NEGATIVE FEEDBACK 411 



In the system corresponding to Fig. 2(a), the signal power will be 



— T~' ^^'^ 



Equation (10) can be used to determine the noise power level for a 

 frequency-modulation system without amplitude limitation by setting 

 F = \. If balanced detection is used the term in a^ becomes zero. 

 It has been shown by Carson and Fry ^ that the addition of an ideal 

 limiter removes all terms but the third, with either single or balanced 

 detectors. Hence for the limiter system the noise ratio becomes 



Since Afi = T^Aco this can be put in a form similar to (16) 



Ps F^A^ \ 3Aw2 



Comparing (16) and (19) it is seen that the noise ratio in the feedback 

 system is greater than that for the limiter system by the factor (15). 

 This is a consequence of the increase in noise level which occurs during 

 modulation in the former system. The ratio of noise level during non- 

 signaling periods to signal level is identical in the two systems. 



While the noise increment which appears during modulation is 

 usually not of great consequence from a practical standpoint, it can be 

 reduced by increasing the feedback factor beyond the point dictated 

 by the signal band which it is permissible to transmit. In previous 

 discussions it has been assumed that the application of a given amount 

 of negative feedback is to be accompanied by a corresponding increase 

 in modulation level at the transmitter. In this way the modulation of 

 the intermediate frequency wave is kept constant so as to maintain a 

 fixed signal level as the band width of the transmitted wave is in- 

 creased. Having arrived at a limiting value of band spread the feed- 

 back factor can be increased further. Suppose that modulation of 

 the transmitter is to be limited to a value of A12 = /^lAco, but that the 

 feedback applied to the receiver is made to exceed Fi by a factor 

 which we shall call F2. Then the actual feedback factor will be ^^1^2 

 and we have 



P^ = .IT (20) 



p 27VVi 



-T Ar — ^ ^ ^ „ 





Qa (21) 



