Phase shift method of SSB generation: pros and cons

The phase-shift (phase discrimination) method generates SSB directly from its mathematical form, without a sideband filter:

$$s_{SSB}(t)=\frac{A_c}{2}\left[m(t)\cos\omega_ct\mp\hat m(t)\sin\omega_ct\right]$$

where $\hat m(t)$ is the Hilbert transform of $m(t)$ (each component shifted by $-90°$). Minus gives USB, plus gives LSB.

Block diagram

             +-->[Bal. mod 1]-- m cos wct --+
             |        ^                     |
 m(t) -------+        | cos wct             v
             |   [Carrier osc]            ( + / - )--> SSB
             |        |                     ^
             |   [-90 deg]                  |
             |        | sin wct             |
             +->[-90]->[Bal. mod 2]-- m^ sin wct
                 m^(t)

Working

1. Balanced modulator 1 multiplies $m(t)$ by $\cos\omega_ct$, giving DSB-SC with both sidebands.
2. A wideband $-90°$ phase shifter (Hilbert transformer) produces $\hat m(t)$, and a carrier phase shifter gives $\sin\omega_ct$. Balanced modulator 2 gives $\hat m(t)\sin\omega_ct$.
3. The summer/subtractor combines them. One sideband appears in phase in both paths and adds; the other is in antiphase and cancels.

Proof with a tone $m=A_m\cos\omega_mt$, $\hat m=A_m\sin\omega_mt$:

$$\begin{aligned} m\cos\omega_ct&=\tfrac{A_m}{2}[\cos(\omega_c-\omega_m)t+\cos(\omega_c+\omega_m)t]\\ \hat m\sin\omega_ct&=\tfrac{A_m}{2}[\cos(\omega_c-\omega_m)t-\cos(\omega_c+\omega_m)t] \end{aligned}$$

Subtracting gives $A_m\cos(\omega_c+\omega_m)t$ (USB only); adding gives $A_m\cos(\omega_c-\omega_m)t$ (LSB only).

Pros

1. No sharp sideband filter is needed, so SSB can be generated directly at any carrier frequency (no multiple up-conversion).
2. Works for messages with energy near zero frequency (no need for a gap between sidebands, unlike the filter method).
3. Switching between USB and LSB is easy: just change adder to subtractor.
4. Lighter, smaller circuits for low carrier frequencies.

Cons

1. A wideband $90°$ phase shifter that gives exactly $90°$ at all audio frequencies (e.g. 300–3400 Hz) with equal gain is very difficult to build.
2. Any phase or amplitude imbalance leaves a residual unwanted sideband (poor sideband suppression, typically 30–40 dB vs 50–60 dB for filters).
3. Two balanced modulators must be closely matched, and the circuit needs careful adjustment and is sensitive to drift.