Amplitude Modulation - AM modulation - Amplitude Modulation Definition, Waveform and Equation

This lecture explains What is Amplitude Modulation (AM modulation). Amplitude Modulation Definition along with waveform of amplitude modulation and Equation of Amplitude Modulation has been covered here.
Amplitude Modulation Definition:-
Amplitude Modulation may be defined as a system, where the maximum amplitude of the carrier wave varies, according to the instantaneous value (amplitude) of the modulating (message or baseband) signal.
Note: [In case of Frequency modulation (FM), the frequency of the carrier wave varies, according to the instantaneous value of the modulating signal, while in Phase Modulation (PM), the phase of the carrier wave varies, according to the instantaneous value of the modulating signal.]
What Will You Learn Here?
After watching this video, you will understand:-
#What is Amplitude Modulation (AM)
#Time Domain analysis of the Amplitude Modulation
#Equations of Amplitude Modulation (Time Domain)
#Waveforms of Modulating signal, Carrier signal and Amplitude Modulated wave and
#Properties of the amplitude modulation

Equations of Amplitude Modulation (Time Domain)
As per the definition of the amplitude modulation we can express it mathematically as-
Amplitude Modulation, we know that, here in the equations, given in the image-
x(t) is the Modulating signal (also called as Message signal or Baseband signal)
c(t) = Acos(wct) carrier wave
Here ‘A’ is the amplitude of the carrier wave and
‘wc’ is the angular frequency of the carrier wave
Here you can see in the equations, that the carrier wave has a constant amplitude (A) and constant high frequency (wc).
But the Modulating signal (message signal) can have multiple frequencies and variable amplitude.
So now as per the definition of amplitude modulation; let’s now superimpose this modulating signal over the high frequency carrier wave’s amplitude.
s(t) = [A+x(t)]cos(wct)
=x(t) cos(wct)+ Acos(wct)…(i)
Here in these equations, we have superimposed the amplitude of the carrier wave by the message signal x(t). This superimposition is shown in the equation by putting the modulating signal x(t) with the Amplitude of the Carrier wave.
Waveforms (Amplitude Modulation)
Now I'm going to show you, some waveforms of modulating signal, Carrier signal and amplitude modulated wave.
See the Image given below to view the Waveforms.
All the waveforms shown here are in Time Domain-
Here are some observations and properties of the waveforms shown in the image 3 above.

Modulating signal x(t) (message signal/baseband signal)
#It has multiple frequencies and
#Variable amplitude

Carrier wave c(t) (as in this case)
It has High frequency and
Constant amplitude

Amplitude modulated wave s(t)
As you can see, the waveforms in the image 3; the amplitude of the high frequency carrier wave gets modulated by the message signal. Here observe, how the variations take place.
Initially the amplitude of the carrier wave was constant but now the amplitude of the carrier wave present in the waveform of the modulated wave s(t), has changed as per the shape of the message signal x(t). You can easily observe that, this shape is same as the shape of the message signal x(t).
The shape that you see here, which is obtained by joining the peak amplitudes of the carrier wave, present in the waveform of amplitude modulated wave s(t), is called as the envelope of the modulated wave. As the shape of this envelope is same as that of the modulating signal x(t), it has the information, that is contained by the modulating signal. This envelope, containing information, can be extracted from the modulated wave at the receiving end by a process called as the Demodulation or detection.
In AM modulation, neither the frequency nor the phase of the carrier wave are changed, only the amplitude of the carrier wave is varied, as per the instantaneous value of the modulating signal. So the information is present in the amplitude variations of the high frequency carrier wave, no information is present in the frequency or phase of the carrier, as both of these are kept constant.
Observe one more thing in the waveform of modulated wave s(t) that it contains two identical shapes similar to the shape of the modulating signal x(t). These are called as the sidebands of the modulated wave and complete information of the message signal is contained by each of the sideband. We can get all the information of the message signal from any of these sidebands. These sidebands are called as the Upper Side Band (USB) and Lower Side Band (LSB).
Equation of Amplitude Modulated wave (envelope form)
We saw that the equation of AM signal is-
s(t) = [A+x(t)]cos(wct)
Let’s replace [A+x(t)] by E(t)
So we can write the equation of the Amplitude Modulated wave as
s(t) = E(t)cos(wct)
Here E(t) is the envelope of the AM wave.

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Видео Amplitude Modulation - AM modulation - Amplitude Modulation Definition, Waveform and Equation канала Engineering Made Easy