Why SSB preferred; AM power at 100% modulation

Why SSB is preferred

SSB (single sideband suppressed carrier) sends only one sideband. It is preferred over DSB-FC and DSB-SC because:

• Half bandwidth: SSB needs only $f_m$, while DSB-FC and DSB-SC need $2f_m$. Twice as many channels fit in a band.
• Power saving: The carrier carries no information. At $\mu = 1$, DSB-FC wastes 2/3 of the power in the carrier; DSB-SC still sends a redundant second sideband. SSB puts all power in one sideband (about 83% saving over DSB-FC at $\mu=1$).
• Better S/N: Narrower bandwidth means less noise power at the receiver.
• Less selective fading: Only one sideband, so phase differences between sidebands cannot cancel each other.

Numerical

Given $P_t = 1000$ W, $\mu = 1$ (100%).

$$P_t = P_c\left(1 + \frac{\mu^2}{2}\right) \Rightarrow P_c = \frac{P_t}{1 + \mu^2/2}$$ $$\begin{aligned} P_c &= \frac{1000}{1 + 0.5} = 666.67\ \text{W} \\ P_{SB,\,total} &= P_t - P_c = 1000 - 666.67 = 333.33\ \text{W} \\ P_{USB} = P_{LSB} &= \frac{\mu^2}{4}P_c = \frac{1}{4}(666.67) = 166.67\ \text{W} \end{aligned}$$

Answer: Carrier power = 666.67 W; power in each sideband = 166.67 W (USB = LSB).