NEGATIVE FEEDBACK 413 



limits of the characteristic of the over-all intermediate-frequency 

 system have the effect of holding the maximum peaks of noise to a 

 value equal to the highest signal peaks obtainable in the absence of the 

 disturbance. Furthermore, the existence of high noise peaks in the 

 presence of modulation can result in the momentary assumption by the 

 instantaneous intermediate frequency of values outside of the region 

 to which the system is normally responsive. Thus the output signal 

 will appear to be chopped by the higher noise peaks, and as a conse- 

 quence its energy content will be considerably reduced. 



The above effects are, of course, present in systems using limiters and 

 have already been discussed in greater detail by Crosby.® 



Distortion Reduction 



One of the chief benefits which can be realized through the use of 

 negative feedback is the reduction of non-linear distortion products 

 generated in the forward branch of the system. While the distortion 

 in properly designed amplifiers is sufficiently low for many purposes, 

 cases frequently arise in which the requirements are much more severe. 

 In an amplifier which is to handle several channels in a high grade 

 multiplex system, the distortion products should be of the order of 60 

 decibels below the fundamental of the output. This degree of excel- 

 lence is most readily obtained by using negative feedback. 



In radio systems designed for multiplex service it is of equal impor- 

 tance that the distortion level be kept at a correspondingly low level if 

 crosstalk is to be avoided. It is therefore of interest to inquire into 

 the manner in which distortion is modified in the present feedback 

 system. 



An analysis of the effect of feedback upon distortion is given in Ap- 

 pendix A. If the transmitter is modulated with a signal wave 5 = S{t) 

 so that its instantaneous frequency becomes 



o) + piS (23) 



then, in the presence of non-linearity in the receiver, the output of the 

 system can be written as a power series in the variable frequency term 

 piS. Thus for the first three orders we shall have 



a = aAB[b,p,S + hi{p,Sf + 63(pi5)«]. (24) 



If feedback is applied without altering the modulation level at the 

 transmitter it is shown that the above series becomes 



<T,= aAB[ ^pi5 + ||(pi5)2 



+ 1 



2bl 



)j(pi5)^). (25) 



