NEGATIVE FEEDBACK 407 



will be proportional to the product of the amplitudes A and B of the 

 incoming and local oscillator waves, the resultant index of the inter- 

 mediate wave, and the slope factor ai. Thus we can write the output 

 voltage amplitude 



Eo = aaiAB{xi — X2)p = aaiAB(piEi — kpiEo). (6) 



Therefore 



„ attiABpiEi 



1 + akaiABpi 



(7) 



Setting aaiAB = p. and kp2 = — iS we obtain the familiar form encoun- 

 tered in the analysis of feedback amplifiers 



p.(piEi) 



Without feedback the output of the system is merely p.{piEi). The 

 feedback factor 1 + aaJzABp-i is a measure of the extent to which the 

 over-all gain of the system has been modified by feedback. If this 

 factor is greater than unity the feedback is negative, while if k is made 

 negative by reversing the feedback connections the effect is regenera- 

 tive, and instability is encountered when the factor becomes zero. 

 It will be noted that when aaikABpi^ 1, (7) becomes 



£. = ^- (9) 



Thus for large amounts of feedback, the output signal becomes inde- 

 pendent of such factors as fading of the incoming wave, variations in 

 the local oscillator voltage, or changes in detector efficiency. Hence 

 automatic gain control is secured. This feature is equivalent to that 

 found in ordinary feedback amplifiers in that for large amounts of 

 feedback the over-all gain becomes independent of variations in the 

 performance of the amplifier proper. 



Reduction of Noise 



The application of negative feedback in the manner described 

 brings about a reduction in signal level by decreasing the effective 

 modulation of the received wave. It then becomes possible to increase 

 the modulation level at the transmitter to a corresponding degree and 

 thus to restore the output signal to its former value. This process is 

 made possible through the use of frequency rather than amplitude 

 modulation since the permissible degree of modulation is then deter- 



