Variable Frequency Electric Circuit Theory with Application 

 to the Theory of Frequency-Modulation 



By JOHN R. CARSON AND THORNTON C. FRY 



In this paper the fundamental formulas of variable frequency 

 electric circuit theory are first developed. These are then applied 

 to a study of the transmission, reception and detection of frequency 

 modulated waves. A comparison with amplitude modulation is 

 made and quantitative formulas are developed for comparing the 

 noise-to-signal power ratio in the two modes of modulation. 



FREQUENCY modulation was a much talked of subject twenty 

 or more years ago. Most of the interest in it then centered 

 around the idea that it might afford a means of compressing a signal 

 into a narrower frequency band than is required for amplitude modu- 

 lation. When it was shown that not only could this hope not be 

 realized,* but that much wider bands might be required for frequency 

 modulation, interest in the subject naturally waned. It was revived 

 again when engineers began to explore the possibilities of radio trans- 

 mission at very short wave lengths where there is little restriction on 

 the width of the frequency band that may be utilized. 



During the past eight years a number of papers have been published 

 on frequency modulation, as reference to the attached bibliography 

 will show. That by Professor E. H. Armstrong f deals with this 

 subject in comprehensive fashion. In his paper the problem of 

 discrimination against extraneous noise is discussed, and it is pointed 

 out that important advantages result from a combination of wide 

 frequency bands together with severe amplitude limitation of the 

 received signal waves. His treatment is, however, essentially non- 

 mathematical in character, and it is therefore believed that a mathe- 

 matical study of this phase of the problem will not be unwelcome. 

 This the present paper aims to supply by developing the basic mathe- 

 matics of frequency modulation and applying it to the question of 

 noise discrimination with or without amplitude limitation. 



The outstanding conclusions reached in the present paper, as 

 regards discrimination against noise by frequency modulation, may 

 be briefly summarized as follows: 



* See Bibliography, No. 1. 

 t See Bibliography, No. 12. 



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