Frequency modulation

Frequency modulation (FM) is a form of modulation which represents information as variations in the instantaneous frequency of a carrier wave. (Contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant.)

Theory

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If the signal to be transmitted is

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:x_m(t),

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which is restricted in amplitude to be

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: left| x_m(t) ight| le 1 ,

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and the sinusoidal carrier is

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:x_c(t) = A cos (2 pi f_c t),

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where fc is the carrier's base frequency in hertz and A is an arbitrary amplitude, the carrier will be modulated by the signal as in

Related Topics:
Carrier - Hertz

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:x_c(t) = A cos left( 2 pi int_{0}^{t} f( au), d au ight) = A cos left( 2 pi int_{0}^{t} left , d au ight)

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:where, f(t) = f_c + f_Delta x_m(t)

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In this equation, f(t) is the instantaneous frequency of the oscillator and fΔ is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.

Related Topics:
Instantaneous frequency - Frequency deviation

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Although it may seem that this limits the frequencies in use to fc ± fΔ, this neglects the distinction between instantaneous frequency and spectral frequency. The frequency spectrum of an actual FM signal has components extending out to infinite frequency, although they become negligibly small beyond a point.

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For a simplified case, the harmonic distribution of a sine wave signal modulated by another sine wave signal can be represented with Bessel functions - this provides a basis for a mathematical understanding of frequency modulation in the frequency domain.

Related Topics:
Harmonic - Sine wave - Bessel function

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A rule of thumb, Carson's rule states that nearly all the power of a frequency modulated signal lies within a bandwidth of

Related Topics:
Rule of thumb - Carson's rule - Bandwidth

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:2(f_Delta +f_m),

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where fΔ is the peak deviation of the instantaneous frequency f(t) from the center carrier frequency fc (assuming xm(t) is in the range ±1) and fm is the highest modulating frequency of xm(t).

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Note that frequency modulation can be regarded as a special case of phase modulation where the carrier phase modulation is the time integral of the FM modulating signal.

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Frequency-shift keying refers to the simple case of frequency modulation by a simple signal with only discrete states, such as in Morse code or radio-teletype applications.

Related Topics:
Frequency-shift keying - Morse code - Radio-teletype

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Manchester encoding may be regarded as a simple version of frequency shift keying, where the high and low frequencies are respectively double and the same as the bit rate, and the bit transitions are synchronous with carrier transitions.

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When used in supervisory signaling in telephony, the term frequency-change signaling has been used to describe frequency modulation.

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The phrase frequency-modulated, an adjective, should have a hyphen when used attributively.

Related Topics:
Adjective - Attributively

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