Question

Consider the message signal $m\left(t\right)$ shown in the figure below:



This signal is applied frequency modulator whose carrier frequency is $100MHz$ and frequency sensitivity is $100Hz/V$. The maximum phase deviation of the resultant $FM$ signal will be

• A. $\frac{\pi }{2}$ radians
• B. $\frac{3\pi }{2}$ radians
• C. $\pi$ radians
• D. $\frac{3\pi }{20}$ radians

Answer 1

The correct option is C $\pi$ radians

The maximum phase deviation of an $FM$ signal can be given by.

$\Delta {\varphi }_{max}=2\pi k_f{\left|{\int }_{-\infty }^{t}m\right(\tau \left)d\tau \right|}_{max}$

For the given message signal $m\left(t\right)$

${\left|{\int }_{\infty }^{t}m\right(\tau \left)d\tau \right|}_{max}=$ Area of the first rectangular portion (i.e., for $0\le t\le 1ms$)
$=\left(1ms\right)\times 5V=\frac{5}{1000}\text{V-sec}$
So, $\Delta {\varphi }_{max}=2\pi \times 100\times \frac{5}{1000}$ radians $=\pi$ radians