# Amplitude Modulation (AM)

### Amplitude Modulation (AM):-

Modulation:-  It is defined as the process in which one of the characeteristic of carrier signal  is varied in accordance with the instantaneous values of message signal (Amplitude of the message signal).

The fundamental goal of modulation is to produce an information bearing modulated signal with efficient utilization of the channel.

Amplitude modulation:- It is defined as the process in whch the amplitude of the carrier signal is varied in accordance with the  intantaneous values of message signal.

To generate a modulated signal we are in need of two signals  called as message signal & carrier signal.

• m(t)  – message signal/modulating signal/original signal/actual signal.
• C(t)- Carrier signal/unmodulated carrier signal.
• SAM(t)- Amplitude modulated signal/ Amplitude modulated Carrier.

Now these two signals are being given as inputs to an Amplitude Modulator , which in turn generates an Amplitude modulated signal SAM(t).

Here C(t) represents carrier signal  $C(t)=A&space;_{c}cos&space;2\pi&space;f_{c}t$ , the amplitude of the un modulated carrier is $A_{c}$ , when this unmodulated carrier is amplitude modulated , the new amplitude will become $A_{c}(1+k_{a}m(t))$ and the modulated carrier wave is SAM(t)

$S_{AM}(t)=A_{c}(1+k_{a}m(t))cos&space;2\pi&space;f_{c}t$.

ka is known as amplitude sensitivity.

In AM the frequency of the carrier signal fc is assumed to be much larger than the highest frequency present in  the base band signal and in the AM swave $\left&space;|&space;k_{a}m(t)\right&space;|$ is assumed to be less than 1

i.e, $\left&space;|&space;k_{a}m(t)\right&space;|<&space;1$ for all t

if $\left&space;|&space;k_{a}m(t)\right&space;|>&space;1$ in any case with large value of amplitude sensitivity ka then the envelope of the resultant signal doesn’t represent base band signal, this causes over modulation which causes a phase reversal of the carrier wave at zero-crossings.

$\therefore&space;\left&space;|&space;k_{a}m(t)\right&space;|&space;=1$ is the limiting (or) maximum value of AM.

this $\left&space;|&space;k_{a}m(t)\right&space;|$ is called modulation index.

Note:- AM is also known as conventional AM.

### Frequency spectrum of AM:-

AM signal is given as $S_{AM}(t)=A_{c}(1+k_{a}m(t))cos&space;2\pi&space;f_{c}t$ to obtain the frequency spectrum of AM signal one must represent the signal in frequency domain

i.e by taking the fourier transform of SAM(t) we will obtain SAM(f) . Let us assume M(f) is in the figure shown below and has a bandwidth ‘B’ Hz.

$S_{AM}(t)=A_{c}(1+k_{a}m(t))cos&space;2\pi&space;f_{c}t$

$S_{AM}(t)=A_{c}cos&space;2\pi&space;f_{c}t+&space;A_{c}k_{a}m(t)cos&space;2\pi&space;f_{c}t$

by taking fourier transform of sAM(t)

$S_{AM}(f)=\frac{A_{c}}{2}(\delta&space;(f-f_{c})\delta&space;(f+f_{c}))+&space;\frac{A_{c}k_{a}}{2}(M(f-f_{c})+M(f+f_{c}))$

the frequency spectrum consists of two impulse functions at $f=\pm&space;f_{c}$and the frequency band $(f_{c}&space;to(f_{c}+f_{m}))&space;and&space;-(f_{c}&space;to(f_{c}+f_{m}))$ are called as Upper side band frequencies $(f_{c}&space;to(f_{c}-f_{m}))&space;and&space;-(f_{c}&space;to(f_{c}-f_{m}))$ are Lower side band frequencies.

Note:- Information or message is available in two sidebands LSB and USB.

BW os AM signal = 2 X BW of message signal.

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## Author: Lakshmi Prasanna

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.