telecommunications Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...

, the Carson's bandwidth rule defines the approximate bandwidth requirements of

communications system A communications system is a collection of individual telecommunications networks systems, relay stations, tributary stations, and terminal equipment usually capable of interconnection and interoperation to form an integrated whole. Commu ...

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. Carson's bandwidth rule is expressed by the relation: :

CBR = 2 (\Delta f + f_m)

:where: ::

CBR

is the bandwidth requirement; ::

\Delta f

is the peak

frequency deviation Frequency deviation (f_) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with fre ...

; ::

f_m

is the highest frequency in the modulating signal. For example, a typical VHF/UHF two-way radio signal using FM mode, with 5 kHz peak deviation, and a maximum audio frequency of 3 kHz, would require an approximate bandwidth of = . Standard broadcast stereo FM, with a peak deviation of 75 kHz, has a highest modulating frequency (which combines and ) of 53 kHz (assuming no RDS or other subcarriers). Most of the energy therefore falls within an approximate bandwidth of = . (Geographically close FM broadcast transmitters are almost always assigned nominal center frequencies at least 400 kHz apart). Carson's bandwidth rule is often applied to

transmitter In electronics and telecommunications, a radio transmitter or just transmitter (often abbreviated as XMTR or TX in technical documents) is an electronic device which produces radio waves with an antenna (radio), antenna with the purpose of sig ...

s, antennas, optical sources, receivers,

photodetector Photodetectors, also called photosensors, are devices that detect light or other forms of electromagnetic radiation and convert it into an electrical signal. They are essential in a wide range of applications, from digital imaging and optical ...

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

10\log\left(\frac\right) \approx 17\;\mathrm

less than the carrier inside, therefore Carson's Rule is of little use in spectrum planning.

References

* *''Leon W. Couch II'', "''Digital and Analog Communication Systems, 6th Edition''", ''Prentice-Hall, Inc., 2001''. Telecommunication theory Rules of thumb de:Carson-Formel {{radio-stub