Analog Communication - SSBSC Modulators

In this chapter, let us discuss about the modulators, which generate SSBSC wave. We can generate SSBSC wave using the following two methods.

Frequency discrimination method

Phase discrimination method

Frequency Discrimination Method

The following figure shows the block diagram of SSBSC modulator using frequency discrimination method.

In this method, first we will generate DSBSC wave with the help of the product modulator. Then, apply this DSBSC wave as an input of band pass filter. This band pass filter produces an output, which is SSBSC wave.

Select the frequency range of band pass filter as the spectrum of the desired SSBSC wave. This means the band pass filter can be tuned to either upper sideband or lower sideband frequencies to get the respective SSBSC wave having upper sideband or lower sideband.

Phase Discrimination Method

The following figure shows the block diagram of SSBSC modulator using phase discrimination method.

This block diagram consists of two product modulators, two $-90^0$ phase shifters, one local oscillator and one summer block. The product modulator produces an output, which is the product of two inputs. The $-90^0$ phase shifter produces an output, which has a phase lag of $-90^0$ with respect to the input.

The local oscillator is used to generate the carrier signal. Summer block produces an output, which is either the sum of two inputs or the difference of two inputs based on the polarity of inputs.

The modulating signal $A_m cosleft ( 2 pi f_mt ight )$ and the carrier signal $A_c cosleft ( 2 pi f_ct ight )$ are directly appped as inputs to the upper product modulator. So, the upper product modulator produces an output, which is the product of these two inputs.

The output of upper product modulator is

$$s_1left ( t ight )=A_mA_c cos left ( 2 pi f_mt ight ) cosleft ( 2 pi f_ct ight )$$

$$ Rightarrow s_1left ( t ight )=frac{A_mA_c}{2} left { cos left [ 2 pileft ( f_c+f_m ight )t ight ]+ cosleft [ 2 pileft ( f_c-f_m ight )t ight ] ight }$$

The modulating signal $A_m cosleft ( 2 pi f_mt ight )$ and the carrier signal $A_c cosleft ( 2 pi f_ct ight )$ are phase shifted by $-90^0$ before applying as inputs to the lower product modulator. So, the lower product modulator produces an output, which is the product of these two inputs.

The output of lower product modulator is

$$s_2left ( t ight )=A_mA_c cosleft ( 2 pi f_mt-90^0 ight ) cosleft (2 pi f_ct-90^0 ight )$$

$Rightarrow s_2left ( t ight )=A_mA_c sin left ( 2 pi f_mt ight )sin left ( 2 pi f_ct ight )$

$Rightarrow s_2left ( t ight )=frac{A_mA_c}{2} left { cos left [ 2 pileft ( f_c-f_m ight )t ight ]- cosleft [ 2 pileft ( f_c+f_m ight )t ight ] ight }$

Add $s_1left ( t ight )$ and $s_2left ( t ight )$ in order to get the SSBSC modulated wave $sleft ( t ight )$ having a lower sideband.

$sleft ( t ight )=frac{A_mA_c}{2}left { cosleft [ 2 pileft ( f_c+f_m ight )t ight ]+cosleft [ 2 pileft ( f_c-f_m ight )t ight ] ight }+$

$frac{A_mA_c}{2}left { cosleft [ 2 pileft ( f_c-f_m ight )t ight ]-cosleft [ 2 pileft ( f_c+f_m ight )t ight ] ight }$

$Rightarrow sleft ( t ight )=A_mA_c cos left [ 2 pileft ( f_c-f_m ight )t ight ]$

Subtract $s_2left ( t ight )$ from $s_1left ( t ight )$ in order to get the SSBSC modulated wave $sleft ( t ight )$ having a upper sideband.

$sleft ( t ight )=frac{A_mA_c}{2}left { cosleft [ 2 pileft ( f_c+f_m ight )t ight ]+cosleft [ 2 pileft ( f_c-f_m ight )t ight ] ight }-$

$frac{A_mA_c}{2}left { cosleft [ 2 pileft ( f_c-f_m ight )t ight ]-cosleft [ 2 pileft ( f_c+f_m ight )t ight ] ight }$

$Rightarrow sleft ( t ight )=A_mA_c cos left [ 2 pileft ( f_c+f_m ight )t ight ]$

Hence, by properly choosing the polarities of inputs at summer block, we will get SSBSC wave having a upper sideband or a lower sideband.