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Certain fundamental characteristics of the theory of frequency modulation for arbitrarily large degrees of modulation and unrestricted modulation frequencies are developed from the differential equation for a dissipationless circuit with fixed inductance and variable capacitance. The several modes of modulating the frequency are discussed and classified; it is shown that they give the same results only when the amount of modulation is very small. The case of "inverse capacity modulation" is then treated in detail. This treatment discloses the possibility of unstable oscillations occurring with certain values of the parameters; the nature and physical significance of these unstable oscillations are determined, and it is explained why they are not ordinarily observable in radio-frequency modulation or in the warble tone generator. The frequency spectrum of the stable oscillations is found, and a means of calculating the amplitude given. For certain adjustments of the circuit the oscillations may be represented by a true Fourier series, while in general this is not the case. Frequency modulation in radiotelephony, the warble tone, and the special case where the natural period of the unmodulated circuit and the frequency of modulation are of comparable magnitude, represent successively more complicated cases of the same general phenomena; the latter is of special interest. The nature of the phenomena accompanying other than a sinusoidal inverse capacity variation is mentioned.
W.L. Barrow (Tue,) studied this question.