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The differential equation of a frequency modulated transmitter is considered and the expression of the current as a function of time is derived. Frequency analysis of this function is made for two specific cases, (A) sinusoidal frequency modulation (telephony) and (B), right-angle frequency modulation (telegraphy with "marking" and "spacing" wave). The distribution and amplitudes of the frequencies present are seen to depend upon the value of an absolute parameter, the "frequency modulation index," equal to the ratio of the maximum frequency deviation to the imposed modulating frequency. The overall width of the band occupied is found to be approximately double the highest of these two frequencies. In the case of high-speed frequency modulated telegraphy, however, side frequencies of noticeable amplitude may occur outside this band. Charts are included showing the derived frequency spectra.
Balth. van der Pol (Tue,) studied this question.