Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency-Modulation

R E Q U E N C Y modulation was a much talked of subject twenty or more years ago. Most of the interest in it then centered around the idea t h a t it might afford a means of compressing a signal into a narrower frequency band than is required for amplitude modulation. 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 transmission at very short wave lengths where there is little restriction on the width of the frequency band t h a t 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. T h a t 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 nonmathematical in character, and it is therefore believed that a mathematical study of this phase of the problem will not be unwelcome. This the present paper aims to supply by developing the basic mathematics of frequency modulation and applying it to the question of noise discrimination with or without amplitude limitation.