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  • Stuck here, help me understand: - An amplitude modulated signal is given by V(t) = 10[1+0.3 (2.2X104t)](5.5 X 105t). Here t in seconds - Communication Systems - JEE Main

An amplitude modulated signal is given by V(t) = 10[1+0.3\cos (2.2X104t)]\sin(5.5 X 105t). Here t in seconds. The sideband frequencies (in kHz) are, \left [ Given \pi =\frac{22}{7} \right ]

 

  • Option 1)

    1785 and 1715

  • Option 2)

    89.25 and 85.75

  • Option 3)

    892.5 and 857.5

  • Option 4)

    178.5 and 171.5

Answers (1)

best_answer

 

Side band frequency -

AM wave contains three frequency f_{c},\left ( f_{c}+f_{m} \right )\: and \: \left ( f_{c}-f_{m} \right )

 

- wherein

f_{c} is carrier frequency, f_{c} -f_{m} \:and\: f_{c}+f_{m} are side band frequency.

V(t)=10[1+0.3(2.2\times 10^{4}t)\sin (5.5\times 10^{5}t)]

=10+[\frac{3}{2}\sin (57.2\times 10^{4}t)]

-\frac{3}{2}\sin (52.8\times 10^{4}t)

\omega _{1}=57.2\times 10^{4}

\Rightarrow f_{1}=9.1\times 10^{4}

=91 KH_{2}

\omega _{2}=52.8\times 10^{4}

\Rightarrow f_{2}\approx 84 KHZ

Best option is 89.25 and 85.75

 

 

 

 


Option 1)

1785 and 1715

Option 2)

89.25 and 85.75

Option 3)

892.5 and 857.5

Option 4)

178.5 and 171.5

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