# Carson bandwidth rule

In telecommunication, Carson's bandwidth rule defines the approximate 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.[1]

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, and $f_m$ is the highest frequency in the modulating signal.

For example, an FM signal with 5 kHz peak deviation, and a maximum audio frequency of 3 kHz, would require an approximate bandwidth 2(5+3) = 16 kHz.

For example, standard broadcast FM has a peak deviation of 75 kHz above and below the carrier. With stereo FM, the highest modulating frequency (which combines L+R and L-R) is 53 kHz. So most of the energy of standard stereo FM falls in an approximate bandwidth of 2(75+53) = 256 kHz. (Geographically close FM broadcast transmitters are almost always assigned nominal center frequencies at least 500 kHz apart).

Carson's bandwidth rule is often applied to transmitters, antennas, optical sources, receivers, photodetectors, 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 only about $10\log\left(\frac{0.02}{0.98}\right)$ = 17 dB less than the carrier inside, therefore Carson's Rule is of little use in spectrum planning.

## References

1. ^ J.R. Carson, "Notes on the theory of modulation", Proc. IRE, vol. 10, no. 1 (Feb. 1922), pp. 57-64.