Frequency modulation (FM) is the encoding of
information in a
carrier wave
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has ...
by varying the
instantaneous frequency
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
of the wave. The technology is used in
telecommunications,
radio broadcasting
Radio broadcasting is transmission of audio (sound), sometimes with related metadata, by radio waves to radio receivers belonging to a public audience. In terrestrial radio broadcasting the radio waves are broadcast by a land-based radio ...
,
signal processing, and
computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
.
In
analog
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use analog ...
frequency modulation, such as radio broadcasting, of an audio signal representing voice or music, the instantaneous
frequency deviation Frequency deviation (f_) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with fre ...
, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.
Digital data can be encoded and transmitted with a type of frequency modulation known as
frequency-shift keying (FSK), in which the instantaneous frequency of the carrier is shifted among a set of frequencies. The frequencies may represent digits, such as '0' and '1'. FSK is widely used in computer
modems, such as
fax modems, telephone
caller ID
Caller identification (Caller ID) is a telephone service, available in analog and digital telephone systems, including voice over IP (VoIP), that transmits a caller's telephone number to the called party's telephone equipment when the call i ...
systems, garage door openers, and other low-frequency transmissions.
Radioteletype
Radioteletype (RTTY) is a telecommunications system consisting originally of two or more electromechanical teleprinters in different locations connected by radio rather than a wired link. Radioteletype evolved from earlier landline teleprinter ...
also uses FSK.
Frequency modulation is widely used for
FM radio broadcasting
Broadcasting is the distribution of audio or video content to a dispersed audience via any electronic mass communications medium, but typically one using the electromagnetic spectrum ( radio waves), in a one-to-many model. Broadcasting beg ...
. It is also used in
telemetry,
radar, seismic prospecting, and monitoring
newborn
An infant or baby is the very young offspring of human beings. ''Infant'' (from the Latin word ''infans'', meaning 'unable to speak' or 'speechless') is a formal or specialised synonym for the common term ''baby''. The terms may also be used to ...
s for seizures via
EEG
Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex ...
,
two-way radio
A two-way radio is a radio that can both transmit and receive radio waves (a transceiver), unlike a broadcast receiver which only receives content. It is an audio (sound) transceiver, a transmitter and receiver in one unit, used for bidirection ...
systems,
sound synthesis
A synthesizer (also spelled synthesiser) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis and f ...
, magnetic tape-recording systems and some video-transmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger
signal-to-noise ratio and therefore rejects
radio frequency interference
Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
better than an equal power
amplitude modulation (AM) signal. For this reason, most music is broadcast over
FM radio.
However, under severe enough
multipath conditions it performs much more poorly than AM, with distinct high frequency noise artifacts that are audible with lower volumes and less complex tones. With high enough volume and carrier deviation audio distortion starts to occur that otherwise wouldn't be present without multipath or with an AM signal.
Frequency modulation and
phase modulation
Phase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of ...
are the two complementary principal methods of
angle modulation
Angle modulation is a class of carrier modulation that is used in telecommunications transmission systems. The class comprises frequency modulation (FM) and phase modulation (PM), and is based on altering the frequency or the phase, respectively, ...
; phase modulation is often used as an intermediate step to achieve frequency modulation. These methods contrast with
amplitude modulation, in which the
amplitude of the carrier wave varies, while the frequency and phase remain constant.
Theory
If the information to be transmitted (i.e., the
baseband signal
In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable into a ...
) is
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:
:
where
,
being the sensitivity of the frequency modulator and
being the amplitude of the modulating signal or baseband signal.
In this equation,
is the ''
instantaneous frequency
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
'' of the oscillator and
is the ''
frequency deviation Frequency deviation (f_) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with fre ...
'', which represents the maximum shift away from ''f
c'' in one direction, assuming ''x''
''m''(''t'') is limited to the range ±1.
While most of the energy of the signal is contained within ''f
c'' ± ''f''
Δ, it can be shown by
Fourier analysis that a wider range of frequencies is required to precisely represent an FM signal. The
frequency spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.
[
]
Sinusoidal baseband signal
Mathematically, a baseband modulating signal may be approximated by a sinusoidal continuous wave signal with a frequency ''fm''. This method is also named as single-tone modulation. The integral of such a signal is:
:
In this case, the expression for y(t) above simplifies to:
:
where the amplitude of the modulating sinusoid is represented in the peak deviation (see frequency deviation Frequency deviation (f_) is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with fre ...
).
The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.
Modulation index
As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the carrier frequency
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
:
:
where is the highest frequency component present in the modulating signal ''x''''m''(''t''), and is the peak frequency-deviation—i.e. the maximum deviation of the ''instantaneous frequency
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
'' from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.
If , the modulation is called narrowband FM (NFM), and its bandwidth is approximately . Sometimes modulation index is considered as NFM, otherwise wideband FM (WFM or FM).
For digital modulation systems, for example binary frequency shift keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:
:
where is the symbol period, and is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest ''fundamental'' of the modulating binary waveform. In the case of digital modulation, the carrier is never transmitted. Rather, one of two frequencies is transmitted, either or , depending on the binary state 0 or 1 of the modulation signal.
If , the modulation is called ''wideband FM'' and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve the signal-to-noise ratio significantly; for example, doubling the value of , while keeping constant, results in an eight-fold improvement in the signal-to-noise ratio. (Compare this with chirp spread spectrum
In digital communications, chirp spread spectrum (CSS) is a spread spectrum technique that uses wideband linear frequency modulated chirp pulses to encode information. A chirp is a sinusoidal signal whose frequency increases or decreases over ...
, which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).
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 remains 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.
Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index > 1) than the signal frequency. For example, narrowband FM (NFM) is used for two-way radio
A two-way radio is a radio that can both transmit and receive radio waves (a transceiver), unlike a broadcast receiver which only receives content. It is an audio (sound) transceiver, a transmitter and receiver in one unit, used for bidirection ...
systems such as Family Radio Service, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for FM broadcasting
FM broadcasting is a method of radio broadcasting using frequency modulation (FM). Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to provide high fidelity sound over broadcast radio. FM broadcasting is cap ...
, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20 kHz bandwidth and subcarriers up to 92 kHz.
Bessel functions
For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using Bessel functions of the first kind, as a function of the sideband number and the modulation index. The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. For particular values of the modulation index, the carrier amplitude becomes zero and all the signal power is in the sidebands.[T.G. Thomas, S. C. Sekhar ''Communication Theory'', Tata-McGraw Hill 2005, page 136]
Since the sidebands are on both sides of the carrier, their count is doubled, and then multiplied by the modulating frequency to find the bandwidth. For example, 3 kHz deviation modulated by a 2.2 kHz audio tone produces a modulation index of 1.36. Suppose that we limit ourselves to only those sidebands that have a relative amplitude of at least 0.01. Then, examining the chart shows this modulation index will produce three sidebands. These three sidebands, when doubled, gives us (6 × 2.2 kHz) or a 13.2 kHz required bandwidth.
Carson's rule
A rule of thumb, ''Carson's rule'' states that nearly all (≈98 percent) of the power of a frequency-modulated signal lies within a bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
of:
:
where , as defined above, is the peak deviation of the instantaneous frequency from the center carrier frequency , is the Modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal and is the highest frequency in the modulating signal.
Condition for application of Carson's rule is only sinusoidal signals. For non-sinusoidal signals:
:
where W is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation ratio which the ratio of frequency deviation to highest frequency of modulating non-sinusoidal signal.
Noise reduction
FM provides improved signal-to-noise ratio (SNR), as compared for example with AM. Compared with an optimum AM scheme, FM typically has poorer SNR below a certain signal level called the noise threshold, but above a higher level – the full improvement or full quieting threshold – the SNR is much improved over AM. The improvement depends on modulation level and deviation. For typical voice communications channels, improvements are typically 5–15 dB. FM broadcasting using wider deviation can achieve even greater improvements. Additional techniques, such as pre-emphasis of higher audio frequencies with corresponding de-emphasis in the receiver, are generally used to improve overall SNR in FM circuits. Since FM signals have constant amplitude, FM receivers normally have limiters that remove AM noise, further improving SNR.
Implementation
Modulation
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 voltage-controlled oscillator
A microwave (12–18GHz) voltage-controlled oscillator
A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillat ...
.
* For indirect FM modulation, the message signal is integrated to generate a phase-modulated signal. This is used to modulate a crystal-controlled oscillator, and the result is passed through a frequency multiplier to produce an FM signal. In this modulation, narrowband FM is generated leading to wideband FM later and hence the modulation is known as indirect FM modulation.
Demodulation
Many FM detector circuits exist. A common method for recovering the information signal is through a Foster–Seeley discriminator or ratio detector. A phase-locked loop
A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...
can be used as an FM demodulator. ''Slope detection'' demodulates an FM signal by using a tuned circuit which has its resonant frequency slightly offset from the carrier. As the frequency rises and falls the tuned circuit provides a changing amplitude of response, converting FM to AM. AM receivers may detect some FM transmissions by this means, although it does not provide an efficient means of detection {{Unreferenced, date=March 2018
In general, detection is the action of accessing information without specific cooperation from with the sender.
In the history of radio communications, the term " detector" was first used for a device that detected ...
for FM broadcasts.
Applications
Doppler effect
When an echolocating bat
Bats are mammals of the order Chiroptera.''cheir'', "hand" and πτερόν''pteron'', "wing". With their forelimbs adapted as wings, they are the only mammals capable of true and sustained flight. Bats are more agile in flight than most ...
approaches a target, its outgoing sounds return as echoes, which are Doppler-shifted upward in frequency. In certain species of bats, which produce constant frequency (CF) echolocation calls, the bats compensate for the Doppler shift by lowering their call frequency as they approach a target. This keeps the returning echo in the same frequency range of the normal echolocation call. This dynamic frequency modulation is called the Doppler Shift Compensation (DSC), and was discovered by Hans Schnitzler in 1968
Magnetic tape storage
FM is also used at intermediate frequencies by analog VCR
A videocassette recorder (VCR) or video recorder is an electromechanical device that records analog audio and analog video from broadcast television or other source on a removable, magnetic tape videocassette, and can play back the recording. ...
systems (including VHS) to record the luminance (black and white) portions of the video signal. Commonly, the chrominance component is recorded as a conventional AM signal, using the higher-frequency FM signal as bias. FM is the only feasible method of recording the luminance ("black-and-white") component of video to (and retrieving video from) magnetic tape without distortion; video signals have a large range of frequency components – from a few hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...
to several megahertz, too wide for equalizers to work with due to electronic noise below −60 dB. FM also keeps the tape at saturation level, acting as a form of noise reduction; a limiter can mask variations in playback output, and the FM capture effect removes print-through and pre-echo. 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
Time base correction (TBC) is a technique to reduce or eliminate errors caused by mechanical instability present in analog recordings on mechanical media.
Without time base correction, a signal from a videotape recorder (VTR) or videocassette ...
.
These FM systems are unusual, in that they have a ratio of carrier to maximum modulation frequency of less than two; contrast this with FM audio broadcasting, where the ratio is around 10,000. Consider, for example, a 6-MHz carrier modulated at a 3.5-MHz rate; by Bessel analysis, the first sidebands are on 9.5 and 2.5 MHz and the second sidebands are on 13 MHz and −1 MHz. The result is a reversed-phase sideband on +1 MHz; on demodulation, this results in unwanted output at 6 – 1 = 5 MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.
Sound
FM is also used at audio frequencies
An audio frequency or audible frequency (AF) is a periodic function, periodic vibration whose frequency is human hearing range, audible to the average human. The International System of Units, SI unit of frequency is the hertz (Hz). It is the pr ...
to synthesize sound. This technique, known as FM synthesis
Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency with a modulator. The frequency of an oscillator is altered "in accordance with the amplitud ...
, was popularized by early digital synthesizers and became a standard feature in several generations of personal computer sound card
A sound card (also known as an audio card) is an internal expansion card that provides input and output of audio signals to and from a computer under the control of computer programs. The term ''sound card'' is also applied to external audio ...
s.
Radio
Edwin Howard Armstrong (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio.
He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922. Armstrong 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 section of the Institute of Radio Engineers
The Institute of Radio Engineers (IRE) was a professional organization which existed from 1912 until December 31, 1962. On January 1, 1963, it merged with the American Institute of Electrical Engineers (AIEE) to form the Institute of Electrical ...
on November 6, 1935. The paper was published in 1936.
As the name implies, wideband FM (WFM) requires a wider signal bandwidth
Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to ''passband bandwidth'' or ''baseband bandwidth''. ...
than amplitude modulation by an equivalent modulating signal; this also makes the signal more robust against noise and interference. Frequency modulation is also more robust against signal-amplitude-fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmi ...
transmission, hence the term " FM radio" (although for many years the BBC #REDIRECT BBC #REDIRECT BBC
Here i going to introduce about the best teacher of my life b BALAJI sir. He is the precious gift that I got befor 2yrs . How has helped and thought all the concept and made my success in the 10th board exam. ...
...
). FM
"captures" the stronger of two stations on the same frequency while rejecting the other (compare this with a similar situation on an AM receiver, where both stations can be heard simultaneously). However,
. Frequency
was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.
An FM signal can also be used to carry a
and demultiplexing before and after the FM process. The FM modulation and demodulation process is identical in stereo and monaural processes. A high-efficiency radio-frequency
). For a given signal strength (measured at the receiver antenna), switching amplifiers use
. This gives FM another advantage over other modulation methods requiring linear amplifiers, such as AM and
. Analog TV sound is also broadcast using FM. Narrowband FM is used for voice communications in commercial and
settings. In broadcast services, where audio fidelity is important, wideband FM is generally used. In
, narrowband FM (NBFM) is used to conserve bandwidth for land mobile, marine mobile and other radio services.
There are reports that on October 5, 1924, Professor
, reported about his new method of telephony, based on a change in the period of oscillations. Demonstration of frequency modulation was carried out on the laboratory model.