Mumbai University > Computer Engineering > Sem 3 > Electronic Circuits and Communication Fundamentals

Marks: 10 marks

Year: May 2016

In amplitude modulation, the amplitude of a carrier signal is varied by the modulating signal. Here, information signal is the modulating signal and high frequency signal which is 'being modulated is the carrier signal. Formally, AM is defined as system of modulation in which the instantaneous value of the carrier amplitude changes in accordance with the amplitude of the modulating signal. Fig. 3.1 shows a single frequency sine wave modulating a higher frequency carrier signal. Looking at Fig. we can see that the frequency of the carrier signal remains constant during modulation process but its amplitude varies in accordance with the modulating signal.

Expression for AM

The instantaneous values of modulating signal and carrier signal can be reprensented as given below.

Instantaneous value of modulating signal

$e_m=E_m \sin ω_m t$

$e_m$=instantaneous amplitude

$E_m$= maximum amplitude

$ω_m=2πf_m$=angular frequency and

$f_m$=frequency of modulating signal

Where $e_c=E_c \sin ω_c t$

$e_c$=instantaneous amplitude

$E_c$= maximum amplitude

$ω_c=2πf_c$=angular frequency and

$f_c$=frequency of carrier signal

Instantaneous value of amplitude modulated signal

Using above given mathematical expression for modulating and carrier signals, we can create a new mathematical expression for the complete modulated wave, as given below

$$E_{AM}=E_c+e_m \\ =E_c+E_m \sin \omega_mt$$

The instantaneous value of the amplitude modulated wave can be given as

$$e_{AM}=E_{AM} \sin \theta \\ =E_{AM} \sin \omega_c t \\ =(E_c+E_m \sin \omega_mt)\sin \omega_ct$$