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In this chapter, let us discuss about the modulators, which generate DSBSC wave. The following two modulators generate DSBSC wave.

- Balanced modulator
- Ring modulator

Following is the block diagram of the Balanced modulator.

**Balanced modulator** consists of two identical AM modulators. These two modulators are arranged in a balanced configuration in order to suppress the carrier signal. Hence, it is called as Balanced modulator.

The same carrier signal $c\left ( t \right )= A_c \cos \left ( 2 \pi f_ct \right )$ is applied as one of the inputs to these two AM modulators. The modulating signal $m\left ( t \right )$ is applied as another input to the upper AM modulator. Whereas, the modulating signal $m\left ( t \right )$ with opposite polarity, i.e., $-m\left ( t \right )$ is applied as another input to the lower AM modulator.

Output of the upper AM modulator is

$$s_1\left ( t \right )=A_c\left [1+k_am\left ( t \right ) \right ] \cos\left ( 2 \pi f_ct \right )$$

Output of the lower AM modulator is

$$s_2\left ( t \right )=A_c\left [1-k_am\left ( t \right ) \right ] \cos\left ( 2 \pi f_ct \right )$$

We get the DSBSC wave $s\left ( t \right )$ by subtracting $s_2\left ( t \right )$ from $s_1\left ( t \right )$. The summer block is used to perform this operation. $s_1\left ( t \right )$ with positive sign and $s_2\left ( t \right )$ with negative sign are applied as inputs to summer block. Thus, the summer block produces an output $s\left ( t \right )$ which is the difference of $s_1\left ( t \right )$ and $s_2\left ( t \right )$.

$$\Rightarrow s\left ( t \right )=A_c\left [ 1+k_am\left ( t \right ) \right ] \cos\left ( 2 \pi f_ct \right )-A_c\left [ 1-k_am\left ( t \right ) \right ] \cos\left ( 2 \pi f_ct \right )$$

$$\Rightarrow s\left ( t \right )=A_c \cos\left ( 2 \pi f_ct \right )+A_ck_am\left ( t \right ) \cos\left ( 2 \pi f_ct \right )- A_c \cos\left ( 2 \pi f_ct \right )+$$

$A_ck_am\left ( t \right ) \cos\left ( 2 \pi f_ct \right )$

$\Rightarrow s\left ( t \right )=2A_ck_am\left ( t \right ) \cos\left ( 2 \pi f_ct \right )$

We know the standard equation of DSBSC wave is

$$s\left ( t \right )=A_cm \left ( t \right ) \cos\left ( 2 \pi f_ct \right )$$

By comparing the output of summer block with the standard equation of DSBSC wave, we will get the scaling factor as $2k_a$

Following is the block diagram of the Ring modulator.

In this diagram, the four diodes $D_1$,$D_2$,$D_3$ and $D_4$ are connected in the ring structure. Hence, this modulator is called as the **ring modulator**. Two center tapped transformers are used in this diagram. The message signal $m\left ( t \right )$ is applied to the input transformer. Whereas, the carrier signals $c\left ( t \right )$ is applied between the two center tapped transformers.

For positive half cycle of the carrier signal, the diodes $D_1$ and $D_3$ are switched ON and the other two diodes $D_2$ and $D_4$ are switched OFF. In this case, the message signal is multiplied by +1.

For negative half cycle of the carrier signal, the diodes $D_2$ and $D_4$ are switched ON and the other two diodes $D_1$ and $D_3$ are switched OFF. In this case, the message signal is multiplied by -1. This results in $180^0$ phase shift in the resulting DSBSC wave.

From the above analysis, we can say that the four diodes $D_1$, $D_2$, $D_3$ and $D_4$ are controlled by the carrier signal. If the carrier is a square wave, then the Fourier series representation of $c\left ( t \right )$ is represented as

$$c\left ( t \right )=\frac{4}{\pi}\sum_{n=1}^{\infty }\frac{\left ( -1 \right )^{n-1}}{2n-1} \cos\left [2 \pi f_ct\left ( 2n-1 \right ) \right ]$$

We will get DSBSC wave $s\left ( t \right )$, which is just the product of the carrier signal $c\left ( t \right )$ and the message signal $m\left ( t \right )$ i.e.,

$$s\left ( t \right )=\frac{4}{\pi}\sum_{n=1}^{\infty }\frac{\left ( -1 \right )^{n-1}}{2n-1} \cos\left [2 \pi f_ct\left ( 2n-1 \right ) \right ]m\left ( t \right )$$

The above equation represents DSBSC wave, which is obtained at the output transformer of the ring modulator.

DSBSC modulators are also called as **product modulators** as they produce the output, which is the product of two input signals.

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