Intelecommunications, theCarson's bandwidth rule defines the approximatebandwidth requirements ofcommunications system components for acarrier signal that isfrequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency. Carson's rule does not apply well when the modulating signal contains discontinuities, such as a square wave. Carson's rule originates fromJohn Renshaw Carson's 1922 paper.^[1]

Carson's bandwidth rule is expressed by the relation:

${\displaystyle CBR=2(\mathrm{\Delta }f+f_m)}$

where:

${\displaystyle CBR}$ is the bandwidth requirement;

${\displaystyle \mathrm{\Delta }f}$ is the peakfrequency deviation;

${\displaystyle f_m}$ is the highest frequency in the modulating signal.

For example, a typical VHF/UHF two-way radio signal using FM mode,^[2] with 5kHz peak deviation, and a maximum audio frequency of 3 kHz, would require an approximate bandwidth of2 × (5 kHz + 3 kHz)=16 kHz.

Standard broadcaststereo FM, with a peak deviation of 75 kHz, has a highest modulating frequency (which combinesL + R andL − R) of 53 kHz (assuming noRDS or other subcarriers). Most of the energy therefore falls within an approximate bandwidth of2 × (75 + 53)=256 kHz. (Geographically close FM broadcast transmitters are almost always assigned nominal center frequencies at least 400 kHz apart).

Carson's bandwidth rule is often applied totransmitters,antennas, optical sources,receivers,photodetectors, and other communications system components.

Any frequency modulated signal will have aninfinite number of sidebands and hence an infinite bandwidth but, in practice, all significant sideband energy (98% or more) is concentrated within the bandwidth defined by Carson's rule. It is a useful approximation, but setting the arbitrary definition of occupied bandwidth at 98% of the power still means that the power outside the band is about${\displaystyle 10\log \left(\frac{0.98}{0.02}\right)\approx 17\mathrm{d}\mathrm{B}}$ less than the carrier inside, therefore Carson's Rule is of little use inspectrum planning.^{[citation needed]}

•  This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22.
• Leon W. Couch II, "Digital and Analog Communication Systems, 6th Edition",Prentice-Hall, Inc., 2001.ISBN 0-13-081223-4

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