Question

A frequency modulated signal with a carrier frequency of ${}^{\prime \prime }{f}_c^{\prime \prime }$ is given by,

$s\left(t\right)=20\cos [2\pi f_{c}t+12\sin (2000\pi t)+5\cos (2000\pi t\left)\right]$

The maximum phase deviation of the signal s(t) is equal to

• A. 17 rad
• B. 13 rad
• C. 5 rad
• D. 12 rad

Answer 1

The correct option is B 13 rad

The phase of the given modulated signal is,

$\varphi \left(t\right)=12\sin \left(2000\pi t\right)+5\cos \left(2000\pi t\right)rad$

$=\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}\left[\cos \right(2000\pi t-\alpha \left)\right]rad$
$=13\cos (2000\pi t-\alpha )rad$

Where, $\alpha ={\tan }^{-1}\left(\frac{12}{5}\right)$

Maximum phase deviation of the signal s(t) is,
$\Delta {\varphi }_{max}=|\varphi \left(t\right){|}_{max}=13rad$