Variation of Bandwidth with Modulation Index in Frequency Modulation

Equations are derived for the carrier and side-frequency amplitudes which are obtained when a carrier wave is frequency-modulated by a complex audio signal. The bandwidth occupied by such a frequency-modulated wave is defined as the distance between the two frequencies beyond which none of the side frequencies is greater than 1 per cent of the carrier amplitude obtained when the modulation is removed. Curves are given to show the amount this bandwidth exceeds the extremes of deviation for a range of modulation indexes from 0.1 to 10,000, for sinusoidal, square, rectangular, and triangular modulation. For more precise definitions of bandwidth, curves are also given for side-frequency amplitude limits of 0.1 per cent and 0.01 per cent of the carrier-wave amplitude. For complex modulatlon the total bandwidth can be estimated by computing the bandwidth that would be required by each audio-frequency component, if it were on separately, and adding the results.