2-B
2. Given the message signal shown below modulated as an AM signal with µ = 0.8, find
10
m(t)
-10
-10?³
a) The amplitude and power of the AM carrier signal
b) The sideband power, Ps, and power efficiency, ?.
Figure 1: Magnitude in volts and time in
seconds
(a) Carrier Amplitude = \frac{M_p}{µ} = \frac{10}{0.8} = 12.5
Carrier Power, P_c = \frac{A^2}{2} = 78.125
(b) Sideband Power, P_s = 16.67
Power efficiency, ? = 17.6 %
\frac{1}{T_0/4} \int_0^{T_0/4} \left(\frac{40t}{T_0}\right)^2 dt
= \frac{4}{T_0} \frac{40^2}{T_0^2} \frac{1}{3} t^3 |_0^{T_0/4}
= \frac{4}{T_0} \frac{40^2}{3 \cdot 4^3} T_0 = \frac{10^2}{3} = 33.3
P_s = \frac{µ^2}{2} P_m = 16.67
? = \frac{16.67}{78.125 + 16.67} \times 100 \% \approx 17.6
