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.)

In analog applications, the carrier frequency is varied in direct proportion to changes in the amplitude of an input signal. Digital data can be represented by shifting the carrier frequency among a set of discrete values, a technique known as frequency-shift keying.

FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (see FM broadcasting). A narrowband form is used for voice communications in commercial and amateur radio settings. This type of FM modulation is generally called wide-FM, or W-FM. In other parts of the spectrum, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.

FM is also used at intermediate frequencies by most analog VCR systems, including VHS, to record the luminance (black and white) portion of the video signal. FM is the only feasible method of recording to and retrieving from magnetic tape without extreme distortion a signal with a very large range of frequency components -- a video signal has components from a few hertz to several megahertz.

FM is also used at audio frequencies to synthesize sound. This technique, known as FM synthesis, was popularized by early digital synthesizers and became a standard feature for several generations of personal computer sound cards.

Applications in radio

Edwin Armstrong presented his paper: "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation"  (https://michael.industrynumbers.com/fm.pdf) , which first described FM radio, before the New York section of the Institute of Radio Engineers on November 6, 1935.

Frequency modulation requires a wider bandwidth than amplitude modulation by an equivalent modulating signal, but this also makes the signal more robust against interference. Frequency modulation is also more robust against simple signal amplitude fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio transmission: hence the term "FM radio" (although for many years the BBC insisted on calling it "VHF radio", which is quite logical, since commercial FM broadcasting uses a well-known part of the VHF band; in certain countries, expressions referencing the more familiar wavelength notion are still used in place of the somewhat mysterious modulation technique name).

FM receivers inherently exhibit a phenomenon called capture, where the tuner is able to clearly receive the stronger of two stations being broadcast on the same frequency. Problematically, however, frequency drift or lack of selectivity may cause one station or signal to be suddenly overtaken by another on an adjacent channel. Frequency drift typically constituted a problem on very old or inexpensive receivers, while inadequate selectivity may plague any tuner.

An FM signal can also be used to carry a stereo signal: see FM stereo. However, this is done by using multiplexing and demultiplexing before and after the FM process, and is not part of FM proper. The rest of this article ignores the stereo multiplexing and demultiplexing process used in "stereo FM", and concentrates on the FM modulation and demodulation process, which is identical in stereo and mono processes.

Theory

If the signal to be sent is

<math>

x_m(t) <math>

and the sinusoidal carrier is

<math>

x_c(t) = A \cos (2 \pi f_c t) <math>

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

<math>

x_c(t) = A \cos (2 \pi f(t)) = A \cos (2 \pi [f_c + f_\Delta x(t)]) <math>

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

Although it may seem that this limits the frequencies in use to f_c ± f_Δ, 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.

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.

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

<math>2(\Delta f+f_m)<math>

where Δf is the peak instantaneous deviation of the carrier from the centre frequency and f_m is the highest modulating frequency.

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.

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.

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.

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

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

Modulation Index

As with other modulation indices, in AM this quantity indicates by how much the modulated variable varies around its unmodulated level. For FM, it relates to the variations in the frequency of the carrier signal:

<math>h = \frac{\Delta{}f}{f_m}<math>

With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases, but the spacing between spectra stays the same.

If the frequency deviation is held constant and the modulation index increased, the bandwidth stays roughly the same, but the spacing between spectra decreases.

See also

• Frequency modulation synthesis (FM as an audio synthesis method)
• Modulation index
• Modulation, for a list of other modulation techniques
• History of radio

External links

• http://www.rfcafe.com/references/electrical/frequency_modulation.htm
• http://www.fas.org/man/dod-101/navy/docs/es310/FM.htmde:Frequenzmodulation

es:Modulación de frecuencia fr:Modulation de fréquence nl:Frequentiemodulatie pt:modulação em frequência ja:周波数変調 no:Frekvensmodulasjon pl:FM fi:FM