 # CARSON’S RULE Calculating FM Modulation Bandwidth

## CARSON’S RULE Calculating FM Modulation Bandwidth

CALCULATING FM MODULATION BANDWIDTH

A formula is used for calculating FM modulation bandwidth or occupancy for the FM signal. If you are designing an FM system on microwave or satellite, you will need to take care that your signal does not cross-talk into other signals on the system.

CALCULATING FM MODULATION BANDWIDTH
Frequency Modulation creates modulation sidebands that theoretically extend to infinite bandwidth. These sidebands consist of Bessel Functions of any order. From a practical standpoint the band occupancy of an FM modulated carrier only needs to count the Bessel Function sidebands of significant amplitude. The formula that calculates this bandwidth is called CARSON’S RULE.

CARSON’S RULE requires knowing the modulating frequency and the maximum frequency deviation of the transmitted carrier. As an example, a monaural RF band modulator will have a peak deviation of 75KHz and the highest audio frequency is 15KHz. To calculate the CARSON’S RULE bandwidth occupancy of this signal, add the highest audio frequency to the peak deviation (15KHz + 75KHz = 90KHz), then multiply by two to include both the upper and lower sideband (90KHz X 2 = 180KHz). The CARSON’S BANDWIDTH for this signal is 180KHz. Since there are many Bessel Function sidebands beyond 180KHz, FM channels must be spaced considerably farther apart than 180KHz. The FCC has determined that a spacing of 400KHz provides sufficient “Guard Band” to effectively prevent inter-channel cross-talk, but that 180KHz is sufficient bandwidth to receive the original modulation with less than 1% distortion. The distortion is due to a failure to receive all of the modulation energy.

Similar CARSON RULE calculations can be used for other modulation bandwidths and peak deviations, with similar considerations for Guard Bands between channels.

Amplitude Modulation bandwidth can be considered exactly two times the highest frequency of modulation, while Frequency Modulation bandwidth is described by Bessel Functions that extend much higher than those of Amplitude Modulation. In fact the “FM Advantage” in signal-to-noise ratio stems exactly from spreading the modulation over a greater bandwidth than Amplitude Modulation.

CARSON’S RULE
BANDWIDTH = 2 X (PEAK DEVIATION + HIGHEST MODULATING FREQUENCY)