DSB-AM vs SSB; ring modulator for DSB-SC

DSB-AM vs SSB: power and bandwidth

Single tone, carrier amplitude $A_c$, index $\mu$, load $R$; $P_c = A_c^2/2R$.

Power saving of SSB over DSB-FC at $\mu = 1$:

$$\frac{1.5P_c - 0.25P_c}{1.5P_c} = \frac{1.25}{1.5} = 83.3\%$$

So SSB saves half the bandwidth and about 83% of the power.

Ring modulator for DSB-SC

The ring (double-balanced) modulator has four diodes in a ring between two centre-tapped transformers; a square-wave carrier, much larger than the message, is fed between the centre taps and acts as a switch.

            T1        D1        T2
 m(t) o--+ )||( a---->|----b )||( +--o
         | )||( |\       /| )||( |    to
         | )||( | D3   D4 | )||( |    BPF
 o-------+ )||( |   \ /   | )||( +--o
              | |    X    |  |
              | |   / \   |  |
              | c---->|----d  |
              |       D2      |
              +--- c(t) ------+
          (square-wave carrier between
           centre taps of T1 and T2)

Working:

• Carrier positive: D1, D2 ON; D3, D4 OFF → output $= +m(t)$.
• Carrier negative: D3, D4 ON; D1, D2 OFF → transformer connections reversed → output $= -m(t)$.

So $v(t) = m(t)c_s(t)$ with $c_s(t)$ a ±1 square wave:

$$v(t) = m(t)\cdot\frac{4}{\pi}\left[\cos\omega_ct - \frac13\cos3\omega_ct + \frac15\cos5\omega_ct - \dots\right]$$

The square wave has no DC, so no message term appears, and no carrier term appears either. A BPF at $f_c$ (bandwidth $2W$) gives

$$s(t) = \frac{4}{\pi}m(t)\cos\omega_ct \quad \text{(DSB-SC)}$$

 m(t)   ~~~~/\~~~~~/\~~~
 c_s(t) +-+ +-+ +-+ +-+
 v(t)   m(t) sign-flipped each half cycle
 s(t)   DSB-SC with phase reversal at m(t)=0

Requirement: $f_c > W$ (in practice $f_c \gg W$) so that the bands around $f_c$ and $3f_c$ do not overlap; the diodes must be matched for good carrier suppression.