Editing Carson bandwidth rule

{{Short description|Rule in telecommunications}}

In [[telecommunications]], the '''Carson's bandwidth rule''' defines the approximate [[Bandwidth (signal processing)|bandwidth]] requirements of [[communications system]] components for a [[carrier signal]] that is [[frequency 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 from [[John Renshaw Carson]]'s 1922 paper.<ref>J.R. Carson, "Notes on the theory of modulation", [[Proc. IRE]], vol. 10, no. 1 (Feb. 1922), pp. 57-64.</ref>

Carson's bandwidth rule is expressed by the relation:
:<math>CBR = 2 (\Delta f + f_m)</math>
:where:
::<math>CBR</math> is the bandwidth requirement;
::<math>\Delta f</math> is the peak [[frequency deviation]];
::<math>f_m</math> is the highest frequency in the modulating signal.

For example, a typical VHF/UHF two-way radio signal using FM mode,<ref>{{cite web|url=http://hamradioschool.com/g8b06-carsons-rule/|title=(G8B06) Carson's Rule - Ham Radio School.com|date=25 April 2014}}</ref> with 5 [[kHz]] peak deviation, and a maximum audio frequency of 3&nbsp;kHz, would require an approximate bandwidth of {{nowrap|2 × (5 kHz + 3 kHz) }}= {{nowrap|16 kHz}}.

Standard broadcast [[stereo FM]], with a peak deviation of 75&nbsp;kHz, has a highest modulating frequency (which combines {{nowrap|L + R}} and {{nowrap|L − R}}) of 53&nbsp;kHz (assuming no [[Radio Data System|RDS]] or other subcarriers). Most of the energy therefore falls within an approximate bandwidth of {{nowrap|2 × (75 + 53) }}= {{nowrap|256 kHz}}. (Geographically close FM broadcast transmitters are almost always assigned nominal center frequencies at least 400&nbsp;kHz apart).

Carson's bandwidth rule is often applied to [[transmitter]]s, [[antenna (radio)|antenna]]s, optical sources, [[receiver (radio)|receiver]]s, [[photodetector]]s, and other communications system components.

Any frequency modulated signal will have an ''infinite'' 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 <math>10\log\left(\frac{0.98}{0.02}\right) \approx 17\;\mathrm{dB}</math> less than the carrier inside, therefore Carson's Rule is of little use in [[spectrum planning]].{{Cn|date=May 2016|reason=Why? It seems to be exactly what the FCC uses in land mobile. Cite.}}

==References==
<references/>
*{{FS1037C}}
*''Leon W. Couch II'', "''Digital and Analog Communication Systems, 6th Edition''", ''Prentice-Hall, Inc., 2001''. {{ISBN|0-13-081223-4}}

{{DEFAULTSORT:Carson Bandwidth Rule}}
[[Category:Telecommunication theory]]
[[Category:Rules of thumb]]

[[de:Carson-Formel]]

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