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  4. A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

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Q. A baseband signal of $3.5 \,MHz$ frequency is modulated with a carrier signal of $3.5\, GHz$ frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

JEE MainJEE Main 2022Communication Systems

Solution:

$f_{c}=3.5 \,GHz $
$f_{m}=3.5\, MHz$
Side band frequencies are $f_{c}-f_{m} \& f_{c}+f_{m}$.
which are almost $f_{c}$
$\lambda=\frac{ c }{ f _{ c }}$
Minimum length of antenna $=$
$\frac{ c }{ f _{ c } 4}=\frac{\lambda}{4}=\frac{3 \times 10^{8}}{3.5 \times 10^{9} \times 4}$
$=21.4 \,mm$