# Difference between revisions of "Frequency modulation"

m (Voidxor moved page Frequency Modulation to Frequency modulation: Not a proper noun) |
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− | '''Frequency |
+ | '''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). |
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− | 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>. |
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− | == Visualisation == |
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+ | == Acquired bandwidth == |
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− | ''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. |
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− | == |
+ | == External links == |

+ | * [[Wikipedia:History of radio|History of radio]] at Wikipedia |
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+ | * [[Wikipedia:Frequency modulation|Frequency modulation]] at Wikipedia |
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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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− | <center><math> u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f)) </math></center> |
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− | where <math> \Delta f </math> is the frequency deviation from the center frequency at <math> u_{in} = 1V </math>. |
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− | == Aquired Bandwidth == |
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− | ...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>: |
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− | <center><math>bandwidth = 2 \ (\Delta f + f_{m}) </math></center> |
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− | == Noise Immunity == |
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− | 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. |
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− | == Links == |
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− | * [[Wikipedia:Frequency Modulation|Frequency Modulation on Wikipedia]] |
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− | * [[Wikipedia:History_of_radio|A nice introduction to the History of Radio on Wikipedia]] |
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[[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

- History of radio at Wikipedia
- Frequency modulation at Wikipedia