# DSBSC Modulation and Demodulation in Simulink  DSBSC Modulator and Demodulator Block Diagram executed in Simulink

### Modulation  Message Signal : 2V(p-p) 200 Hz  Carrier Signal: 2V(p-p) 1500 Hz

The DSBSC modulation is one type of modulation in which the message is carried on the amplitude of a sinusoidal signal.

Mathematically DSBSC wave can be said to be equal to the product of message and carrier signal.

If Message Signal is

𝑓𝑚(𝑡) =𝑉𝑚 𝑠𝑖𝑛𝜔𝑚𝑡

and Carrier Signal is

𝑓𝑐(𝑡) =𝑉𝑐 𝑠𝑖𝑛𝜔𝑐𝑡

Then their product will be,

𝑓𝑚(𝑡)* 𝑓𝑐(𝑡)=𝑉𝑚 𝑉𝑐 (𝑠𝑖𝑛𝜔𝑚𝑡∗𝑠𝑖𝑛𝜔𝑐𝑡)

Which gives,

𝐹1(𝑡)=𝐴∗[cos((𝜔𝑐−𝜔𝑚)𝑡)−cos((𝜔𝑐+𝜔𝑚)𝑡)]  Modulated Wave

Thus 𝐹(𝑡) can be said to be a DSBSC wave since it has two sideband components 𝜔𝑐−𝜔𝑚 and 𝜔𝑐+𝜔𝑚 .

The product of the two signals is obtained by using a Product-Modulator Circuit.  DSBSC Spectrum

### DeModulation

Demodulation of a DSBSC involves a Product-Modulator Circuit followed by a low pass filter. Here the one input to the Modulator is the DSBSC wave and the other input is a signal of unit amplitude which has exactly the same frequency and phase as that of carrier signal.

𝐹2(𝑡)=𝐴∗[cos((𝜔𝑐−𝜔𝑚)𝑡)−cos((𝜔𝑐+𝜔𝑚)𝑡)]∗𝑠𝑖𝑛𝜔𝑐𝑡

Therefore

𝐹2(𝑡)=(𝐴/2)sin((2𝜔𝑐−𝜔𝑚)𝑡)+(𝐴/2)sin((2𝜔𝑐+𝜔𝑚)𝑡)+(𝐴/2)𝑠𝑖𝑛𝜔𝑚𝑡+(𝐴/2)𝑠𝑖𝑛𝜔𝑚𝑡  Reciever Demodulated Wave

The frequencies 2𝜔𝑐−𝜔𝑚 and 2𝜔𝑐+𝜔𝑚 are removed by the low pass filter.

The low pass filter is selected to have pass band edge frequency of twice the frequency of message signal.

Thus the message signal is obtained as

𝐹2(𝑡)=(𝐴/2)𝑠𝑖𝑛𝜔𝑚𝑡+(𝐴/2)𝑠𝑖𝑛𝜔𝑚𝑡  Recovered Message Signal

Here the two terms are obtained from two sidebands each, thus it can be said that transmission of information is possible even with a single sideband!

### Conclusion

DSBSC transmits the message signal with two sidebands, thus it consumes less power as compared to DSBFC, However the circuit gets complex.

Its demodulation always requires the availability of the carrier signal in the demodulator. The carrier at the demodulator must have the same frequency and phase of the carrier at the transmitter or some parts of the message signal will be lost.

The generation of the carrier signal at exactly the same frequency and phase of the carrier at the modulation is relatively expensive and may drive the cost of the demodulator to be higher.

The file related to this simulation are availabe on Github

1. Alonzo Shimada says: