Mumbai University > Electronics Engineering > Sem4 > Fundamentals of Communication Engineering

Marks: 5M

Year: May2014

• 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 voltage and modulating voltage be $v_c$ and $v_m$, both represented as,

  $v_c = V_c \text{sin} ω_ct \\ v_m = V_m \text{sin} ω_mt$

• In amplitude modulation, amplitude of unmodulated carrier $V_c$ is varied proportional to the instantaneous modulating voltage $V_m$ sin $ω_{mt}$.

• 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 its 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 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,

  $v_{AM}= V_c sinω_c t+ \frac{mV_c}2 cos⁡(ω_c-ω_m )t - \frac{mV_c}2 cos⁡(ω_c+ω_m )t$

Fig2. Time domain representation of AM wave

• Thus we can say that apart from the original signal there are two additional sine waves which are one above the carrier and the other below the carrier frequency. Therefore, the complete AM signal consists of a carrier wave and two additional frequencies one on each side which are called the side 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 $f_c+f_m$ and the frequency of lower sideband (LSB) is $f_c-f_m$. The spectrum of amplitude modulated wave is given below in the Fig3.

• The central frequency has the highest amplitude which is the carrier frequency $f_c$. 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,

$$BW= (f_c+f_m)-(f_c-f_m )= 2f_m$$