# Amplitude Modulation - AM

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

Where,

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

Where

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.

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