Difference between revisions of "Amplitude modulation"

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(Mathematical Setting)
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==What is AM?==
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'''Amplitude modulation''' ('''AM''') is a [[modulation scheme]], notably used in AM radio.
  
Amplitude Modulation is the done by modulating the Amplitude of an sinoid Carrier signal using the incoming signal.
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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.
  
The Carrier signal is sinusoid with a fixed [[Frequency]], usually much higher than the highest frequency occuring in the spectrum of the modulating signal.
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== Mathematical setting ==
Amplitude Modulation schemes have been widely used in Analog Radio.
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Base for transmission is a sinusoid carrier signal with continuous carrier frequency <math>f_c</math>:
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: <math>\omega_c := 2 \pi f_c</math>
  
==Mathematical Setting==
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This is modulated by the incoming signal, here modeled by a simple sine with frequency <math>f_m</math>:
[[Image:AM_mathematical_desc.jpg|Description]]
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: <math>\omega_m := 2 \pi f_m</math>
  
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.
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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:
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: <math>u_{AM}(t) = U_c \cdot cos(\omega_c \ t) \cdot [1 + m \cdot cos(\omega_m \ t)]</math>
  
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.
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where <math>U_c</math> is the modulation amplitude and <math>m</math> the modulation index.
  
''we should add an frequeny response picture below in the example''
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[[File:AM mathematical desc.jpg|Description]]
  
==An Example==
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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.
  
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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.
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== Example ==
 
{|
 
{|
|[[Image:AM_picture1.jpg|frame|Carrier Signal in time domain]]  
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| [[File:AM picture1.jpg|frame|Carrier signal in time domain]]  
|[[Image:AM_picture4.jpg|frame|Carrier Signal in frequency domain (to be added)]]
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| [[File:AM picture4.jpg|frame|Carrier signal in frequency domain (to be added)]]
 
|-
 
|-
|[[Image:AM_picture2.jpg|frame|Modulating Signal in time domain]]
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| [[File:AM picture2.jpg|frame|Modulating signal in time domain]]
|[[Image:AM_picture5.jpg|frame|Modulating Signal in frequency domain (to be added)]]
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| [[File:AM picture5.jpg|frame|Modulating signal in frequency domain (to be added)]]
 
|-
 
|-
|[[Image:AM_picture3.jpg|frame|AM Signal]]
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| [[File:AM picture3.jpg|frame|AM signal]]
|[[Image:AM_picture6.jpg|frame|AM Signal in frequency domain (to be added)]]
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| [[File:AM picture6.jpg|frame|AM signal in frequency domain (to be added)]]
 
|}
 
|}
  
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== Special kinds ==
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* Double sideband suppressed carrier (DSSC)
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* Single side band (SSB)
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* [[Vestigial side band modulation]] (VSB) (used in digital TV applications)
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* [[Quadrature Amplitude Modulation]] (QAM) (used in digital TV applications)
  
==Special Kinds of AM==
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== Acquired bandwidth ==
 
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An AM signal shows up as a single peak in the frequency spectrum.
*DSSC, Double Sideband Supressed Carrier
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*SSB, Single Side Band
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*Residual Sideband Modulation (modulation used for analog TV applications)
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*[[Quadrature_Amplitude_Modulation|QAM, Quadrature Amplitude Modulation]]
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==Aquired Bandwidth==
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''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?''
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''what about noise sensitivity?''
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== Noise sensitivity ==
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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.
  
==Links==
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== External links ==
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* [[Wikipedia:Amplitude modulation]] at Wikipedia
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* [[Wikipedia:History of radio|History of radio]] at Wikipedia
  
* [[Wikipedia:Amplitude_modulation|Amplitude Modulation Article on Wikipedia]]
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[[Category:Technology]]

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