What is Amplitude Modulation?

The amplitude of the carrier signal varies in accordance with the instantaneous amplitude of the modulating signal in Amplitude Modulation. That is the amplitude of the carrier signal containing no information varies as per the amplitude of the signal containing information, at each instant. 

Concept of Amplitude Modulation

Consider the following diagram

The message signal shown above is in the form of a modulating wave. Then there is a carrier wave signal which has a higher frequency. This carrier wave has no information. At last shown is the modulated wave form. There is interconnection between the positive and negative ends of the carrier wave which helps to recover the exact shape of the modulating signal. This is called an Envelope. This is exactly the same as the message signal.

Therefore, we can say that Amplitude Modulation is the process of changing the amplitude of a carrier signal in accordance with the amplitude of the modulating signal. The carrier amplitude varies linearly by the modulating signal which usually consists of a range of audio frequencies. Then there is no effect on the frequency of the carrier. 

Forms

The basic forms of AM are:

• Double Sideband Large carrier modulation (DSBLC) /Double Sideband Full Carrier (DSBFC) 
• Double Sideband Suppressed carrier (DSBSC) modulation.
• Single Sideband (SSB) modulation

Generation of DSB-FC (Double Side Band Full Wave Carrier)

Time-Domain Representation

Let the us consider the modulating signal as,

Let the carrier signal be

Where:

 A_m : It is the Amplitude of the modulating signal

A_c : Amplitude of carrier signal respectively.

f_m : It is the Frequency of the modulating signal 

f_c : The carrier signal frequency.

Then Amplitude modulated wave will be

Then modulation index will be 

Modulation index

If A_max :The maximum amplitudes of the modulated wave

A_min :The minimum amplitudes of the modulated wave.

When cos(2πf_mt) is 1, We will get the maximum amplitude of the modulated wave

 A_max=A_c + A_m 

When cos(2πf_mt) is -1, We will get the minimum amplitude of the modulated wave

A_min = A_c – A_m

A_max + A_min = Ac + A_m + A_c –A_m = 2A_c

A_c = A_max + A_min/2

Hence we can write,

A_max – A_min = A_c + A_m – A_c +A_m = 2A_m

A_m = A_max – A_min /2

Therefore  modulation index is now

Bandwidth:

Bandwidth is the difference between the highest and lowest frequencies of the signal.

BW = f_max – f_min

s(t) = A_c [1+ μ cos(2πf_mt)] cos(2πf_ct)

Therefore,

s(t) = A_c cos(2πf_ct) + Ac μ cos(2πf_mt) cos(2πf_ct)

s(t) = A_c cos(2πf_ct) + Ac μ/2 cos 2π (f_c + f_m) t + A_c μ/2 cos 2π (f_c – f_m) t

The main three frequencies in amplitude modulated wave are 

• Carrier frequency f_c
• Upper sideband frequency f_c+f_m 
• and lower sideband frequency f_c−f_m

Where we can write

f_max=f_c+f_m and f_min=f_c−f_m

BW=f_c+f_m−(fc−f_m)

BW=f_c+f_m−(f_c−f_m)

BW= 2f_m

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