SSB vs AM and DSB-SC; balanced modulator

SSB vs conventional AM and DSB-SC

SSB transmits only one sideband, without the carrier. Conventional AM sends the carrier and both sidebands, and DSB-SC sends both sidebands without the carrier.

DSB-SC generation by balanced modulator

A balanced modulator uses two identical AM modulators in a balanced configuration, so that the carrier cancels and only the sidebands remain.

 m(t) ---> AM modulator 1 --> s1(t) --+
                ^                     | (+)
                |                    (S)--> s(t) = s1 - s2
          Ac cos wc t                 | (-)
                |                     |
                v                     |
 -m(t) --> AM modulator 2 --> s2(t) --+

Modulator 1 gets $+m(t)$ and modulator 2 gets $-m(t)$; the same carrier goes to both.

$$\begin{aligned} s_1(t) &= A_c[1 + k_am(t)]\cos\omega_ct \\ s_2(t) &= A_c[1 - k_am(t)]\cos\omega_ct \\ s(t) &= s_1(t) - s_2(t) = 2A_ck_a\,m(t)\cos\omega_ct \end{aligned}$$

The output is DSB-SC: the carrier terms cancel exactly.

Practical circuit: two diodes (or transistors) with a centre-tapped transformer. The carrier is fed so that its currents flow in opposite directions through the two halves of the output transformer and cancel, while the message drives the diodes in opposite senses so that the sideband currents add.

Spectrum: for a single tone $m(t) = A_m\cos\omega_mt$:

$$s(t) = A_ck_aA_m[\cos(\omega_c+\omega_m)t + \cos(\omega_c-\omega_m)t]$$

        |    LSB   (no carrier)   USB
        |     |                    |
 -------+-----+---------+----------+----> f
             fc-fm      fc       fc+fm

Requirement: the two modulators must be perfectly matched; any imbalance lets some carrier through (carrier leakage).