Realization of Amplitude Modulation using MATLAB.

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_mcos (2 πf_mt)

And the carrier signal is, c(t)= A_ccos(2πf_ct)

So the modulated signal is,

 s(t)= A_c cos(2πf_ct)+ A_m cos(2πf_mt)

      = A_c (1+k_a m(t))sin(2πf_ct)

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 kam(t)<1 and fc>>ωm  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.

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;

Simulation Result:

Figure 01: The Carrier Signal, Message Signal and Amplitude Modulated Signal.

Discussion:

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

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

3.     It can send massage without interference.

4.     The condition  kam(t)<1  should be satisfied.

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.