Terpene

"FM" redirects here. For other uses, see FM (disambiguation).

Passband modulation techniques
Analog modulation
AM · SSB · QAM · FM · PM · SM
Digital modulation
FSK · MFSK · ASK · OOK · PSK · QAM MSK · CPM · PPM · TCM · SC-FDE
Spread spectrum
CSS · DSSS · FHSS THSS · OFDM
v · d · e
See also: Random modulation, Demodulation, modem, line coding, PAM, PWM, PCM

[edit] Theory

Suppose the baseband data signal (the message) to be transmitted is $x m (t)$ and the sinusoidal carrier is $x_c(t) = A_c \cos (2 \pi f_c t)\,$ , 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:

$y(t) = A_c \cos \left( 2 \pi \int_{0}^{t} f(\tau) d \tau \right)$

$= A_{c} \cos \left( 2 \pi \int_{0}^{t} \left[ f_{c} + f_{\Delta} x_{m}(\tau) \right] d \tau \right)$

$= A_{c} \cos \left( 2 \pi f_{c} t + 2 \pi f_{\Delta} \int_{0}^{t}x_{m}(\tau) d \tau \right)$

In this equation, $f(\tau)\,$ is the instantaneous frequency of the oscillator and $f_{\Delta}\,$ 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.

[edit] Sinusoidal baseband signal

While it is an over-simplification, a baseband modulated signal may be approximated by a sinusoidal Continuous Wave signal with a frequency f_m. The integral of such a signal is

$\int_{0}^{t}x_m(t)dt = \frac{A_m \cos (2 \pi f_m t)}{2 \pi f_m}\,$

Thus, in this specific case, equation (1) above simplifies to:

$y(t) = A_{c} \cos \left( 2 \pi f_{c} t + \frac{f_{\Delta}}{f_{m}} \cos \left( 2 \pi f_{m} t \right) \right)\,$

where the amplitude $A_{m}\,$ of the modulating sinusoid, is represented by the peak deviation $f_{\Delta}\,$ (see frequency deviation).

The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions - this provides a basis for a mathematical understanding of frequency modulation in the frequency domain.

[edit] Modulation index

As with other modulation indices, 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:

$h = \frac{\Delta{}f}{f_m} = \frac{f_\Delta |x_m(t)|}{f_m} \$

where $f_m\,$ is the highest frequency component present in the modulating signal x_m(t), and $\Delta{}f\,$ is the Peak frequency-deviation, i.e. the maximum deviation of the instantaneous frequency from the carrier frequency. If $h \ll 1$ , the modulation is called narrowband FM, and its bandwidth is approximately $2 f_m\,$ . If $h \gg 1$ , the modulation is called wideband FM and its bandwidth is approximately $2 f_\Delta\,$ . While wideband FM uses more bandwidth, it can improve signal-to-noise ratio 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.

Frequency modulation can be classified as narrow band if the change in the carrier frequency is about the same as the signal frequency, or as wide-band if the change in the carrier frequency is much higher (modulation index >1) than the signal frequency. ^[1] For example, narrowband FM is used for two way radio systems such as Family Radio Service where the carrier is allowed to deviate only 2.5 kHz above and below the center frequency, carrying speech signals of no more than 3.5 kHz bandwidth. Wide-band FM is used for FM broadcasting where music and speech is transmitted with up to 75 kHz deviation from the center frequency, carrying audio with up to 20 kHz bandwidth.

[edit] Carson's rule

Main article: Carson bandwidth rule

A rule of thumb, Carson's rule states that nearly all (~98%) of the power of a frequency-modulated signal lies within a bandwidth $B_T\,$ of

$\ B_T = 2(\Delta f +f_m)\,$

where $\Delta f\,$ , as defined above, is the peak deviation of the instantaneous frequency $f(t)\,$ from the center carrier frequency $f_c\,$ .

[edit] Noise quieting

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

[edit] Bessel functions

The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. Based on the Bessel functions.^{[clarification needed]}^{[citation needed]}

Modulation index	Sideband
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	−0.05	0.50	0.45	0.22	0.07	0.02	0.01
3.0	−0.26	0.34	0.49	0.31	0.13	0.04	0.01
4.0	−0.40	−0.07	0.36	0.43	0.28	0.13	0.05	0.02
5.0	−0.18	−0.33	0.05	0.36	0.39	0.26	0.13	0.05	0.02
5.53	0	−0.34	−0.13	0.25	0.40	0.32	0.19	0.09	0.03	0.01
6.0	0.15	−0.28	−0.24	0.11	0.36	0.36	0.25	0.13	0.06	0.02
7.0	0.30	0.00	−0.30	−0.17	0.16	0.35	0.34	0.23	0.13	0.06	0.02
8.0	0.17	0.23	−0.11	−0.29	−0.10	0.19	0.34	0.32	0.22	0.13	0.06	0.03
8.65	0	0.27	0.06	−0.24	−0.23	0.03	0.26	0.34	0.28	0.18	0.10	0.05	0.02
9.0	−0.09	0.25	0.14	−0.18	−0.27	−0.06	0.20	0.33	0.31	0.21	0.12	0.06	0.03	0.01
10.0	−0.25	0.04	0.25	0.06	−0.22	−0.23	−0.01	0.22	0.32	0.29	0.21	0.12	0.06	0.03	0.01
12.0	0.05	−0.22	−0.08	0.20	0.18	−0.07	−0.24	−0.17	0.05	0.23	0.30	0.27	0.20	0.12	0.07	0.03	0.01

[edit] Practical Implementation

[edit] 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 VCO.
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 give an FM signal.^[2]

[edit] Demodulation

Main article: Detector_(radio)#Frequency_and_phase_modulation_detectors

Many FM detector circuits exist. One common method for recovering the information signal is through a Foster-Seeley discriminator. A phase-locked loop 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 frequency. 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, though it does not provide an efficient method of detection for FM broadcasts.

[edit] Applications

[edit] Magnetic tape storage

FM is also used at intermediate frequencies by all analog VCR systems, including VHS, to record both the luminance (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 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, and therefore acts as a form of noise reduction, and a simple limiter can mask variations in the 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.

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, while the second sidebands are on 13 MHz and −1 MHz. The result is a sideband of reversed phase on +1 MHz; on demodulation, this results in an unwanted output at 6−1 = 5 MHz. The system must be designed so that this is at an acceptable level.^[3]

[edit] Sound

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.

[edit] Radio

Main article: FM broadcasting

Edwin Howard Armstrong (1890–1954) was an American electrical engineer who invented frequency modulation (FM) radio.^[4] He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922.^[5] He 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 on November 6, 1935. The paper was published in 1936.^[6]

As the name implies, wideband FM (WFM) requires a wider signal bandwidth than amplitude modulation by an equivalent modulating signal, but this also makes the signal more robust against noise and 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 called it "VHF radio", because commercial FM broadcasting uses a well-known part of the VHF band—the FM broadcast band).

FM receivers employ a special detector for FM signals and exhibit a phenomenon called capture effect, 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. 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 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 and typically cost less than a linear amplifier. This gives FM another advantage over other modulation schemes that require linear amplifiers, such as AM and QAM.

FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (see FM broadcasting). Normal (analog) TV sound is also broadcast using FM. A narrow band form is used for voice communications in commercial and amateur radio settings. In broadcast services, where audio fidelity is important, wideband FM is generally used. In two-way radio, narrowband FM (NBFM) is used to conserve bandwidth for land mobile radio stations, marine mobile, and many other radio services.

[edit] Miscellaneous

Frequency-shift keying is the frequency modulation using only a discrete number of frequencies. Morse code transmission has been implemented this way, as were most early telephone-line modems.^[7] Radio teletype also use FSK.^[8]

FM modulation is also used in telemetry applications, radar, seismic prospecting and newborn EEG seizures modelling.^[9]

[edit] See also

Chirp
FM-UWB (FM and Ultra Wideband)
Modulation, for a list of other modulation techniques
History of radio

[edit] References

^ B. P. Lathi, Communication Systems, John Wiley and Sons, 1968 ISBN 0 471 51832 8, p, 214-217
^ "Communication Systems" 4th Ed, Simon Haykin, 2001
^ : "FM Systems Of Exceptional Bandwidth" Proc. IEEE vol 112, no. 9, p. 1664, September 1965
^ http://world.std.com/~jlr/doom/armstrng.htm
^ US 1342885
^ Armstrong, E. H. (May 1936). "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation". Proceedings of the IRE (IRE) 24 (5): 689–740. doi:10.1109/JRPROC.1936.227383.
^ Stan Gibilisco (2002). Teach yourself electricity and electronics. McGraw-Hill Professional. p. 477. ISBN 9780071377300. http://books.google.com/?id=-Q6SBAKsmXkC&pg=PA477&dq=morse-code+frequency-shift-keying+sent-using-fsk.
^ David B. Rutledge (1999). The Electronics of Radio. Cambridge University Press. p. 310. ISBN 9780521646451. http://books.google.com/?id=ZvJYLhk4N64C&pg=RA2-PA310&dq=radio-teletype+fsk.
^ B. Boashash, editor, “Time-Frequency Signal Analysis and Processing – A Comprehensive Reference”, Elsevier Science, Oxford, 2003; ISBN 0080443354

[edit] Further reading

A. Bruce Carlson. Communication Systems, 4th edition. McGraw-Hill Science/Engineering/Math. 2001. ISBN 0070111278, ISBN 978-0070111271.
Gary L. Frost. Early FM Radio: Incremental Technology in Twentieth-Century America. Baltimore: Johns Hopkins University Press, 2010. ISBN 0801894409, ISBN 978-0801894404.

[edit] External links

v · d · eAnalogue television broadcasting topics

Systems	180 lines • 405 lines (System A) • 441 lines • System B (also G and H) • System M

Color systems	NTSC • PAL • PAL-M • PAL-S • PALplus • SECAM

Video	Back porch and front porch • Black level • Chrominance • Chrominance subcarrier • Colorburst • Color killer • Color TV • Composite video • Frame (video) • Horizontal scan rate • Horizontal blanking interval • Luminance • Nominal analogue blanking • Overscan • Raster scan • Safe area • Television lines • Vertical blanking interval • White clipper

Sound	Multichannel television sound • NICAM • Sound-in-Syncs • Zweikanalton

Modulation	Frequency modulation • Quadrature amplitude modulation • Vestigial sideband modulation (VSB)

Transmission	Amplifiers • Antenna (radio) • Cavity amplifier • Differential gain • Differential phase • Diplexer • Dipole antenna • Dummy load • Frequency mixer • Intercarrier method • Intermediate frequency • Output power of an analog TV transmitter • Pre-emphasis • Residual carrier • Split sound system • Superheterodyne transmitter • Television receive-only • Television transmitter • Terrestrial television • Transmitter station • Transposer

Frequencies & Bands	Frequency offset • Microwave transmission • Television channel frequencies • UHF • VHF

Propagation	Beam tilt • Distortion • Earth bulge • Field strength in free space • Knife-edge effect • Noise (electronics) • Null fill • Path loss • Radiation pattern • Skew • Television interference

Testing	Distortionmeter • Vectorscope • VIT signals • Zero reference pulse

Artifacts	Dot crawl • Ghosting • Hanover bars • Sparklies

source: https://web.archive.org/web/20110224165826/http://en.wikipedia.org/wiki/FM

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