**Objective:**

- To study and learn the amplitude modulation.
- To learn the MATLAB coding for amplitude modulation.
- To observe the amplitude modulation wave form.

**Theory:**

The amplitude
modulation is a process in which the amplitude of carrier

*c(t)*is varied about a mean value with the massage signal*m(t).***Amplitude modulation (AM) is the family of modulation schemes in which the amplitude of a sinusoidal carrier is changed as a function of the modulating message signal.**
Let, the massage signal
is,

*m(t)= A*_{m}cos (2 πf_{m}t)
And the carrier signal
is,

*c(t)= A*_{c}cos(2πf_{c}t)
So the modulated signal
is,

s(t)=

*A*_{c}*cos(2πf*_{c}t)+ A_{m}*cos(2πf*_{m}t)*= A*

_{c }(1+k_{a}m(t))sin(2πf_{c}t)
Here A

_{c }and A_{m }is the amplitude of carrier and message signal f_{c}and f_{m }is the frequency of carrier and message signal and k_{a}is a constant called the amplitude sensitivity of the modulated signal.
If
then
modulation will be perfect. In amplitude modulation only the amplitude of the
carrier wave is changed in accordance the signal. However the frequency of the
modulated wave remains the same.

k

a

m ( t )

<1
and

f

c

>>

ω

m

**Require instrument:**

1. Mat lab software

2. Computer

**MATLAB code:**

Fc= input('Carrier signal Frequency=');

Fm=input('Message Signal Frequency=');

Ac=input('Carrier signal Amplitude=');

Am=input('Message Signal Amplitude=');

t=0:0.1:100;

A=2*pi*Fc*t;

Ct=Ac*cos(A);

subplot(3,1,1);

plot(t,Ct,'r')

xlabel('Time');

ylabel('Amplitude');

title('Carrier Signal');

grid on;

B=2*pi*Fm*t;

Mt=Am*cos(B);

subplot(3,1,2);

plot(t,Mt,'g')

xlabel('Time');

ylabel('Amplitude');

title('Message Signal');

grid on;

M=Fm/Fc;

Mod=M*Mt.*Ct;

AM=Ct+Mod;

subplot(3,1,3);

plot(t,AM,'b')

xlabel('Time');

ylabel('Amplitude');

title('Amplitude Modulated Signal');

grid on;

**Figure 01: The**

**Carrier Signal, Message Signal**

**and Amplitude Modulated Signal.**

**Discussion:**

1. The
carrier frequency
is much greater than the message frequency
.

f

c

f

m

2. The
amplitude of the carrier and message signal should take the same value.

3. It
can send massage without interference.

4. The
condition
should be satisfied.

k

a

m ( t )

<1

**Conclusion:**

Amplitude modulated
signals are generated by multiplying message signals with a carrier and adding
the carrier to this product. The amplitude of the message signal is varied to
produce different values of the modulation index. The MATLAB environment can be
an effective tool for viewing the effects of various forms of modulation.