Question

Consider the modulator shown in the figure below:



Both the message signals, $m_1\left(t\right)$ and $m_2\left(t\right)$ are band-limited to $5kHz$. If $f_1=20kHz$ and $f_c=2MHz$, then the bandwidth of the output signal $s\left(t\right)$ will be

• A. $30kHz$
• B. $10kHz$
• C. $50kHz$
• D. $20kHz$

Answer 1

The correct option is C $50kHz$

Let us consider two different spectral shapes for $m_1\left(t\right)$ and $m_2\left(t\right)$ as follows:



The corresponding spectrum of $x\left(t\right)$ can be plotted as,

$f_{x\left(max\right)}=25kHz$

$BW$ of the outut signal $s\left(t\right)$ will be
$\left(BW\right)=2f_{x\left(max\right)}=50kHz$