6.4.4 Bandwidth
As can be seen from Equation (6.33), the frequency spectrum of an FM signal is theoretically infinite, since modulation produces sidebands extending indefinitely on either side of the carrier frequency. In practice, however, the amplitudes of sidebands decrease rapidly with increasing order, and components that are sufficiently far from the carrier contribute negligibly to the received signal. Thus, the band-limiting of practical FM systems does not cause significant distortion.
A sideband is considered significant if its amplitude is greater than 1% of the amplitude of the unmodulated carrier. On this assumption, the bandwidth required for an FM wave is given by:
In terms of the deviation ratio, D, the expression becomes:
This empirical relationship is known as Carson’s rule. It accounts for nearly all (~98%) of the total transmitted power and provides a practical measure of FM bandwidth for most engineering purposes. For larger deviation ratios, additional sidebands may be significant; a conservative rule-of-thumb is:
Although FM provides far superior noise immunity and signal-to-noise performance compared with AM, the trade-off is that FM requires considerably more spectrum. For wideband FM, the occupied bandwidth is typically an order of magnitude greater than that of an equivalent AM signal, with ratios of approximately 7–15 being common in practice.
By way of example, in North America, the maximum frequency deviation, Δfmax, for commercial FM broadcast is 75 kHz and a maximum modulating frequency, fm(max), of 15 kHz. Since D is then 75/15 = 5 > 2, using Equation 6.37) the bandwidth required is 184 kHz, which conforms to the standard FM broadcast channel allocation of 200 kHz (the remaining bandwidth being guard space). Note that commercial AM broadcast with an fm(max) of 15 kHz would require 30 kHz of bandwidth, such that the FM transmission requires 6 times more bandwidth.
In military combat net radio, the difference is even more marked. With a maximum voice frequency of 3.1 kHz, the SSB AM HF radio has 3 kHz channel spacing while the FM VHF radio for the same voice channel has 25 kHz spacing—requiring over 8 times more bandwidth.
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