# Introduction to Double Sideband Suppressed Carrier (DSB-SC) System . Explain The Generation of DSB-SC Signal

## Double Sideband Suppressed Carrier (DSB-SC) System

### Definition and Mathematical Expression

The equation of AM wave in its simplest form i.e. single tone modulation, is expressed as :

From this equation, it is obvious that the carrier component in AM wave remains constant in amplitude and frequency . This means that the carrier of amplitude modulated wave does not convey any information .

In power calculation of AM signal, it has been observed that for single-tone sinusoidal modulation, the ratio of the total power to the carrier power is :

where m_{a }is the modulating index

Thus, for 100% modulation about 67% of the total power is required for transmitting the carrier which does not contain any information .

Hence, if the carrier is supressed, only the sidebands remain and in this way a saving of two-third power may be achieved at 100% modulation .

The resulting signal obtained by supressing the carrier from the modulated wave is called **Double sideband supressed carrier (DSB-SC)** system .

## Generation of DSB-SC Signal

A DSB-SC signal can be obtained by simply multiplying modulating signal x(t) with carrier signal cosω_{c}t . So we need to use a device called product modulator for the generation of DSB-SC waves .

Fig 1

There are two forms of product modulators as under :

- Linear Modulator
- Non-linear Modulator

## Linear Modulator for DSB-SC Generation

A linear modulator is a system whose gain or transfer function can be varied with time by applying a time varying signal at certain points .

The gain is proportional to signal f(t) .

G = K f(t)

Where G = gain

K = constant of proportionality

f(t) = gain varying signal

Let us consider fig.2 in which the carrier signal cosω_{c}t is applied at the input terminal and x(t) is applied as the gain varying signal .

Fig 2 :Linear Modulator

The gain of the modulator is G = K x(t) .

Therefore, the output is given by :

Or,

This is a modulated signal (DSB-SC) .

AS an alternative we can use the carrier as gain varying signal and x(t) as the input signal as shown in fig 3 .

Fig 3: Another variation of Linear Modulator

The gain of the modulator is given by :

G = K cosω_{c}t

Therefore,

This is same as before .

## Balanced Modulator (Suppression of Carrier )

The balanced modulators are used to suppress the unwanted carrier in AM wave .

Fig.4 : Block Diagram of Balanced Modulator

The carrier and modulating signals are applied to the inputs of the balanced modulator and we get the DSB signal with supressed carrier at the output of the balanced modulator . Hence, the output consists of the upper and lower sidebands only .

### Principle of Operation

The principle of operation of a balanced modulator states that if two signals at different frequencies are passed through a non-linear resistance then at the output, we get an AM signal with suppressed carrier . The device having a non-linear resistance can be a diode or a JFET or even a bipolar transistor .

### Types of Balanced Modulator

The suppression of carrier can be done using the following two balanced modulators :

- Using the diode ring modulator or lattice modulator
- Using the FET balanced modulator

## Balanced Modulator using AM Modulator

The block diagram of a balanced modulator is shown in fig.5 .

Fig 5 : Balance Modulator for DSB-SC genaration

It consists of two standard amplitude modulators arranged in the balanced configuration so as to suppress the carrier completely .

### Working Operation and Analysis

The carrier signal c(t) is connected to both AM modulators M_{1 }and M_{2 }.

The message signal x(t) is applied as it is to M_{1 }and its inverted version -x(t) is applied to M_{2}.

At the outputs of modulators M_{1 }and M_{2} , we get standard AM signals s_{1}(t) and s_{2}(t) as under :

output of M_{1} : s_{1}(t) = E_{c}[1 + m x (t)] cos (2π f_{c}t)

output of M_{2} : s_{2}(t) = E_{c}[1 – m x (t)] cos (2π f_{c}t)

These are then applied to a subtractor and the subtractor produces the desired DSB-SC signal as under :

Subtractor output = s_{1}(t) – s_{2}(t) = E_{c}[1 + m x (t)] cos (2π f_{c}t) – E_{c}[1 – m x (t)] cos (2π f_{c}t)

= E_{c}cos (2π f_{c}t)[{1 + m x (t)}-{1 – m x (t)}]

= E_{c}cos (2π f_{c}t)[1 + m x (t)- 1 + m x (t)]

= 2m E_{c}x (t)cos (2π f_{c}t)

The R.H.S. of this expression consists of product of x(t) and c(t) = E_{c}cos (2π f_{c}t) .

Hence, it represents a DSB-SC signal .