Difference between revisions of "Frequency modulation"

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m (Voidxor moved page Frequency Modulation to Frequency modulation: Not a proper noun)
(Wikification. Copy edit. Simplify.)
 
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'''Frequency Modulation''' is a [[Modulation Scheme]] where the incoming signal modulates the frequency of the Carrier Signal by a tiny fraction. Used e.g. in FM Radio.
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'''Frequency modulation''' ('''FM''') is an analog [[modulation scheme]] where the signal modulates the frequency of the carrier signal by a tiny fraction. It is used in FM radio.
   
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The digital equivalent is [[frequency shift keying]] (FSK).
A variation of Frequency Modulation is sometimes also used for digital Transmissions, this is then called ''Frequency Shift Keying'' or FSK-Modulation.
 
   
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== Mathematical setting ==
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The output voltage of a FM modulator with input voltage <math>u_{in}</math> is described by:
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: <math>u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f))</math>
   
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where <math>\Delta f</math> is the frequency deviation from the center frequency at <math>u_{in} = 1V</math>.
== Visualisation ==
 
   
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== Acquired bandwidth ==
''it would be nice to have a gnuplot picture here, is it possible to upload the gnuplot script for toying, too?''
 
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Acquired bandwidth can be determined using [[Wikipedia:Carson bandwidth rule|Carson's bandwidth rule]]: two times the sum of the peak deviation <math>\Delta f</math> from the highest frequency occurring in the spectrum of the modulating signal <math>(f_m)</math>:
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: <math>bandwidth = 2 \ (\Delta f + f_{m})</math>
   
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== Noise immunity ==
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Noise immunity is higher than [[amplitude modulation]] because noise does not shift the frequency of a signal, but adds to it with the superposition principle.
   
== Mathematical Setting ==
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== External links ==
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* [[Wikipedia:History of radio|History of radio]] at Wikipedia
 
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* [[Wikipedia:Frequency modulation|Frequency modulation]] at Wikipedia
The output voltage of a FM modulator with input voltage <math> u_{in} </math> is described by
 
 
 
<center><math> u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f)) </math></center>
 
 
 
where <math> \Delta f </math> is the frequency deviation from the center frequency at <math> u_{in} = 1V </math>.
 
 
 
== Aquired Bandwidth ==
 
 
...can be determined using [[Wikipedia:Carson bandwidth rule|Carson's Bandwidth Rule]]: two times sum of the peak deviation <math> \Delta f </math> from the highest frequency occuring in the spectrum of the modulating signal <math> (f_m) </math>:
 
 
<center><math>bandwidth = 2 \ (\Delta f + f_{m}) </math></center>
 
 
 
== Noise Immunity ==
 
 
is higher than the one of Amplitude Modulation Schemes since athmospheric disturbances and noise usually don't shift the frequency of a signal but add their contribution to the amplitude of the transmitted signal. Amplitude variations don't affect FM much.
 
 
 
== Links ==
 
 
* [[Wikipedia:Frequency Modulation|Frequency Modulation on Wikipedia]]
 
 
* [[Wikipedia:History_of_radio|A nice introduction to the History of Radio on Wikipedia]]
 
   
 
[[Category:Technology]]
 
[[Category:Technology]]

Latest revision as of 07:07, 26 December 2016

Frequency modulation (FM) is an analog modulation scheme where the signal modulates the frequency of the carrier signal by a tiny fraction. It is used in FM radio.

The digital equivalent is frequency shift keying (FSK).

Mathematical setting

The output voltage of a FM modulator with input voltage <math>u_{in}</math> is described by:

<math>u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f))</math>

where <math>\Delta f</math> is the frequency deviation from the center frequency at <math>u_{in} = 1V</math>.

Acquired bandwidth

Acquired bandwidth can be determined using Carson's bandwidth rule: two times the sum of the peak deviation <math>\Delta f</math> from the highest frequency occurring in the spectrum of the modulating signal <math>(f_m)</math>:

<math>bandwidth = 2 \ (\Delta f + f_{m})</math>

Noise immunity

Noise immunity is higher than amplitude modulation because noise does not shift the frequency of a signal, but adds to it with the superposition principle.

External links