Amplitude Modulation (AM) is the process in which the amplitude of the Carrier signal is varied in accordance with the information Signal. If the un-modulated carrier signal is represented by
A sin2pfc t
and the modulating signal is represented by
B sin2pfa t
fc = Carrier frequency
A = Maximum value of un-modulated signal
fa = Frequency of the modulating signal
B = Maximum value of the un-modulated signal.
p = Pi
The modulated signal can be represented mathematically as
A+B (sin2pfc t)( sin2pfa t )
The carrier signal, modulating signal and the modulated signal is shown in the below fig.
Factoring, we get
A [1 + (B/A) sin2pfa t] sin2pfc t)
In term of voltage, we have
V = V [ 1 + (B/A) sin2pfa t ] (sin2pfc t )
Making use of trigonometry, the equation representing the amplitude-modulated signal can be written as
V=VC sin2pfc t + (mVc /2) Cos2p (fc - fa) t
m = modulation index and is given by M = B/A = peak value of modulating signal/peak value of un-modulated carrier.
The modulated signal consists of three components: one at frequency fc , one at frequency fc – fa , and one at frequency fc + fa. fc + fa is called upper frequency band and fc - fa is called lower frequency band. The frequency spectrum of these three components is shown in fig.