# SSB modulation Transmitter Circuit: Phase Discrimination Method

SSB(Single Sideband) Modulation is AM modulation method wherein a single sideband is transmitted to conserve transmission bandwidth. There are two methods to for SSB modulation: frequency discrimination method and phase discrimination method. In SSB modulation using frequency discrimination method, first a DSB signal is produced and using filter either the upper or low sideband is removed to produce SSB signal. In SSB modulation Phase discrimination method, two DSB signals are generated which are out of phase and summer or subtracter circuit is used to either produce upper or lower sideband SSB signal. Here it is shown how to build SSB modulation transmitter circuit using phase discrimination method.

The following shows the circuit diagram of SSB modulation transmitter circuit.

In the above circuit diagram, the message signal or the modulating signal is multiplied with carrier signal using two DSB modulator(product modulator). In the upper arm, the message signal is multiplied with the carrier signal using the AD633 analog multiplier integrated circuit(IC).

If m(t) is the message signal and c(t) is the carrier signal then at the output of the upper product modulator is,

$$s_I(t) = m(t)c(t)$$    --------->(1)

$$s_I(t) = A_m cos(w_m t) A_c cos(w_c t) = A_m A_c cos(w_m t) cos(w_c t)$$

or, $$s_I(t) = \frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}+ cos\{(w_c+w_m) t\}]$$  -------->(2)

where, $$m(t)=A_m cos(w_m t)$$ and $$c(t)=A_c sin(w_c t)$$

The DSB signal $$s_I(t)$$ generated at the upper channel is called in-phase signal.

At the lower arm of the modulator, the message signal m(t) is passed through a 90 degree wideband phase shift circuit. This phase shifter circuit also called Hilbert transformer or Hilbert filter is designed with operational amplifier and hence it is called active phase shifter circuit. This phase shifter circuit can also be designed using passive filter but since the reactance of capacitor is dependent on the input signal frequency the passive filter may not yield wideband response. The output of the phase shifter circuit is,

$$\hat{m(t)} = A_m sin(w_m t)$$     -------->(3)

This is called Hilbert transform of m(t).

Similarly, the carrier signal is 90 degree phase shifted using passive phase shifter circuit consisting of low pass filter and high pass filter. Here since the carrier signal is not usually changing we can use passive phase shift circuit. The output of the 90 degree phase shifter circuit is,

$$c(t-) = A_c sin(w_ct)$$    ------->(4)

Thus at the lower product modulator, the signal  $$\hat{m(t)}$$ is multiplied with the output of the passive phase shifter circuit $$c_1(t)$$ and we get at the output of the lower DSB modulator the following,

$$s_Q(t) = \hat{m(t)} c(t-)$$

$$s_Q(t) = A_m sin(w_m t) A_c sin(w_c t)$$

$$s_Q(t) = \frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}- cos\{(w_c+w_m) t\}]$$ ------->(5)

This DSB signal $$s_Q(t)$$ generated at the lower channel is called quadrature signal.

Now after the two DSB AM modulators, using the switch, we can either connect the outputs to the op-amp summer circuit or connect the output to the op-amp subtracter circuit. If we connect to the summer circuit then we get lower sideband SSB signal.

From (2) and (5),

$$s_l(t) = s_I(t)+s_Q(t)$$

or, $$s_l(t) =\frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}+ cos\{(w_c+w_m) t\}]+\frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}- cos\{(w_c+w_m) t\}]$$

or,  $$s_l(t) =\frac{A_m A_c}{2} cos\{(w_c-w_m) t\}+\frac{A_m A_c}{2} cos\{(w_c-w_m) t\}$$

or,  $$s_l(t) = A_m A_c cos\{(w_c-w_m) t\}$$  ------>(6)

If we use the subtractor circuit then we get upper sideband SSB modulated signal.

Again using (2) and (5),

$$s_u(t) = s_I(t)-s_Q(t)$$

or, $$s_u(t) =\frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}+ cos\{(w_c+w_m) t\}]-\frac{A_m A_c}{2} [cos\{(w_c-w_m) t\}- cos\{(w_c+w_m) t\}]$$

or,  $$s_u(t) =\frac{A_m A_c}{2} cos\{(w_c+w_m) t\}+\frac{A_m A_c}{2} cos\{(w_c+w_m) t\}$$

or,  $$s_u(t) = A_m A_c cos\{(w_c+w_m) t\}$$  ------>(7)

Thus we get either upper or lower SSB modulated signal given in equation (5) and (6).

Usually the SSB modulated signal is expressed combining both (5) and (6) as follows,

$$s_{ssb}(t) = s_I(t) \mp s_Q(t)$$   ------>(8)

This equation(7) represents the equation for SSB signal and is the formula for SSB modulation.

If we use +ve sign, then $$s_{ssb}(t) = s_l(t)$$ and if we use -ve sign $$s_{ssb}(t) = s_u(t)$$.

The above circuit diagram of the SSB modulation transmitter can be simply represented using the following SSB modulation block diagram.

The following video demonstrates how the above SSB modulator circuit works.

So in this way we can design transmitter circuit for SSB modulation. The advantage of SSB modulation over standard AM and DSB-SC AM is that comparatively lower transmission bandwidth is required. The SSB signal generated can be demodulated using SSB demodulator circuit that uses coherent method.

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