The Bell System Technical Journal 



Vol XVIII July, 1939 No. 3 



Frequency-Modulation : Theory of the Feedback 

 Receiving Circuit 



By JOHN R. CARSON 



THIS paper may be regarded both as a continuation of a prior one 

 by the writer and Thornton C. Fry ' and as a companion of that 

 by J. G. Chaffee - the inventor of the circuit under consideration. For 

 an understanding of the present, an acquaintance with the prior paper ' 

 is absolutely necessary, since the fundamental analysis and the formu- 

 las there developed are too lengthy to be repeated here. References 

 to that paper will be designated by (Ref.). 



As the name implies, in the feedback circuit part of the incoming 

 signal, after passing through a band-pass filter, a frequency detector ^ 

 and a demodulator, is fed back through a variable frequency oscillator. 

 The output of the variable frequency oscillator is connected to one 

 branch of a modulator on the other branch of which the incoming high- 

 frequency wave is impressed. While this method of feedback differs 

 in some respects from that of the well known feedback amplifier, it is a 

 fair inference that some if not all of the very important advantages of 

 the feedback amplifier may also be present in the circuit under discus- 

 sion. This inference is verified by the mathematical analysis of this 

 paper. 



After a brief development of the elementary theory and formulas of 

 the feedback circuit as a receiver of frequency-modulated waves, the 

 greater part of the paper is devoted to deriving formulas for the signal- 

 to-noise power ratio — a criterion of fundamental importance in estimat- 

 ing the merits of the system. These are then compared with the corre- 



1 "Variable Frequency Electric Circuit Theory," this Journal, October 1937. 



^"The Application of Negative Feedback to Frequency-Modulation Systems," 

 /. R. E. Proceedings, May 1939; this issue of the Bell Sys. Tech. Journal. 



^ The function of the "frequency detector" is to detect or render explicit the 

 variation of the "instantaneous frequency" of the frequency-modulated wave. A 

 more precise term, therefore, would be "frequency variation detector," but for 

 brevity the term used in the text is preferable. 



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