Topic: Communication Systems
A message signal given by $m(t)=(\frac{1}{2})\cos(\omega_1 t)-(\frac{1}{2})\sin(\omega_2 t)$ is amplitude modulated with a carrier of frequency $\omega_c$ to generate $s(t)=[1+m(t)]\cos(\omega_c t)$. What is the power efficiency achieved by this modulation scheme?
- A. 8.33%
- B. 11.11%
- C. 20%
- D. 25%
Answer: C. 20%
Explanation: Power of message signal $P_m = \frac{(1/2)^2}{2} + \frac{(-1/2)^2}{2} = \frac{1}{8} + \frac{1}{8} = \frac{1}{4}$.
Carrier power $P_c = \frac{1^2}{2} = \frac{1}{2}$.
Sideband power $P_{sb} = \frac{P_m}{2} = \frac{1/4}{2} = \frac{1}{8}$.
Total power $P_t = P_c + P_{sb} = \frac{1}{2} + \frac{1}{8} = \frac{5}{8}$.
Efficiency $\eta = \frac{P_{sb}}{P_t} = \frac{1/8}{5/8} = \frac{1}{5} = 20\%$.