Compare DSB-AM, DSB-SC, SSB, VSB; SSB by phase discrimination

Performance comparison

SSB generation by phase discrimination (phase-shift) method

          +-->[Balanced mod 1]--v1--+
          |         ^               |
 m(t) ----+   Ac cos wc t           v
          |         |              (+/-) ---> SSB
          |     [-90 deg]           ^
          |         |               |
          +-[-90]->[Balanced mod 2]-v2
         m^(t)   Ac sin wc t

1. Balanced modulator 1 multiplies $m(t)$ with $A_c\cos\omega_ct$.
2. A wideband $-90^\circ$ phase shifter (Hilbert transformer) produces $\hat m(t)$; balanced modulator 2 multiplies it with the $-90^\circ$ shifted carrier $A_c\sin\omega_ct$.
3. The outputs are subtracted for USB or added for LSB.

Derivation with $m(t) = A_m\cos\omega_mt$:

$$\begin{aligned} v_1 &= A_mA_c\cos\omega_mt\cos\omega_ct = \tfrac{A_mA_c}{2}[\cos(\omega_c-\omega_m)t + \cos(\omega_c+\omega_m)t] \\ v_2 &= A_mA_c\sin\omega_mt\sin\omega_ct = \tfrac{A_mA_c}{2}[\cos(\omega_c-\omega_m)t - \cos(\omega_c+\omega_m)t] \\ v_1 - v_2 &= A_mA_c\cos(\omega_c+\omega_m)t \quad \text{(USB)} \\ v_1 + v_2 &= A_mA_c\cos(\omega_c-\omega_m)t \quad \text{(LSB)} \end{aligned}$$

General: $s(t) = A_c[m(t)\cos\omega_ct \mp \hat m(t)\sin\omega_ct]$.

Advantages: no sharp filter; works at any carrier frequency; sideband switched by changing sign. Disadvantage: the $90^\circ$ shifter must be exact over the entire audio band, otherwise the unwanted sideband is only partly cancelled.