In frequency modulation, the frequency of a rapidly varying signal is modulated by a slowly varying signal. The mathematical description of the modulation of the frequency of a sinusoidal carrier by another sinusoid is given in the formula below where wc is carrier frequency, wm is the modulation frequency, and m is the modulation index. A plot of the resulting signal in the time domain (amplitude versus time) is shown in the interactive graph labeled Time Domain.
An expansion of the formula shows that the resulting signal consists of a large number of frequency components, or sidebands. This is in contrast to the case of amplitude modulation where only two sidebands are created. The sidebands are spaced apart by the modulation frequency, wm, and centered about the carrier frequency, wc. The figure labeled Frequency Domain shows the carrier and sideband components as a plot of amplitude versus frequency.
Only the most significant components are shown. An infinite number of higher order components have negligible amplitude. In fact, the amplitude of each component is given by a Bessel function of the appropriate component order. In mathematical notation the amplitude of the nth sideband is Jn(m), where m is the modulation index.
These graphs are interactive. The parameters of the mathematical model can be adjusted by dragging the sliders with your mouse. You may also click and drag the graphical objects inside the Time and Frequency Domain graphs. For example, the figure above shows how the carrier frequency can be adjusted by dragging the center arrow in the Frequency Domain graph. A complete mathematical definition and analysis of Frequency Modulation is available in the application note listed below.
View FM Interactive Demo
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