 # Frequency Modulation Frequency modulation uses the instantaneous frequency of a modulating signal (voice, music, data, etc.) to directly vary the frequency of a carrier signal. Modulation index, β, is used to describe the ratio of maximum frequency deviation of the carrier to the maximum frequency deviation of the modulating signal. The concept was pioneered by Edwin H. Armstrong in the late 1920s and patented in the early 1930s.

Depending on the modulation index chosen, the carrier and certain sideband frequencies may actually be suppressed. Zero crossings of the Bessel functions, Jn(β), occur where the corresponding sideband, n, disappears for a given modulation index, β. The composite spectrum for a single tone consists of lines at the carrier and upper and lower sidebands (of opposite phase), with amplitudes determined by the Bessel function values at those frequencies.

FM General Equation

 Let the carrier be xc(t) = Xc·cos (Ωct), and the modulating signal be xm(t) = β·sin (Ωmt) Then x(t) = Xc·cos [Ωct + β·sin (Ωmt)]

Modulation Index Narrowband FM (NBFM)

Narrowband FM is defined as the condition where β is small enough to make all terms after the first two in the series expansion of the FM equation negligible.

Narrowband Approximation: β = Δω/Ωm < 0.2 (could be as high as 0.5, though)

BW ~ 2ωm

Wideband FM (WBFM)

Wideband FM is defined as when a significant number of sidebands have significant amplitudes.

BW ~ 2Δω

Carson's Rule

J.R. Carson showed in the 1920's that a good approximation that for both very small and very large β,

BW ~ 2 (Δω + Ωm)) = 2*Ωm (1 + β)

In the following examples, the carrier frequency is eleven time the modulation frequency. Red (dashed) lines represent the modulation envelope. Blue (solid) lines represent the modulated carrier.

Modulation Index (β) = 1

Here, the maximum frequency (fmax) causes a maximum deviation of 1*fmax in the carrier. From the modulation index formula: Modulation Index (β) = 5

Here, the maximum frequency (fmax) causes a maximum deviation of 5*fmax in the carrier. From the modulation index formula: Modulation Index (β) = 25

Here, the maximum frequency (fmax) causes a maximum deviation of 25*fmax in the carrier. From the modulation index formula: Note: FM waveforms created with MathCAD 4.0 software.    About RF Cafe Copyright: 1996 - 2024Webmaster:    Kirt Blattenberger,    BSEE - KB3UON RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while typing up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived... All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged. My Hobby Website:  AirplanesAndRockets.com Please Support RF Cafe by purchasing my  ridiculously low−priced products, all of which I created. These Are Available for Free