Question

An amplitude modulated signal is plotted below which one of the following best describes the above signal ?

• A. $(9+\sin (2\pi \times {10}^{4}t\left)\sin \right(2.5\pi \times {10}^{5}t)\text{V}$
• B. $(1+9\sin (2\pi \times {10}^{4}t\left)\sin \right(2.5\pi \times {10}^{5}t)\text{V}$
• C. $(9+\sin (2.5\pi \times {10}^{5}t\left)\sin \right(2\pi \times {10}^{4}t)\text{V}$
• D. $(9+\sin (4\pi \times {10}^{4}t\left)\sin \right(5\pi \times {10}^{5}t)\text{V}$

Answer 1

The correct option is A $(9+\sin (2\pi \times {10}^{4}t\left)\sin \right(2.5\pi \times {10}^{5}t)\text{V}$

After analysing the graph, we may conclude that,
$A_s+A_c=10\text{and}{A}_c-A_s=8$
After solving, we get, $A_s=1,A_c=9$

And, $T_s=100\mu s,T_c=8\mu s$
$\Rightarrow f_s=\frac{2\pi }{T_s}=2\pi \times {10}^4\text{Hz}$
And, $f_c=\frac{2\pi }{T_c}=25\pi \times {10}^4\text{Hz}$
The general equation of an AM wave is,

$c_m\left(t\right)=A_c(1+\frac{A_s}{A_c}\sin {\omega }_{s}t)\sin {\omega }_{c}t$
$\therefore c_m\left(t\right)=(9+\sin (2\pi \times {10}^{4}t\left)\right)\sin (25\pi \times {10}^{4}t)$

Hence, $\left(C\right)$ is the correct answer.