SSB vs full carrier AM; ring modulator

SSB versus conventional AM

SSB-SC transmits only one sideband with the carrier suppressed, while conventional AM (DSB-FC) sends the carrier and both sidebands.

Ring modulator for DSB-SC

A ring modulator uses four diodes connected in a ring between two centre-tapped transformers. The carrier is applied between the centre taps and acts as a switch; the message enters at the input transformer.

        T1      D1       T2
 m(t) ))|(( a----|>|----b ))|(( s(t)
        |(( \           / ))|
        |((  D4       D2  ))|
        |(( /           \ ))|
        )|( d----|<|----c ))|
          |      D3       |
          +----( c(t) )---+
       (carrier between centre taps)

Operation

1. The carrier amplitude is much larger than $m(t)$, so the carrier alone decides which diodes conduct.
2. Positive carrier half cycle: D1 and D3 conduct, D2 and D4 are off. The message passes to the output with its original polarity.
3. Negative carrier half cycle: D2 and D4 conduct, D1 and D3 are off. The connections are crossed, so the message reaches the output inverted.
4. So the output is $m(t)$ multiplied by a bipolar square wave $c(t)$ of frequency $f_c$:

$$c(t) = \frac{4}{\pi}\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2n-1}\cos[2\pi f_c(2n-1)t]$$ $$v(t) = m(t)c(t) = \frac{4}{\pi}m(t)\cos\omega_ct - \frac{4}{3\pi}m(t)\cos 3\omega_ct + \dots$$

5. The square wave has no DC term, so no carrier and no baseband $m(t)$ appear at the output. A band-pass filter centred at $f_c$ (bandwidth $2W$) keeps only

$$s(t) = \frac{4}{\pi}m(t)\cos\omega_ct$$

which is DSB-SC. The circuit is balanced, so the carrier leakage is very small when the diodes are matched. The condition $f_c > W$ (in practice $f_c \gg W$) keeps the bands around $f_c$ and $3f_c$ separate.