Amplitude modulation: Difference between revisions

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'''Amplitude modulation''' ('''AM''') is a [[modulation scheme]], notably used in AM radio.
== What is AM? ==


⚫
An amplitude transceiver modulates the amplitude of an sinusoid carrier signal using the incoming signal. The carrier signal is sinusoid with a fixed [[Frequency]], usually much higher than the highest frequency occurring in the spectrum of the modulating signal.
[[Modulation Scheme]], have been widely used in Analog Radio.used by e.g. by analog radio.


⚫
== Mathematical setting ==
An Amplitude Modulator modulates the Amplitude of an sinoid Carrier signal using the incoming signal.
⚫
Base for transmission is a sinusoid carrier signal with continuous carrier frequency <math>f_c</math>:
⚫
: <math>\omega_c := 2 \pi f_c</math>


⚫
This is modulated by the incoming signal, here modeled by a simple sine with frequency <math>f_m</math>:
⚫
The Carrier signal is sinusoid with a fixed [[Frequency]], usually much higher than the highest frequency occuring in the spectrum of the modulating signal.
⚫
: <math>\omega_m := 2 \pi f_m</math>


⚫
== Mathematical Setting ==

⚫
Base for transmission is a sinusoid Carrier Signal with continous Carrier frequency <math>f_c</math>:

⚫
<center><math>\omega_c := 2 \ \pi \ f_c </math></center>

⚫
This is modulated by the incoming signal, here modelled by a simple sine with frequency <math>f_m</math>:

⚫
<center><math>\omega_m := 2 \ \pi \ f_m </math></center>


The actual signal coming out of the AM modulator is simply the product of both functions <math>\omega_c \cdot \omega_m</math>. Evaluating this in detail leads to the expression:
The actual signal coming out of the AM modulator is simply the product of both functions <math>\omega_c \cdot \omega_m</math>. Evaluating this in detail leads to the expression:
⚫
: <math>u_{AM}(t) = U_c \cdot cos(\omega_c \ t) \cdot [1 + m \cdot cos(\omega_m \ t)]</math>


⚫
where <math>U_c</math> is the modulation amplitude and <math>m</math> the modulation index.
⚫
<center><math>u_{AM}(t) = U_c \cdot cos(\omega_c \ t) \cdot [1 + m \cdot cos(\omega_m \ t)]</math></center>


⚫
[[File:AM mathematical desc.jpg|Description]]
⚫
where <math>U_c</math> is the Modulation Amplitude and <math>m</math> the modulation index.


⚫
The first formula describes what happens in time domain. It's basically multiplying of two cosine signals leading to the time domain picture in the example below.


⚫
The second formula describes the frequency response, the frequency spectrum consists of three spectrum lines at each time, t. The first term is the carrier, for sure the carrier is in the spectrum, the second and third terms describe two spectrum lines around the carrier, and their amplitude is dependent on the modulation index, m. As the modulating signal varies the lines around the carrier frequency are varying.
''FIXME: is this formula correct, shouldn't theh transformation in frequency domain depend on frequency instead of time? As soon this is cleared we can transform the image entirely into TeX...''

⚫
[[Image:AM_mathematical_desc.jpg|Description]]

⚫
The first formula desribes what happens in time domain. It's basically multiplying of two cosine signals leading to the time domain picture in the example below.

⚫
The second formula describes the frequency response, the frequency spectrum consists of three spectrum lines at each time t. The first term is the carrier, for shure the carrier is in the spectrum, the second and third termes describe two spectrum lines around the carrier, and their amplitude is dependend on the modulation index m. As the modulating sognakll variies the lines around the carrier frequency are variing.

''we should add an frequeny response picture below in the example''
''FIXME: ENDOFFIXME''


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== An Example ==


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== Example ==
{|
{|
|[[Image:AM_picture1.jpg|frame|Carrier Signal in time domain]]
| [[File:AM picture1.jpg|frame|Carrier signal in time domain]]
|[[Image:AM_picture4.jpg|frame|Carrier Signal in frequency domain (to be added)]]
| [[File:AM picture4.jpg|frame|Carrier signal in frequency domain (to be added)]]
|-
|-
|[[Image:AM_picture2.jpg|frame|Modulating Signal in time domain]]
| [[File:AM picture2.jpg|frame|Modulating signal in time domain]]
|[[Image:AM_picture5.jpg|frame|Modulating Signal in frequency domain (to be added)]]
| [[File:AM picture5.jpg|frame|Modulating signal in frequency domain (to be added)]]
|-
|-
|[[Image:AM_picture3.jpg|frame|AM Signal]]
| [[File:AM picture3.jpg|frame|AM signal]]
|[[Image:AM_picture6.jpg|frame|AM Signal in frequency domain (to be added)]]
| [[File:AM picture6.jpg|frame|AM signal in frequency domain (to be added)]]
|}
|}


== Special kinds ==
* Double sideband suppressed carrier (DSSC)
* Single side band (SSB)
⚫
* [[Vestigial side band modulation]] (VSB) (used in digital TV applications)
* [[Quadrature Amplitude Modulation]] (QAM) (used in digital TV applications)


== Special Kinds of AM ==
== Acquired bandwidth ==
⚫
An AM signal shows up as a single peak in the frequency spectrum.

*DSSC, Double Sideband Supressed Carrier
*SSB, Single Side Band
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*Residual Sideband Modulation (modulation used for analog TV applications)
*[[Quadrature_Amplitude_Modulation|QAM, Quadrature Amplitude Modulation]]


== Aquired Bandwidth ==

⚫
An AM Signal shows up as single Peak in the Frequency Spectrum.

''it would be nice to have a picture showing how AM signals in the frequency spectrum behave and how much bandwidth they allocate. A short overview of AM-related problems would be nice, too. Has anybody of you this info handy?''


== Noise Sensitivity ==

⚫
Echoes, multipath signaly, athmospheric and meteorologic phenomenons like lightings and electrostatic discharges contribute noise that simply gets added to the transmitted signal. Most other Modulation Schemes are less sensitive to noise.



== Links ==
== Noise sensitivity ==
⚫
Echoes, multipath signaling, atmospheric and meteorologic phenomenons like lightings and electrostatic discharges contribute noise that simply gets added to the transmitted signal. Most other Modulation Schemes are less sensitive to noise.


== External links ==
* [[Wikipedia:Amplitude_modulation|Amplitude Modulation Article on Wikipedia]]
* [[Wikipedia:Amplitude modulation]] at Wikipedia
* [[Wikipedia:History of radio|History of radio]] at Wikipedia


[[Category:Technology]]
* [[Wikipedia:History_of_radio|A nice introduction to the History of Radio on Wikipedia]]

Latest revision as of 07:21, 26 December 2016

Amplitude modulation (AM) is a modulation scheme, notably used in AM radio.

An amplitude transceiver modulates the amplitude of an sinusoid carrier signal using the incoming signal. The carrier signal is sinusoid with a fixed Frequency, usually much higher than the highest frequency occurring in the spectrum of the modulating signal.

Mathematical setting

Base for transmission is a sinusoid carrier signal with continuous carrier frequency <math>f_c</math>:

<math>\omega_c := 2 \pi f_c</math>

This is modulated by the incoming signal, here modeled by a simple sine with frequency <math>f_m</math>:

<math>\omega_m := 2 \pi f_m</math>

The actual signal coming out of the AM modulator is simply the product of both functions <math>\omega_c \cdot \omega_m</math>. Evaluating this in detail leads to the expression:

<math>u_{AM}(t) = U_c \cdot cos(\omega_c \ t) \cdot [1 + m \cdot cos(\omega_m \ t)]</math>

where <math>U_c</math> is the modulation amplitude and <math>m</math> the modulation index.

Description

The first formula describes what happens in time domain. It's basically multiplying of two cosine signals leading to the time domain picture in the example below.

The second formula describes the frequency response, the frequency spectrum consists of three spectrum lines at each time, t. The first term is the carrier, for sure the carrier is in the spectrum, the second and third terms describe two spectrum lines around the carrier, and their amplitude is dependent on the modulation index, m. As the modulating signal varies the lines around the carrier frequency are varying.

Example

Carrier signal in time domain
File:AM picture4.jpg
Carrier signal in frequency domain (to be added)
Modulating signal in time domain
File:AM picture5.jpg
Modulating signal in frequency domain (to be added)
AM signal
File:AM picture6.jpg
AM signal in frequency domain (to be added)

Special kinds

Acquired bandwidth

An AM signal shows up as a single peak in the frequency spectrum.

Noise sensitivity

Echoes, multipath signaling, atmospheric and meteorologic phenomenons like lightings and electrostatic discharges contribute noise that simply gets added to the transmitted signal. Most other Modulation Schemes are less sensitive to noise.

External links

Retrieved from "https://www.linuxtv.org/wiki/index.php?title=Amplitude_modulation&oldid=35488"