NEGATIVE FEEDBACK 405 



to the input of the receiver, and are caused to influence the response of 

 the system by modifying the performance of the modulator. 



In the ordinary feedback ampHfier a part of the output voltage is 

 carried back to the input and there combined with the applied voltage. 

 The result is to modify the output and if the gain of the system is 

 thereby reduced the feedback is said to be negative. The many ad- 

 vantages which result from negative feedback have been described by 

 Black ^ and are coming to be more generally appreciated. The present 

 paper deals with a method for adapting this principle to a frequency- 

 modulation receiver and will show an example of its application to an 

 experimental system in the laboratory. 



General Discussion 

 Method of Applying Feedback 



Consider a frequency-modulation receiver in which the incoming 

 wave is combined with the output of a local oscillator in a modulator to 

 produce a wave of intermediate frequency. This is then amplified, 

 converted into an amplitude-modulated wave, and finally detected. 

 The frequency of the intermediate wave is equal to the instantaneous 

 difference in the frequencies of the incoming carrier and the local 

 oscillator. So long as the frequency of this oscillator remains fixed the 

 intermediate wave will be frequency-modulated in exact correspond- 

 ence with the incoming wave. Suppose now that the local oscillator 

 is frequency-modulated from a source of the same frequency and phase 

 as that applied to the transmitter. As the index of modulation at the 

 local oscillator is increased from zero the extent to which the inter- 

 mediate wave is modulated will diminish since its instantaneous fre- 

 quency is equal to the difference in the frequencies of the two sources. 

 It then follows that if these two devices are modulated to the same 

 extent the difference frequency will become constant and the output 

 of the system will be zero. Finally a further increase in modulation of 

 the local oscillator will cause the intermediate wave to be modulated 

 with a 180-degree phase reversal. 



This process can be readily analyzed as follows: Assume the oscilla- 

 tor at the transmitter to have been frequency-modulated by the 

 signal wave 



e = El cos pt. (1) 



The voltage delivered to the modulator by the incoming wave will be 



A cos (coit + Xi sin pt + </)i) (2) 



^ H. S. Black, "Stabilized Feedback Amplifiers," Elec. Engg., vol. 53, pp. 114-120, 

 January 1934. 



