Frequency modulation

Frequency Modulation

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Frequency modulation

See also: Amplitude modulation
Amplitude modulation

Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave....

In telecommunications, frequency modulation (FM) conveys information

Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
over a carrier wave

Carrier wave

In telecommunications, a carrier wave, or carrier is a waveform that is Modulation with an signal for the purpose of conveying information....
by varying its frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
(contrast this with amplitude modulation

Amplitude modulation

Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave....
, in which the amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
of the carrier is varied while its frequency remains constant). In analog

Analog signal

An analog or analogue signal is any continuous function Signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e analogous to another time varying signal....
applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. Digital

Digital

A digital system uses discrete values, usually but not always symbolized numerically to represent information for input, processing, transmission, storage, etc....
data

DATA

Debt, AIDS, Trade in Africa is a multinational Non-governmental organization founded in January 2002 in London by U2's Bono along with Robert Sargent Shriver III and activists from the Jubilee 2000 Drop the Debt campaign....
can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying

Frequency-shift keying

Frequency-shift keying is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave....
.

ose the baseband data signal (the message) to be transmitted is

and is restricted in amplitude to be

and the sinusoidal carrier is

where f_c is the carrier's base frequency and A_c is the carrier's amplitude. The modulator combines the carrier with the baseband data signal to get the transmitted signal,

In this equation, is the instantaneous frequency
Instantaneous phase

In signal processing, the instantaneous phase of a complex-valued function is the real-valued function:' And for a real-valued signal it is determined from the signal's analytic signal, :'...
of the oscillator and is the frequency deviation
Frequency deviation

Frequency deviation is used in Frequency modulation to describe the maximum instantaneous difference between an FM modulated frequency and the Center frequency....
, 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_?, this neglects the distinction between instantaneous frequency and spectral frequency.

Discussion

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Theory

Suppose the baseband data signal (the message) to be transmitted is

and is restricted in amplitude to be

and the sinusoidal carrier is

where f_c is the carrier's base frequency and A_c is the carrier's amplitude. The modulator combines the carrier with the baseband data signal to get the transmitted signal,

In this equation, is the instantaneous frequency
Instantaneous phase

In signal processing, the instantaneous phase of a complex-valued function is the real-valued function:' And for a real-valued signal it is determined from the signal's analytic signal, :'...
of the oscillator and is the frequency deviation
Frequency deviation

Frequency deviation is used in Frequency modulation to describe the maximum instantaneous difference between an FM modulated frequency and the Center frequency....
, 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_?, this neglects the distinction between instantaneous frequency and spectral frequency. The frequency spectrum

Frequency spectrum

Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts ....
of an actual FM signal has components extending out to infinite frequency, although they become negligibly small beyond a point.

The harmonic

Harmonic

In acoustics and telecommunication, a harmonic of a wave is a component frequency of the Signalling that is an integer multiple of the fundamental frequency....
distribution of a sine wave

Sine wave

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....
carrier modulated by a sine wave signal can be represented with Bessel function

Bessel function

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are Canonical#Mathematics solutions y of Bessel's differential equation:...
s - this provides a basis for a mathematical understanding of frequency modulation in the frequency domain.

Modulation index

As with other modulation indices

Modulation index

The modulation index of a modulation scheme describes by how much the modulated variable of the carrier signal varies around its unmodulated level....
, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the frequency of the carrier signal:

where is the highest modulating frequency of x_m(t). If , the modulation is called narrowband FM, and its bandwidth is approximately . If , the modulation is called wideband FM and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve signal-to-noise ratio

Signal-to-noise ratio

Signal-to-noise ratio is an electrical engineering measurement, also used in other fields , defined as the ratio of a signal power to the noise power corrupting the signal....
significantly.

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; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.

Carson's rule

A rule of thumb

Rule of thumb

A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination....
, Carson's rule
Carson bandwidth rule

In telecommunication, John R. Carson's bandwidth rule defines the approximate Bandwidth requirements of communications system components for a carrier wave signal that is frequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency....
states that nearly all (~98%) of the power of a frequency-modulated signal lies within a bandwidth of

where is the peak deviation of the instantaneous frequency from the center carrier frequency (assuming is in the range ).

Noise quieting

The noise power decreases as the signal power increases, therefore the SNR goes up significantly.

Bessel functions

The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. Based on the Bessel functions.

Modulation index	Carrier	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
0.00	1.00
0.25	0.98	0.12
0.5	0.94	0.24	0.03
1.0	0.77	0.44	0.11	0.02
1.5	0.51	0.56	0.23	0.06	0.01
2.0	0.22	0.58	0.35	0.13	0.03
2.41	0	0.52	0.43	0.20	0.06	0.02
2.5	-.05	0.50	0.45	0.22	0.07	0.02	0.01
3.0	-.26	0.34	0.49	0.31	0.13	0.04	0.01
4.0	-.40	-.07	0.36	0.43	0.28	0.13	0.05	0.02
5.0	-.18	-.33	0.05	0.36	0.39	0.26	0.13	0.05	0.02
5.53	0	-.34	-.13	0.25	0.40	0.32	0.19	0.09	0.03	0.01
6.0	0.15	-.28	-.24	0.11	0.36	0.36	0.25	0.13	0.06	0.02
7.0	0.30	0.00	-.30	-.17	0.16	0.35	0.34	0.23	0.13	0.06	0.02
8.0	0.17	0.23	-.11	-.29	-.10	0.19	0.34	0.32	0.22	0.13	0.06	0.03
8.65	0	0.27	0.06	-.24	-.23	0.03	0.26	0.34	0.28	0.18	0.10	0.05	0.02
9.0	-.09	0.25	0.14	-.18	-.27	-.06	0.20	0.33	0.31	0.21	0.12	0.06	0.03	0.01
10.0	-.25	0.04	0.25	0.06	-.22	-.23	-.01	0.22	0.32	0.29	0.21	0.12	0.06	0.03	0.01
12.0	0.05	-.22	-.08	0.20	0.18	-.07	-.24	-.17	0.05	0.23	0.30	0.27	0.20	0.12	0.07	0.03	0.01

Implementation

FM signals can be generated using either direct or indirect frequency modulation.

Direct FM modulation can be achieved by directly feeding the message into the input of a VCO
Voltage-controlled oscillator

A voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while Modulation signals may also be fed into the VCO to cause frequency modulation or phase modulation ; a VCO with digital pulse o...
.
For indirect FM modulation, the message signal is integrated to generate a phase modulated signal
Phase modulation

Phase modulation is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.Unlike its more popular counterpart, frequency modulation , PM is not very widely used....
. This is used to modulate a crystal controlled oscillator
Crystal oscillator

A crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of Piezoelectricity#Materials to create an electrical signal with a very precise frequency....
, and the result is passed through a frequency multiplier
Frequency multiplier

A frequency multiplier is commonly used in a radio receiver or radio transmitter to multiply the base frequency of the oscillator by a predetermined number....
to give an FM signal.

A common method for recovering the information signal is through a Foster-Seeley discriminator

Foster-Seeley discriminator

The Foster-Seeley discriminator is a common type of Frequency modulation Detector , invented in 1936 by Dudley E. Foster and Stuart William Seeley....
.

Applications in broadcasting

FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music

Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
and speech (see FM broadcasting

FM broadcasting

FM broadcasting is a broadcasting technology invented by Edwin Howard Armstrong that uses frequency modulation to provide high-fidelity sound over broadcast radio....
). Normal (analog) TV sound is also broadcast using FM. A narrow band form is used for voice

Human voice

The human voice consists of sound Voice production by a human being using the vocal folds for Speech communication, singing, Laughter, crying, screaming, etc....
communications in commercial and amateur radio

Amateur radio

Amateur radio, often called Etymology of ham radio, is both a hobby and a service in which participants, called "hams," use various types of radio communications equipment to communicate with other radio amateurs for Public services, recreation and self-training....
settings. The type of FM used in broadcast is generally called wide-FM, or W-FM. In two-way radio, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.

Applications in hardware

FM is also used at intermediate frequencies by all analog VCR systems, including VHS

VHS

The Video Home System, better known by its abbreviation VHS, is a recording and playing standard developed by JVC and launched in Europe and Asia in September 1976, and the United States in June 1977....
, to record both the luminance

Luminance (video)

Relative luminance follows the Luminance, but with the values normalized to 1 or 100 for a reference white. Like the photometric definition, it is related to the luminous flux density in a particular direction, which is radiant flux density weighted by the Luminosity_function of the CIE Standard Observer....
(black and white) and the chrominance portions of the video signal. FM is the only feasible method of recording video to and retrieving video from magnetic tape without extreme distortion, as video signals have a very large range of frequency components — from a few hertz

Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
to several megahertz, too wide for equalizer

Equalizer

Equalizer or equaliser may refer to:*An equalization filter*An audio processing tool used for equalization*A blind equalization used in digital communications...
s to work with due to electronic noise below -60 dB

Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
. FM also keeps the tape at saturation level, and therefore acts as a form of noise reduction

Noise reduction

Noise reduction is the process of removing noise from a signal . Noise reduction techniques are conceptually very similar regardless of the signal being processed, however A priori and a posteriori knowledge of the characteristics of an expected signal can mean the implementations of these techniques vary greatly depending on the type of si...
, and a simple limiter

Audio level compression

Dynamic range compression, also called DRC or simply compression, is a process that reduces the dynamic range of an audio signal. Compression is used during sound recording, live sound reinforcement, and broadcasting to control the level of audio....
can mask variations in the playback output, and the FM capture effect removes print-through

Print-through

Print-through is a generally undesirable effect that arises in the use of magnetic tape for storing wiktionary:analogue information, in particular music....
and pre-echo

Pre-echo

Pre-echo is an audio compression artifact where a sound is heard before it occurs . It is most noticeable in impulsive sounds from percussion instruments such as castanets or cymbals....
. A continuous pilot-tone, if added to the signal — as was done on V2000 and many Hi-band formats — can keep mechanical jitter under control and assist timebase correction

Timebase correction

Time base correction is a technique to reduce or eliminate errors caused by mechanical instability present in analog recordings on mechanical media....
. These FM systems are unique in that they have a ratio of carrier to maximum modulation frequency of less than two.(Contrast FM audio broadcasting where the ratio is around 10,000.)

Applications in sound

FM is also used at audio frequencies

Audio frequency

An audio frequency , or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human. While the range of frequencies that any individual can hear is largely related to environmental factors, the generally accepted standard range of audible frequencies is 20 to 20,000 hertz....
to synthesize sound. This technique, known as FM synthesis

Frequency modulation synthesis

In Sound recording and reproduction and music frequency modulation synthesis is a form of sound synthesis where the timbre of a simple waveform is changed by frequency modulation it with a modulating frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone....
, was popularized by early digital synthesizer

Synthesizer

A synthesizer is an electronic instrument capable of producing a variety of sounds by generating and combining signals of different frequency....
s and became a standard feature for several generations of personal computer

Personal computer

A personal computer is any general-purpose computer whose original sales price, size, and capabilities make it useful for individuals, and which is intended to be operated directly by an end user, with no intervening computer operator....
sound card

Sound card

A sound card is a computer expansion card that facilitates the input and output of sound to/from a computer under control of computer programs....
s.

Applications in radio

Main article: FM broadcasting
FM broadcasting

FM broadcasting is a broadcasting technology invented by Edwin Howard Armstrong that uses frequency modulation to provide high-fidelity sound over broadcast radio....

Edwin Armstrong

Edwin Howard Armstrong was an United States electrical engineer and inventor. Armstrong was the inventor of frequency modulation radio. ...
presented his paper: "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation", which first described FM radio, before the New York

New York

The State of New York is a U.S. state in the Mid-Atlantic States and Northeastern United States regions of the United States and is the nation's List of U.S....
section of the Institute of Radio Engineers

Institute of Radio Engineers

The Institute of Radio Engineers was a professional organization which existed from 1912 until 1963, when it merged with the American Institute of Electrical Engineers to form the Institute of Electrical and Electronics Engineers ....
on November 6, 1935. The paper was published in 1936.

As the name implies, wideband FM (W-FM) requires a wider signal bandwidth than amplitude modulation

Amplitude modulation

Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave....
by an equivalent modulating signal, but this also makes the signal more robust against noise

Noise (radio)

Radio noise in radio reception is the superposition of white noise and other disturbing influences on the signal, caused either by thermal noise and other electronic noise from receiver input circuits or by interference from radiated electromagnetic noise picked up by the receiver's antenna ....
and interference

Interference

In physics, interference is the addition of two or more waves that result in a new wave pattern.Interference usually refers to the interaction of waves which are correlated or Coherence with each other, either because they come from the same source or because they have the same or nearly the same frequency....
. Frequency modulation is also more robust against simple signal amplitude fading phenomena. As a result, FM was chosen as the modulation standard

Standardization

Standardization is the process of developing and agreeing upon Standard . A standard is a document that establishes uniform engineering or technical specifications, criteria, methods, processes, or practices....
for high frequency, high fidelity

High fidelity

High fidelity or hi-fi reproduction is a term used by home stereo listeners and home audio enthusiasts to refer to high-quality sound reproduction or video that are very faithful to the original performance....
radio

Radio

Radio is the transmission of signals, by modulation of electromagnetic radiation with frequency below those of visible light.Electromagnetic radiation radio propagation by means of oscillating electromagnetic fields that pass through the air and the vacuum of space....
transmission: hence the term "FM radio" (although for many years the BBC called it "VHF radio", because 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 more abstract modulation technique name).

FM receivers

Receiver (radio)

This article is about a radio receiver, for other uses see Radio .A radio receiver is an electronics circuit that receives its input from an antenna , uses electronic filters to separate a wanted radio signal from all other signals picked up by this antenna, electronic amplifier it to a level suitable for further processing, and finally...
employ a special detector

Detector (radio)

A detector is a device that recovers information of interest contained in a modulated wave. The term dates from the early days of radio when all transmissions were in Morse Code, and it was only necessary to detect the presence of a radio wave using a device such as a coherer without necessarily making it audible....
for FM signals and exhibit a phenomenon

Phenomenon

A phenomenon is any observation occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In physics, a phenomenon may be a feature of matter, energy, or spacetime....
called capture effect
Capture effect

In telecommunication, the capture effect, or FM capture effect, is a phenomenon associated with FM reception in which only the stronger of two signals at, or near, the same frequency will be demodulation....
, where the tuner

Tuner (radio)

A tuner is an adjustable device which passes one radio frequency, or band of frequencies, and excludes others, by using electrical resonance. A tuner performs the process of selecting the desired signal but its output is not directly usable and must be sent to another device....
is able to clearly receive the stronger of two stations being broadcast on the same frequency. Problematically however, frequency drift

Frequency drift

In electrical engineering, and particularly in telecommunications, frequency drift is an unintended and generally arbitrary offset of an oscillator from its Real versus nominal value frequency....
or lack of selectivity

Electronic selectivity

Selectivity is a measure of the performance of a radio receiver to respond only to the tuner transmission and reject other Signalling s nearby, such as another Broadcasting on an adjacent channel....
may cause one station or signal to be suddenly overtaken by another on an adjacent channel

Adjacent channel

In Broadcastinging an adjacent channel is an Amplitude modulation, FM, or television channel that is next to another channel . First-adjacent is immediately next to another channel, second-adjacent is two channels away, and so forth....
. Frequency drift

Drift (telecommunication)

In telecommunication, a drift is a comparatively long-term change in an attribute, value, or operational parameter of a system or equipment.The drift should be characterized, such as "diurnal frequency drift" and "output level 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

Stereophonic sound

Stereophonic sound, commonly called stereo, is the reproduction of sound, using two or more independent Sound recording and reproduction channels, through a symmetrical configuration of loudspeakers, in such a way as to create a pleasant and natural impression of sound heard from various directions, as in natural hearing....
signal: see FM stereo. However, this is done by using multiplexing

Multiplexing

In telecommunications and computer networks, multiplexing is a process where multiple analog message signals or digital data streams are combined into one signal over a shared medium....
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.

A high-efficiency radio-frequency switching amplifier

Switching amplifier

A switching amplifier or class-D amplifier is an electronic amplifier which, in contrast to the active resistance used in linear mode Class AB amplifiers, uses Switched-mode power supply of transistor to regulate power delivery....
can be used to transmit FM signals (and other constant-amplitude signals). For a given signal strength (measured at the receiver antenna), switching amplifiers use less battery power

Low-power

In electronics, the term low-power may mean:* Low-power broadcasting, that the power of the broadcast is less, i.e. the radio waves are not intended to travel as far as from typical transmitters....
and typically cost less than a linear amplifier

Linear amplifier

A linear amplifier is an electronics circuit whose output is proportional to its input, but capable of delivering more power into a Electrical load....
. This gives FM another advantage over other modulation schemes that require linear amplifiers, such as AM and QAM.

Miscellaneous

Frequency modulation can be regarded as a special case of phase modulation

Phase modulation

Phase modulation is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.Unlike its more popular counterpart, frequency modulation , PM is not very widely used....
where the carrier phase modulation is the time integral of the FM modulating signal.

Frequency-shift keying
Frequency-shift keying

Frequency-shift keying is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave....
is the frequency modulation using only a discrete number of frequencies. Morse code

Morse code

Morse code is a type of character encoding that transmits telegraphic information using rhythm. Morse code uses a standardized sequence of short and long elements to represent the alphanumeric, punctuation and special characters of a given message....
transmission has been implemented this way, as were most early telephone-line modem

Modem

Modem is a peripheral device that modulation an analog carrier wave Signal to encode digital information, and also demodulation such a carrier signal to decode the transmitted information....
s and radioteletype

Radioteletype

Radioteletype is a telecommunications system consisting of two or more teleprinters using radio as the transmission medium.The term radioteletype is used to describe:...
applications.

By the phenomenon of slope detection whereby FM is converted to AM in a frequency-selective circuit tuned slightly away from the nominal signal frequency, AM receivers may detect some FM transmissions, though this does not provide an efficient method of detection

Detector (radio)

Frequency modulation

Theory

Modulation index

Carson's rule

Noise quieting

Bessel functions

Implementation

Applications in broadcasting

Applications in hardware

Applications in sound

Applications in radio

Miscellaneous

See also

External links