\ 



NEGATIVE FEEDBACK 431 



back system have been assumed. This corresponds to a deviation ratio 

 of 124.5 kilocycles -^ 4 kilocycles = 31.1, resulting in a theoretical 

 noise deduction of 34.6 decibels at low disturbance levels. The thres- 

 hold of noise improvement, indicated at the point x, is located at a 

 point where the peak signal-to-noise ratio in the amplitude system is 

 equal to the square root of the deviation ratio.® This factor takes ac- 

 count of the higher disturbance level in the intermediate-frequency 

 channel of the wide-band system. Assuming a factor of 10 decibels 

 between maximum peak and root-mean-square values of fluctuation 

 noise this corresponds to a root-mean-square signal-to-noise ratio of 

 24.9 decibels in the amplitude system.^ In the feedback system the 

 point at which crackling was first observed in the presence of modula- 

 tion is shown at Y. This coincides very closely with the theoretical 

 threshold of noise improvement in the limiter system. 



Conclusions 



It has been shown that the application of negative feedback to a 

 frequency-modulation system affords a means for effecting large reduc- 

 tions in both noise and receiver distortion. The theoretical analyses of 

 these effects, while they have been simplified to an extent which makes 

 them inadequate to cover all conditions which can be encountered in 

 practice, are adequately substantiated by the observed performance 

 of the experimental system within the limitations of the theory. 



Substantial benefits are realized only when the amount of feedback 

 is large, and when the disturbance level is not too great. In common 

 with frequency-modulation systems employing amplitude limitation a 

 large reduction in noise must be paid for by increasing the band width 

 of the transmitted wave. While the principles involved in the two 

 systems are quite different, their performance as regards noise modifi- 

 cation, both at high and at low levels of disturbance, exhibits striking 

 similarities. The ability to reduce distortion is, on the other hand, a 

 feature found only in the feedback system. 



Acknowledgment 



The writer wishes to acknowledge his indebtedness to the following 

 of his colleagues: To Dr. H. W. Bode for his investigations of the 

 problem of stability in feedback systems, and to Mr. R. L. Dietzold for 

 the design of the stabilizing network which was used; to Mr. W. R. 

 Bennett whose unpublished work on basic frequency-modulation prob- 



^ In the absence of more exact information regarding the performance of a system 

 using this large a deviation ratio the portion of this curve below the threshold has 

 been omitted. 



