Topic: Communication Systems
For a frequency modulated signal represented by $s(t)=10\sin(6\times 10^{8}t+2\sin 100\pi t)$. The maximum frequency deviation in the carrier from its unmodulated frequency is
- A. 990 Hz
- B. 100 Hz
- C. 50 Hz
- D. 200 Hz
Answer: B. 100 Hz
Explanation: The standard equation of the FM modulated wave is $x(t) = A_{c}\sin\left(\omega_{c}t + \frac{K_{f}A_{m}}{\omega_{m}}\sin \omega_{m}t\right)$.
Comparing this with $s(t) = 10\sin(6\times 10^{8}t+2\sin 100\pi t)$, we get:
$\frac{K_{f}A_{m}}{\omega_{m}} = 2$
$\omega_{m} = 100\pi \Rightarrow 2\pi f_{m} = 100\pi \Rightarrow f_{m} = 50~\text{Hz}$.
Maximum frequency deviation is $\Delta f = K_{f}A_{m} = 2 \times f_{m} = 2 \times 50 = 100~\text{Hz}$.