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Draw the spectrum of an amplitude modulated wave and explain its components.

Subject : Principle of Communication Engineering

Topic : Amplitude Modulation and Demodulation

Difficulty : Low

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• Amplitude modulation is a process of varying the amplitude of high frequency carrier signal in accordance with the amplitude of the low frequency modulating or information signal, and keeping frequency and phase of the carrier signal as constant.
• Let the carrier signal voltage and modulating signal voltage be vc and vm, both represented as,

vc=Vc sinωct

vm=Vm sinωmt

• In amplitude modulation, amplitude of unmodulated carrier Vc is varied proportional to the instantaneous amplitude of modulating signal voltage Vm sin ωmt.

• When there is no modulation, the amplitude of the carrier is equal to its unmodulated value and when modulation is present, amplitude of carrier is varied by modulating signal instantaneous value. This is explained with the help of Fig1. given below

Fig1. Amplitude of AM wave

• The time domain representation of an amplitude modulated wave is given below in Fig2., which shows the modulation of the carrier signal by the instantaneous amplitude of modulating signal. In AM wave, both the carrier and modulating waves are sinusoidal in nature but the modulated wave is not a sine wave. The amplitude of the AM wave is given as,

vAM= Vc sinωct + mVc 2cos(ωc−ωm)t− mVc 2cos(ωc+ωm)t

Fig2. Time domain representation of AM wave

• The central frequency has the highest amplitude which is the carrier frequency fc. Adjoining both the sides of the carrier frequencies are the sideband frequencies with lower amplitude. The bandwidth of the amplitude modulated wave is given by, BW=(fc+fm)−(fc−fm)=2fm

• Thus we can say that apart from the original carrier signal there are two additional sine waves having frequency above carrier frequency i.e (fc+fm) and the other below the carrier frequency i.e (fc-fm). Therefore, the complete AM signal consists of a three component a carrier wave and two additional frequencies one on each side which are called the sideband frequencies.

• The frequency which is above the carrier frequency is called the upper sideband and the frequency below the carrier frequency is called the lower sideband.

• The frequency of the upper sideband (USB) is fc+fm and the frequency of lower sideband (LSB) is fc−fm. The spectrum of amplitude modulated wave is given below in the Fig3.

• The central frequency has the highest amplitude which is the carrier frequency fc. Adjoining both the sides of the carrier frequencies are the sideband frequencies with lower amplitude. The bandwidth of the amplitude modulated wave is given by,

BW=(fc+fm)−(fc−fm)=2fm

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• Amplitude modulation is a process of varying the amplitude of high frequency carrier signal in accordance with the amplitude of the low frequency modulating or information signal, and keeping frequency and phase of the carrier signal as constant.
• Let the carrier signal voltage and modulating signal voltage be vc and vm, both represented as,

vc=Vc sinωct

vm=Vm sinωmt

• In amplitude modulation, amplitude of unmodulated carrier Vc is varied proportional to the instantaneous amplitude of modulating signal voltage Vm sin ωmt.

• When there is no modulation, the amplitude of the carrier is equal to its unmodulated value and when modulation is present, amplitude of carrier is varied by modulating signal instantaneous value. This is explained with the help of Fig1. given below

Fig1. Amplitude of AM wave

• The time domain representation of an amplitude modulated wave is given below in Fig2., which shows the modulation of the carrier signal by the instantaneous amplitude of modulating signal. In AM wave, both the carrier and modulating waves are sinusoidal in nature but the modulated wave is not a sine wave. The amplitude of the AM wave is given as,

vAM= Vc sinωct + mVc 2cos(ωc−ωm)t− mVc 2cos(ωc+ωm)t

Fig2. Time domain representation of AM wave

• The central frequency has the highest amplitude which is the carrier frequency fc. Adjoining both the sides of the carrier frequencies are the sideband frequencies with lower amplitude. The bandwidth of the amplitude modulated wave is given by, BW=(fc+fm)−(fc−fm)=2fm

• Thus we can say that apart from the original carrier signal there are two additional sine waves having frequency above carrier frequency i.e (fc+fm) and the other below the carrier frequency i.e (fc-fm). Therefore, the complete AM signal consists of a three component a carrier wave and two additional frequencies one on each side which are called the sideband frequencies.

• The frequency which is above the carrier frequency is called the upper sideband and the frequency below the carrier frequency is called the lower sideband.

• The frequency of the upper sideband (USB) is fc+fm and the frequency of lower sideband (LSB) is fc−fm. The spectrum of amplitude modulated wave is given below in the Fig3.

• The central frequency has the highest amplitude which is the carrier frequency fc. Adjoining both the sides of the carrier frequencies are the sideband frequencies with lower amplitude. The bandwidth of the amplitude modulated wave is given by,

BW=(fc+fm)−(fc−fm)=2fm