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  • A carrier wave is amplitude modulated to a depth of 50 % .The ratio b/w total power of side bonds to power of unmodulated carrier wave would be Option: 1</s

A carrier wave is amplitude modulated to a depth of 50 % .The ratio b/w total power of side bonds to power of unmodulated carrier wave would be 

Option: 1

1 :1 


Option: 2

1: 2 


Option: 3

1 : 4 


Option: 4

1 : 8 


Answers (1)

best_answer

As we have learned

Total Power of side bands -

P_{sb}= \frac{\left ( \frac{m_{a}E_{c}}{2\sqrt{2}} \right )^{2}}{R}+ \frac{\left ( \frac{m_{a}E_{c}}{2\sqrt{2}} \right )^{2}}{R}= \frac{m{_{a}}^{2}E{_{c}}^{2}}{4R}
 

- wherein

m_{a}= modulation index

E_{c}=amplitude of carrier waves

R = resistance

 

 Depth of modulation = 50 % 

which means modulation index (m_ a)= 1/2 

Now we know 

Total power of side bonds = \frac{m _{a}^{2}E_{c}^{2}}{4R}

Total power of unmodulated carries = \frac{E _{c}^{2}}{2R}

Ratio b/w power of sidebands and carriers = \frac{m _{a}^{2}E_{c}^{2}}{4R}/\frac{E _{c}^{2}}{2R} 

                                                                =   \frac{m_{a}^{2}}{2}

                   ratio = \frac{(1/2)^2}{2}  (m _{a} =1/2)

Ratio = 1/8 

 

 

 

 

 

Posted by

shivangi.bhatnagar

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