written 8.1 years ago by | • modified 8.1 years ago |
Mumbai University > Electronics Engineering > Sem4 > Fundamentals of Communication Engineering
Marks: 5M
Year: May2014
written 8.1 years ago by | • modified 8.1 years ago |
Mumbai University > Electronics Engineering > Sem4 > Fundamentals of Communication Engineering
Marks: 5M
Year: May2014
written 8.1 years ago by |
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
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.
$$BW= (f_c+f_m)-(f_c-f_m )= 2f_m$$