Topic: Electronics Engineering
An angle modulated signal with carrier frequency $\omega_{c}=2\pi\times10^{5}$ is described by the equation $s(t)=10~cos(\omega_{c}t+5~sin(3000~\pi t)+ 10~sin (2000~\pi t))$. What is the frequency deviation $\Delta f$?
- A. 12387.32 Hz
- B. 17500 Hz
- C. 20000 Hz
- D. 15000 Hz
Answer: B. 17500 Hz
Explanation: $\theta_{i}(t) = \omega_{c}t+5~sin(3000\pi t) + 10~sin(2000\pi t)$
$\omega_{i}(t) = \frac{d\theta_{i}(t)}{dt} = \omega_{c} + 5\times3000\pi\times cos(3000\pi t) + 10\times2000\pi~cos(2000\pi t)$
$\Delta f_{inst} = 7500~cos(3000~\pi t) + 10000~cos(2000~\pi t)$
Maximum frequency deviation $\Delta f = 7500 + 10000 = 17500~Hz$.