the lattice section alone, however, the factor dBjdw 

 is greatest at the lower frequencies, as is apparent from the middle 

 curve of Fig. 3. Thus the natural tendency of dissipation in the 

 lattice section is to compensate for the distortion in the other sections 

 of the filter. This compensating tendency can be controlled to a 

 considerable degree, since by equation (2) ^d is proportional to Re. 

 By proper adjustment of the effective resistance of the coils of the 

 lattice section, its loss is made practically complementary to that of 

 the rest of the filter, so that the loss of the complete filter is sub- 

 stantially constant throughout the program range. 



The loss of the filter in the transmitting frequency band is shown in 

 Fig. 5. The average loss below 7,000 cycles per second is about 0.53 

 db and the deviation from this average does not exceed 0.03 db. 

 Considering again a circuit containing 50 filters, the deviation from 

 the average loss introduced by the filters does not exceed 1.5 db in 

 this range. Between 7,000 and 7,500 cycles per second the amplitude 

 distortion per filter is about 0.10 db, and above 7,500 cycles the loss 

 increases in such a way as to tend to mask the small delay distortion 

 in this range. 



