414 BELL SYSTEM TECHNICAL JOURNAL 



When the feedback factor F is large this can be written 



c p 



= a^5 ( ^Pi5 + || {p,SY + 1 [ Z,3 - ^' j {pySf ) . (26) 



Upon increasing the modulation by the factor F so as to restore the 

 original level of the fundamental, the output becomes 



a/ = aAB(h,p,S + ~ b,{p,Sy + (bz -^\ {p,Sf 



(27) 



Second order distortion products are reduced with respect to the 

 fundamental level by the feedback factor. Third (and higher) order 

 products are modified to an extent depending upon the relative values 

 of the distortion coefficients and the amount of feedback. If, as can 

 readily be the case when a balanced detecting system is used, 



63 »^' (28) 



third order products are reduced in the same manner as those of second 

 order. In any case, by applying sufficient feedback a point will be 

 reached where a given increment in feedback will produce a corre- 

 sponding reduction in all distortion products. 



Equation (25) shows that the greatest improvement in distortion is 

 obtained if the modulation level is not increased when feedback is 

 applied. The large reductions result partly from feedback and in part 

 from the fact that the system is operating at reduced percentage of 

 modulation. Under this condition there is no improvement in back- 

 ground noise ratio, though the noise increment which takes place during 

 modulation is diminished; see (10) and (11). Depression of both 

 noise and distortion, but with greater emphasis upon the reduction of 

 the latter, can be effected by raising the modulation level by an amount 

 somewhat less than the feedback factor. This procedure has already 

 been discussed in connection with (22) which gives the resulting noise- 

 to-signal power ratio. Under similar conditions we have, from (25), 



a/' = aAB [^PiS + ir\ ^, {piSf 



^1 L ^2^ 



1 



+ ^4 Us - ^ (puS) 



(29) 



when the feedback factor is large. 



Equations (22) and (29) are most readily interpreted by means of 

 Fig. 3, which illustrates the manner in which the receiver output is 

 modified as the feedback is increased. 



