Question

A modulated signal $C_m(t)$ has the form $C_m(t)=30$ sin $300 \pi t + 10$ (cos $200 \pi t -$ cos $400 \pi t$). The carrier frequency $f_{c}$, the modulating frequency (message frequency) $f_{\omega}$, and the modulation index $\mu$ are respectively given by :

• A. $f_c = 200 \, Hz ; f_{\omega} = 50 \, Hz ; \mu = \frac{1}{2}$
• B. $f_c = 150\, Hz ; f_{\omega} = 50 \, Hz ; \mu = \frac{2}{3}$
• C. $f_c = 150\, Hz ; f_{\omega} = 50 \, Hz ; \mu = \frac{1}{2}$
• D. $f_c = 200 \, Hz ; f_{\omega} = 30 \, Hz ; \mu = \frac{1}{2}$

Answer 1

Answer: (B)

$f_c = 150\, Hz ; f_{\omega} = 50 \, Hz ; \mu = \frac{2}{3}$

Answer 2

$\ell_{m}(t)=30 \sin (300 \pi t)+10 \cos (400 \pi t)$
$f=\frac{\omega}{2 \pi}=\frac{300 \pi}{2 \pi}=150$
$=\frac{20 \pi}{2 \pi}=100$
$\frac{400 \pi}{2 \pi}=200$
$f _{ c }=150\, Hz$
$f _{ m }=50\, Hz$
$\mu=\frac{2}{3}$