Difference between revisions of "Amplitude modulation"
(→Mathematical Setting) 
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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. 

−  Amplitude Modulation is the done by modulating the Amplitude of an sinoid Carrier signal using the incoming signal. 

+  == Mathematical setting == 

−  The Carrier signal is sinusoid with a fixed [[Frequency]], usually much higher than the highest frequency occuring in the spectrum of the modulating signal. 

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

−  Amplitude Modulation schemes have been widely used in Analog Radio. 

+  : <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>: 

−  ==Mathematical Setting== 

+  : <math>\omega_m := 2 \pi f_m</math> 

−  [[Image:AM_mathematical_desc.jpgDescription]] 

+  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 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. 

+  : <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. 

−  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. 

+  [[File:AM mathematical desc.jpgDescription]] 

−  ''we should add an frequeny response picture below in the example'' 

+  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. 

−  ==An Example== 

+  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 == 

{ 
{ 

−  [[ 
+   [[File:AM picture1.jpgframeCarrier signal in time domain]] 
−  [[ 
+   [[File:AM picture4.jpgframeCarrier signal in frequency domain (to be added)]] 
 
 

−  [[ 
+   [[File:AM picture2.jpgframeModulating signal in time domain]] 
−  [[ 
+   [[File:AM picture5.jpgframeModulating signal in frequency domain (to be added)]] 
 
 

−  [[ 
+   [[File:AM picture3.jpgframeAM signal]] 
−  [[ 
+   [[File:AM picture6.jpgframeAM 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) 

−  == 
+  == Acquired bandwidth == 
+  An AM signal shows up as a single peak in the frequency spectrum. 

−  
−  *DSSC, Double Sideband Supressed Carrier 

−  *SSB, Single Side Band 

−  *Residual Sideband Modulation (modulation used for analog TV applications) 

−  *[[Quadrature_Amplitude_ModulationQAM, Quadrature Amplitude Modulation]] 

−  
−  
−  ==Aquired Bandwidth== 

−  
−  ''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 AMrelated problems would be nice, too. Has anybody of you this info handy?'' 

−  +  == 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 == 

−  ==Links== 

+  * [[Wikipedia:Amplitude modulation]] at Wikipedia 

+  * [[Wikipedia:History of radioHistory of radio]] at Wikipedia 

+  [[Category:Technology]] 

−  * [[Wikipedia:Amplitude_modulationAmplitude Modulation Article 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.
Contents
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.
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
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)
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
 Wikipedia:Amplitude modulation at Wikipedia
 History of radio at Wikipedia