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KEY Radyo-TV Yayıncılık ve Teknik Bilgi Merkezi

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, b, is used to describe the ratio of maximum frequency deviation of the carrier to the maximum frequency deviation of the modulating signal.

Depending on the modulation index chosen, the carrier and certain sideband frequencies may actually be suppressed. Zero crossings of the Bessel functions, J_n(b), occur where the corresponding sideband, n, disappears for a given modulation index, b. 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 x_c(t) = X_c·cos (w_ct),
and the modulating signal be
x_m(t) = b·sin (w_mt)

Then x(t) = X_c·cos [w_ct + b·sin (w_mt)]

Modulation Index

b =

Dw
w_m

maximum carrier frequency deviation
modulation frequency

Narrowband FM (NBFM)

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

Narrowband Approximation: b = Dw/w_m < 0.2 (could be as high as 0.5, though)

BW ~ 2w_m

Wideband FM (WBFM)

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

BW ~ 2Dw

Carson's Rule

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

BW ~ 2 (Dw + w_m) = 2*w_m (1 + b)

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 (b) = 1