Question

When a carrier signal, $c\left(t\right)=\cos \left(200\pi t\right)$ and a message signal, $m\left(t\right)=\cos \left(2\pi t\right)$ are applied to unknown modulator circuit, the modulated waveform resulted at the output of the circuit is given by,

$s\left(t\right)=\cos \left(200\pi t\right)\cos \left(5\sin 2\pi t\right)-\sin \left(200\pi t\right)\sin \left(5\sin 2\pi t\right)$

The signal s(t) can be

• A. neither and FM wave nor a PM wave
• B. an FM wave
• C. a PM wave
• D. either an FM wave or a PM wave

Answer 1

The correct option is B an FM wave

$s\left(t\right)=\cos \left(200\pi t\right)\cos \left(5\sin 2\pi t\right)-\sin \left(200\pi t\right)\sin \left(5\sin 2\pi t\right)$

$=\cos [200\pi t+5\sin (2\pi t\left)\right]$

$=[\cos 200\pi t+10\pi \underset{0}{\overset{t}{\int }}\cos \left(2\pi t\right)dt]$

$=[\cos 2\pi f_{c}t+10\pi \underset{0}{\overset{t}{\int }}m\left(t\right)dt]$
The standard form of FM and PM waves can be expressed as,

$s_{FM}\left(t\right)=A_c\cos [2\pi f_{c}t+2\pi k_f\underset{0}{\overset{t}{\int }}m\left(t\right)dt]$

$s_{PM}\left(t\right)=A_c\cos [2\pi f_{c}t+k_{p}m(t\left)\right]$

So, the signal s(t) can be an FM wave.